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“OrtVc1 failed #1.” Workaround In Gaussian09; Warning About (Pre-)Resonance Raman Spectra In GaussView 4/5

Thursday, January 1st, 2015

And Happy New Year.

Two issues (one easily addressable, one only by external workaround) related to the prediction of Raman intensities in Gaussian09 – for which there’s next-to-nothing online to address either of them (likely because they don’t come up that often).

OrtVc1 failed #1.

In simulating the Raman spectra of very long (> C60) polyenes as a continuance of work related to the infinite polyacetylene case (see this post for details: Bond Alternation In Infinite Periodic Polyacetylene: Dynamical Treatment Of The Anharmonic Potential), I reached a length and basis set for which Gaussian provides the following output and error:

...
 Minotr:  UHF open shell wavefunction.
          Direct CPHF calculation.
          Differentiating once with respect to electric field.
                with respect to dipole field.
          Electric field/nuclear overlap derivatives assumed to be zero.
          Using symmetry in CPHF.
          Requested convergence is 1.0D-08 RMS, and 1.0D-07 maximum.
          Secondary convergence is 1.0D-12 RMS, and 1.0D-12 maximum.
          NewPWx=F KeepS1=T KeepF1=T KeepIn=T MapXYZ=F SortEE=F KeepMc=T.
          MDV=    3932153962 using IRadAn=       1.
 Generate precomputed XC quadrature information.
          Solving linear equations simultaneously, MaxMat=      72.
          There are     3 degrees of freedom in the 1st order CPHF.  IDoFFX=0 NUNeed=     3.
      3 vectors produced by pass  0 Test12= 3.94D-11 3.33D-08 XBig12= 2.15D+05 2.71D+02.
 AX will form     3 AO Fock derivatives at one time.
 FoFJK:  IHMeth= 1 ICntrl=       0 DoSepK=F KAlg= 0 I1Cent=   0 FoldK=F
 IRaf= 160000000 NMat=   3 IRICut=       1 DoRegI=T DoRafI=F ISym2E=-1.
 FoFCou: FMM=T IPFlag=           0 FMFlag=      100000 FMFlg1=        2001
         NFxFlg=           0 DoJE=F BraDBF=F KetDBF=F FulRan=T
         wScrn=  0.000000 ICntrl=       0 IOpCl=  1 I1Cent=           0 NGrid=           0
         NMat0=    3 NMatS0=      3 NMatT0=    0 NMatD0=    3 NMtDS0=    0 NMtDT0=    0
 Petite list used in FoFCou.
 FMM levels:  10  Number of levels for PrismC:   9
      3 vectors produced by pass  1 Test12= 3.94D-11 3.33D-08 XBig12= 1.52D+04 3.94D+01.
      3 vectors produced by pass  2 Test12= 3.94D-11 3.33D-08 XBig12= 1.29D+04 3.31D+01.
      3 vectors produced by pass  3 Test12= 3.94D-11 3.33D-08 XBig12= 1.65D+06 4.27D+01.
      3 vectors produced by pass  4 Test12= 3.94D-11 3.33D-08 XBig12= 1.92D+08 6.96D+02.
      3 vectors produced by pass  5 Test12= 3.94D-11 3.33D-08 XBig12= 4.40D+10 7.74D+03.
      3 vectors produced by pass  6 Test12= 3.94D-11 3.33D-08 XBig12= 4.42D+12 1.70D+05.
      3 vectors produced by pass  7 Test12= 3.94D-11 3.33D-08 XBig12= 3.50D+14 1.14D+06.
      3 vectors produced by pass  8 Test12= 3.94D-11 3.33D-08 XBig12= 3.13D+16 1.34D+07.
      3 vectors produced by pass  9 Test12= 3.94D-11 3.33D-08 XBig12= 1.75D+18 4.02D+07.
      3 vectors produced by pass 10 Test12= 3.94D-11 3.33D-08 XBig12= 1.28D+20 7.81D+08.
      3 vectors produced by pass 11 Test12= 3.94D-11 3.33D-08 XBig12= 1.50D+22 7.70D+09.
      3 vectors produced by pass 12 Test12= 3.94D-11 3.33D-08 XBig12= 1.12D+24 5.57D+10.
      3 vectors produced by pass 13 Test12= 3.94D-11 3.33D-08 XBig12= 2.86D+25 5.87D+11.
 OrtVc1:  Ph=1 IOff=     0 IPass=20 DotMx1= 2.08D-06
 OrtVc1:  Ph=1 M=  1181528 NPass=20 Test1= 3.94D-11 Small= 1.18D-06 VSmall= 1.00D-12
 OrtVc1 failed #1.
 Error termination via Lnk1e in /opt/g09/l1002.exe at Sat Oct 11 01:10:22 2014.

What little there is available online for the “OrtVc1 failed #1.” error (from CCL – here and here) is less than helpful in addressing the problem. The problem is also coordinate system-independent (Cartesian and z-matrix formats both provide the same error), but is sensitive to the choice of basis set (6-31G(d,p) would work fine through the Raman intensity predictions, 6-311G(2d,p) would fail at the stage above).

Directing the issue to Gaussian, the provided workaround is straightforward.

The prediction of Raman intensities requires using Coupled Perturbed Hartree-Fock (CPHF), for which a special sensitivity in the code (currently) exits when using both molecular symmetry and the fast multipole method, the use of which (FMM, that is) is governed by Gaussian09 based on the atom count.

The workaround, provided by Dr. Fernando Clemente at Gaussian, Inc., is to divide the calculation into two steps. My input for the first successful run is shown below. A few details:

1. The first stage contains no Raman keywords (just the plain “freq” call).

2. In the second stage, the cphf=rdfreq is reading an incident light frequency of 0 (cm-1 or nm) at the bottom of the input file (“0”). You can run the static or dynamic cases as you like at this stage.

3. Also in the second stage, FMM is turned off (nofmm).

4. Also still in the second stage, the option to calculate Raman intensities is turned on (polar=raman). This is, as it happens, a recommended way to perform Raman intensity calculations – run a typical normal mode analysis, then import the force constants (and geometry) from this calculation into a Link1 step while increasing the basis set size (for better intensity prediction).

%chk=checkpoint.chk
%nprocshared=12
%mem=50000MB
#p integral(grid=ultrafine) freq=hpmodes b3lyp/6-311++g(3df,3pd) scf=novaracc symm=loose

Part 1 - just the frequency calculation

0 1
 C                  0.00000000   48.56668920   -0.34496298
 C                  0.00000000   47.35252242    0.35603740
...
 H                  0.00000000  -49.50718415    0.19804614
 H                 -0.00000000   49.50718415    0.19804614
[blank line 1]
[blank line 2]
--link1--
%chk=checkpoint.chk
%nprocshared=12
%mem=50000MB
#p integral(grid=ultrafine) polar=raman cphf=rdfreq nofmm b3lyp/6-311++g(3df,3pd) geom=checkpoint

Part 2 - Raman intensities

0 1

0
[blank line 1]
[blank line 2]

In theory, your calculation should run just fine.

Raman Intensities And GaussView – Check Your .log File For Resonance

The next problem is GaussView-specific – one that only comes up when you’ve a system with dynamic polarizability (incredibly long polyenes being a prototypical example) or when you perform frequency-dependent Raman calculations and you slip near resonance.

When running a series of Raman intensity calculations with increasing incident light frequency (cphf=rdfreq, then an array of energies), Mode 17 of this particular molecule either has a really large activity (cannot be printed out) or we’re approaching resonance (also a case of really large activity and it can’t be printed out). This isn’t a problem with the code, it’s your molecule.

                     16                     17                     18
                     BG                     AG                     BG
 Frequencies --    218.8851               257.7857               266.9993
 Red. masses --      3.5318                 5.1372                 2.2022
 Frc consts  --      0.0997                 0.2011                 0.0925
 IR Inten    --      0.0000                 0.0000                 0.0000
 Raman Activ --      0.2046                 0.7412                 0.2871
 Depolar (P) --      0.7500                 0.3044                 0.7500
 Depolar (U) --      0.8571                 0.4667                 0.8571
 RamAct Fr= 1--      0.2046                 0.7412                 0.2871
  Dep-P Fr= 1--      0.7500                 0.3044                 0.7500
  Dep-U Fr= 1--      0.8571                 0.4667                 0.8571
...
 RamAct Fr=12--     90.1095           ************                 0.3406
  Dep-P Fr=12--      0.7500                 0.3333                 0.7500
  Dep-U Fr=12--      0.8571                 0.4999                 0.8571

This is all well-and-good if you only rely on the .log file. If you skip the .log file inspection and only ever use GaussView, the result of inspecting the Raman intensities is below.

2015jan1_Mode17_Wrong_Raman_Activity

Note that Mode 17 has the intensity of Mode 18, and Mode 18 has zero intensity. Something is afoot! If you know what to expect out of your system, the missing intensities should be obvious. If not, you’re missing some very important information about your molecule.

The GaussView developers are aware of the problem. In the meantime, you can get around this problem by globally replacing all of the ” ************ ” (note the spaces on either side!) with a huge number (at which point the Raman intensity issue will become obvious – careful to preserve the spacing in the .log file).

The EMSL Basis Set Exchange 6-31G, 6-31G(d), And 6-31G(d,p) Gaussian-Type Basis Set For CRYSTAL88/92/95/98/03/06/09/14/etc. – Conversion, Validation With Gaussian09, And Discussion

Tuesday, December 30th, 2014

Jump to the basis sets and downloadable files here: files, 6-31G, 6-31Gd, 6-31Gdp.

If you use these results: Please drop me a line (damian@somewhereville.com), just to keep track of where this does some good. That said, you should most certainly cite the EMSL and Basis Set references at the bottom of this page.

It’s a fair bet that Sir John Pople would be the world’s most cited researcher by leaps and bounds if people properly cited their use of the basis sets he helped develop.

The full 6-31G, 6-31G(d), and 6-31G(d,p) series (yes, adding 6-31G(d) is a bit of a cheat in this list) from the EMSL Basis Set Exchange is presented here in the interest of giving the general CRYSTALXX (that’s CRYSTAL88, CRYSTAL92, CRYSTAL95, CRYSTAL98, CRYSTAL03, CRYSTAL06, CRYSTAL09, now CRYSTAL14 – providing the names here for those who might be searching by version) user a “standard set” of basis sets that are, for the most part, the same sets one does / could employ in other quantum chemistry codes (with my specific interest being the use and comparison of Gaussian and GAMESS-US in their “molecular” (non-solid-state) implementations). Members of the CRYSTAL developer team provide a number of basis sets for use with the software. While this is good, I will admit that I cannot explain why the developers chose not to include three of the four most famous basis sets in all of (all of) computational chemistry – 3-21G (upcoming), 6-31G(d,p) (presented here), and 6-311G(d,p) (also upcoming).

More “But why?” There are, generally, many basis sets available for most of the Periodic Table in the CRYSTALXX Basis Set Library. In terms of consistency across all calculations to the molecular-centric quantum chemist, the 6-31G(d,p) series is the cut-off family of basis sets for many, many projects in all computational chemistry research – the series is just large enough to provide predictions “good enough” for publication but is also small enough that systems will properly optimize in a reasonable amount of time for standalone use or as “beautification” calculations for larger basis set studies (this is specifically true for crystal structure optimizations, as considerable time can be wasted simply “cleaning up” hydrogen atom (R-H) bond lengths, which are notoriously underestimated by approx. 10% in X-ray studies (but neutron methods give poorer lattice constants generally, so you can’t win for quick clean-ups either way)). Furthermore, 6-31G(d,p) is the “B3LYP” of basis sets – one that most everyone has used in structure optimizations and one that is constantly run across in computational quantum chemistry studies among typical non-hard-theory quantum chemists (which is not meant to be a slight to the broader user base using computational chemistry for its interpretive value – it’s my workhorse basis set for many past studies). These two points drove the conversion all of the published 6-31G(d,p) basis set data to CRYSTALXX to have it generally available as a solid-state density functional theory (DFT) tool.

This blog post doesn’t reinvent any wheels and, therefore, isn’t something I consider worth submitting for journal publication. That said, having these basis sets is better than not, so the complete set and analysis is provided below. But first…

Note 1: Trust But Verify; RHF

When one thinks of the variational principle, one doesn’t often see the choice of software as being a mechanism to a achieve a lowest energy for a system. While it would be really nice if each program agreed on the lowest energy for a basis set (which, theoretically, seems like it would be the correct result), different programs use different approximations, internal tools, and convergence methodologies to “reach bottom.” Within the same code, these approximations, tools, and methods are, assumedly, “internally consistent” and, obviously, it is safe to compare those apples and apples on Apples.

For those looking for a more detailed study of the differences (by energy) of various quantum chemistry codes, I direct your attention to – Journal of Molecular Structure: THEOCHEM 768 (2006) 175–181 (Concerning the precision of standard density functional programs: GAUSSIAN, MOLPRO, NWCHEM, Q-CHEM, and GAMESS), a paper I stared at for many minutes in trying to come to grips with the energy comparisons when I first started the testing.

Obviously, just presenting coefficients on a blog post and expecting people to trust their use blindly for peer-review publications is a non-starter. Simply doing the conversion itself for in-house studies without some kind of comparison to other energies with tested formats is also a non-starter, as a single wrong number or exponent throws the whole basis set into question (and, admittedly, I fought for several days with helium energies before discovering I’d … misplaced one electron in the conversion process). Therefore, part of the conversion process includes a series of tests comparing the results of Gaussian09 and CRYSTAL09 (not timing tests, simply final energies in an attempt to get the CRYSTAL09 energies to look like the other energies enough to trust that the basis set conversion was successful).

What you learn from performing this type of study is the extent to which quantum chemistry codes can differ significantly in their treatment of integrals, functionals, grids, and convergence criteria. As a way out of part of these problems, the best way to perform comparisons is to run good olde Restricted Hartree-Fock (RHF) calculations, avoiding functional and grid size specifications. Convergence methods and integral treatment may still differ, but it’s possible to get agreement between Gaussian09 and CRYSTAL09 to within 10^-9 Hartree (and even this can get better).

Routinely hitting very small energy differences is my way of believing the correctness of the basis set conversions, but I provide all of the files associated with this project below for your own analyses. You are, of course, welcome to (and encouraged to) perform some sample runs of your own before setting out on a full computational project.

NOTE 2: B3LYP vs. B3LYP

As only becomes obvious after many unsuccessful trials and keyword tweaking, Gaussian’s default B3LYP is NOT the default B3LYP used in GAMESS-US and CRYSTALXX (this going back to a long involved discussion of VWN forms). In short – Gaussian’s B3LYP employes the VWN3 electron gas correlation functional, while GAMESS and CRYSTAL09 use the VWN5 electron gas correlation functional in their default implementations. To get Gaussian to run B3LYP with VWN5, the following keyword set is required (this is old hat in the community and is reported on several websites):

bv5lyp iop(3/76=1000002000) iop(3/77=0720008000) iop(3/78=0810010000)

You can interpret this as:

Functional Form Call:
(Becke exchange/VWN5 local correlation/LYP non-local correlation)
HF Exchange: (20% HF exchange) +
DF Exchange: (72% Becke non-local exchange + 80% Slater local exchange) +
Correlation: (81% LYP non-local correlation + 100% V5LYP VWN5 local correlation).

How much does this matter to the energy calculations? Plenty. Here are comparison energies for the Noble Gases using the two functionals and the 6-31G(d,p) out of Gaussian (using the internal 6-31G(d,p) basis set, program option “ultrafine” grid size and program option “tight” convergence criteria):

Element
B3LYP Energy
(Hartree)
B5LYP Energy
(Hartree)
Helium
-2.90704897
-2.89992035
Neon
-128.89435995
-128.85600282
Argon
-527.51714191
-527.44754502

And these differences are for single atoms. The He might look OK-ish to untrained eyes, but the Ar numbers differ by 182.7 kJ/mol (that’s approaching half a C-C bond worth of energy – nothing to attempt comparisons with), showing that these are two very different density functionals.

NOTE 3: A Slight Aside For The Gaussian User

If you’re performing multiple operations in a single input file (and I don’t mean the use of “—Link1—” – I mean optimization and frequency calculations in the same Link0. If you see Gaussian rehash the top of the log file in a run after an operation as if it were running a new file, that’s a new operation), you learn the hard way that “iop” keywords do NOT carry over property prediction operations in Gaussian calculations.

The two sets of frequencies for H2 below are NOT the same. The first employs an opt+freq combination in the same Link0. The input file with the alternatively-defined B3LYP density functional…

%Chk=H2.chk
#p bv5lyp iop(3/76=1000002000) iop(3/77=0720008000) iop(3/78=0810010000) 6-31g(d,p) integral(grid=ultrafine) scf=tight opt=tight freq

H2 optimization and normal mode analysis

0 1
H 0.000 0.000 0.000
H 1.000 0.000 0.000

Produces:

 Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
 activities (A**4/AMU), depolarization ratios for plane and unpolarized
 incident light, reduced masses (AMU), force constants (mDyne/A),
 and normal coordinates:
                      1
                     SGG
 Frequencies --   4451.2678
 Red. masses --      1.0078
 Frc consts  --     11.7653
 IR Inten    --      0.0000
  Atom  AN      X      Y      Z
     1   1     0.00   0.00   0.71
     2   1     0.00   0.00  -0.71

The same input file with a Link1 to properly recall the alternatively-defined B3LYP density functional…

%chk=H2.chk
#p bv5lyp iop(3/76=1000002000) iop(3/77=0720008000) iop(3/78=0810010000) 6-31g(d,p) integral(grid=ultrafine) scf=tight opt=tight

H2 optimization

0 1
H 0.000 0.000 0.000
H 1.000 0.000 0.000

–Link1–
%chk=H2.chk
# bv5lyp iop(3/76=1000002000) iop(3/77=0720008000) iop(3/78=0810010000) 6-31G(d,p) freq guess=read geom=check

H2 normal mode analysis

0 1

Produces:

 Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
 activities (A**4/AMU), depolarization ratios for plane and unpolarized
 incident light, reduced masses (AMU), force constants (mDyne/A),
 and normal coordinates:
                      1
                     SGG
 Frequencies --   4461.8907
 Red. masses --      1.0078
 Frc consts  --     11.8215
 IR Inten    --      0.0000
  Atom  AN      X      Y      Z
     1   1     0.00   0.00   0.71
     2   1     0.00   0.00  -0.71

Which means what? If you run and opt + freq in the same input file keyword series, the opt will read the iop settings but the freq will ignore them (which I find to be mildly ridiculous). For those keeping track, the 4451 cm-1 mode is the energy of the vibration at the B3LYP/6-31G(d,p) level for an H2 molecule whose H-H bond length is that of the alternatively-defined B3LYP density functional. Run an opt + freq with iop specs for the functional, you need to either use a compound input file format (below) or be ready to run, for instance, a freq calculation by taking the coordinates from the optimization calculation, doing so in two separate Gaussian calculations. Your compound input file would look like the one above.

NOTE 4: What The CRYSTAL Website Has To Say About Reproducing Gaussian Numbers

The CRYSTAL FAQ (as of 2014 Jan 14) states the following concerning the reproduction of Gaussian/CRYSTAL results with CRYSTAL/Gaussian.

> Gaussian 98 - CRYSTAL03 energy 


> If I run Gaussian 98 using the input generated by CRYSTAL03 with the keyword
> GAUSS98 I do not obtain the same energy. What is the problem?


> There are 3 main differences between a standard CRYSTAL run and a GAUSSIAN run.

1. CRYSTAL adopts by default bypolar expansion to compute coulomb integrals when the two distributions do not overlap. 
Insert keyword NOBIPOLA to compute all 2 electron integrals exactly; 

2. CRYSTAL adopts a basis set with 5D and 7F AO; 

3. CRYSTAL adopts the NIST conversion factor bohr/Angstrom CODATA98. Insert the keyword BOHRANGS, followed by the conversion factor adopted by Gaussian

As test cases to show what keywords needs to be included for each calculation, they provide the following neopentane example (using the same geometry for both, with the CRYSTAL geometry symmetrized to unique atoms) at the RHF level (avoiding the DFT issues altogether).

The CRYSTAL input is as follows:

Neopentane
MOLECULE
44
3
6       0.000000000     0.000000000     0.000000000
6       0.893151756     -0.893151756    0.893151756
1       1.551948982     -0.296135169    1.551948982
BOHRANGS
0.529177249
END
6 4
0 0 6 2.0 1.0
   .3047524880D+04   .1834737130D-02
   .4573695180D+03   .1403732280D-01
   .1039486850D+03   .6884262220D-01
   .2921015530D+02   .2321844430D+00
   .9286662960D+01   .4679413480D+00
   .3163926960D+01   .3623119850D+00
0 1 3 4.0 1.0
   .7868272350D+01  -.1193324200D+00   .6899906660D-01
   .1881288540D+01  -.1608541520D+00   .3164239610D+00
   .5442492580D+00   .1143456440D+01   .7443082910D+00
0 1 1 0.0 1.0
   .1687144782D+00   .1000000000D+01   .1000000000D+01
0 3 1 0.0 1.0
   .8000000000D+00   .1000000000D+01
1 3
0 0 3 1.0 1.0
   .1873113696D+02   .3349460434D-01
   .2825394365D+01   .2347269535D+00
   .6401216923D+00   .8137573262D+00
0 0 1 0.0 1.0
   .1612777588D+00   .1000000000D+01
0 2 1 0.0 1.0
   .1100000000D+01   .1000000000D+01
99 0
GAUSS98
END
TOLINTEG
20 20 20 20 20
NOBIPOLA
END
FMIXING
30
TOLDEP
8 
END

And the following is for Gaussian (but, I believe, provided by a CRYSTAL run):

# RHF/GEN 5D 7F GEOM=COORD TEST GFPRINT

Neopentane                                                                      

 0 1
   6  0.0000000000000E+00  0.0000000000000E+00  0.0000000000000E+00
   6  8.9315175600000E-01 -8.9315175600000E-01  8.9315175600000E-01
   6 -8.9315175600000E-01  8.9315175600000E-01  8.9315175600000E-01
   6  8.9315175600000E-01  8.9315175600000E-01 -8.9315175600000E-01
   6 -8.9315175600000E-01 -8.9315175600000E-01 -8.9315175600000E-01
   1  1.5519489820000E+00 -2.9613516900000E-01  1.5519489820000E+00
   1 -1.5519489820000E+00  2.9613516900000E-01  1.5519489820000E+00
   1  1.5519489820000E+00  2.9613516900000E-01 -1.5519489820000E+00
   1 -1.5519489820000E+00 -2.9613516900000E-01 -1.5519489820000E+00
   1  1.5519489820000E+00  1.5519489820000E+00 -2.9613516900000E-01
   1 -2.9613516900000E-01  1.5519489820000E+00  1.5519489820000E+00
   1 -1.5519489820000E+00 -1.5519489820000E+00 -2.9613516900000E-01
   1  2.9613516900000E-01  1.5519489820000E+00 -1.5519489820000E+00
   1  1.5519489820000E+00 -1.5519489820000E+00  2.9613516900000E-01
   1  2.9613516900000E-01 -1.5519489820000E+00  1.5519489820000E+00
   1 -1.5519489820000E+00  1.5519489820000E+00  2.9613516900000E-01
   1 -2.9613516900000E-01 -1.5519489820000E+00 -1.5519489820000E+00
 
C  0
       S    6 1.
  0.3047524880000E+04  0.1834737130000E-02
  0.4573695180000E+03  0.1403732280000E-01
  0.1039486850000E+03  0.6884262220000E-01
  0.2921015530000E+02  0.2321844430000E+00
  0.9286662960000E+01  0.4679413480000E+00
  0.3163926960000E+01  0.3623119850000E+00
       SP   3 1.
  0.7868272350000E+01 -0.1193324200000E+00  0.6899906660000E-01
  0.1881288540000E+01 -0.1608541520000E+00  0.3164239610000E+00
  0.5442492580000E+00  0.1143456440000E+01  0.7443082910000E+00
       SP   1 1.
  0.1687144782000E+00  0.1000000000000E+01  0.1000000000000E+01
       D    1 1.
  0.8000000000000E+00  0.1000000000000E+01
****
H  0
       S    3 1.
  0.1873113696000E+02  0.3349460434000E-01
  0.2825394365000E+01  0.2347269535000E+00
  0.6401216923000E+00  0.8137573262000E+00
       S    1 1.
  0.1612777588000E+00  0.1000000000000E+01
       P    1 1.
  0.1100000000000E+01  0.1000000000000E+01
****
 

Running these two calculations give you an energy difference of 0.0000003255398 Hartree.

So, turning the two codes into enough correspondence to trust the basis set conversion at the RHF/UHF level, IT IS REPORTED that one must include the following for CRYSTALXX:

BOHRANGS
0.529177249
... 
GAUSS98
... 
TOLINTEG
20 20 20 20 20
... 
NOBIPOLA
... 
TOLDEP
8 

Technically, the GAUSS98 keyword doesn’t gain you anything except a Gaussian-friendly coordinate file (but I include it here anyway).

Then do the following for Gaussian:

# 5D 7F

This brings your CRYSTALXX into correspondence with GaussianYY, not vice versa (re: B3LYP, cut-offs, etc.).

NOTE 5: DFT Calculations Are A Completely Different Matter

Density functional theory calculations are sensitive both to the proper specification of the density functional (see above for B3LYP) and the fineness of the grid (if you’re doing grid-based DFT). Unfortunately, there isn’t an exact correspondence between the grid specifications of the two programs (or the treatment of the grids in the two programs), which means there isn’t a way to exactly zero-out the differences between this part of the energy comparison for the two. I suppose one could attempt to run infinitely fine meshes to see what happens, but I’ve not seen it reported. That said, there’s enough correspondence in the different qualities of pre-defined grids to get you close enough to, again, wave off differences in the two energies to issues not related to the basis sets themselves.

This brings up a slightly off-topic point of discussion that hopefully will spare you a reviewer’s wrath. When a good journal reviewer sees someone report as their theoretical methods section:

Calculations were performed at the B3LYP/6-31G(d,p) level with the [insert program name] program.

… and nothing else, they become quite put off. There are several factors that will affect the ability of a future researcher to reproduce your data (if necessary). If not providing your input files, the bare minimum that should appear in a theory section includes:

* Electron correlation method (RHF, defined functional, MP2, etc.)
* A Reference To That Electron Correlation Method
* Basis Set
* A Reference To That Basis Set
* Convergence Criteria
* Grid Size for DFT calculations
* Version of the software
* A Reference To That Version of the software

… and if you’re just using program defaults (which is what is assumed when no other information is provided in the Methods Section), there’s no shame in stating that as well.

To beat on the issue of grid specification, here’s a plot of the energy of simple CH4 with varied Gaussian grid specifications (CRYSTAL09 showing a similar sensitivity to grid choice) (PPS = points per shell):

2014dec3_gaussianshells

You can see that, after a certain fineness, the calculations produce the same energies (the “infinitely fine” case for Gaussian in this case. Any finer mesh is overkill. This also shows WHY you need to specify your grid when reporting your results!). The grid, or the fineness of mesh, group into kind-of categories in Gaussian and CRYSTAL. To summarize briefly:

Gaussian Specifications:

Program Option “Coarse” – 35 radial shells and 110 angular points per shell (35,110)
Program Option “Fine” – (75,302)
Program Option “Ultrafine” – (99,590)

CRYSTAL Specifications:

Again, a few pre-defined grids are available.

Default (55,434)
Default grid - corresponds to the sequence:
RADIAL
1
4.0
55
ANGULAR
10
0.4 0.6 0.8 0.9 1.1 2.3 2.4 2.6 2.8 9999.0
1 2 5 8 11 13 11 8 5 1
Large (75,434)
RADIAL
1
4.0
75
ANGULAR
5
0.1667 0.5 0.9 3.05 9999.0
2 6 8 13 8
XLGRID (75,974)
RADIAL
1
4.0
75
ANGULAR
5
0.1667 0.5 0.9 3.5 9999.0
4 8 12 16 12
XXLGRID (99,1454)
RADIAL
1
4.0
99
ANGULAR
5
0.1667 0.5 0.9 3.5 9999.0
6 10 14 18 14

Which is all to be contrasted with the GAMESS-US approach of grid specification:

In GAMESS, you specify the components.

NRAD   = number of radial points in the Euler-MacLaurin                         
         quadrature. (96 is reasonable)                                         
                                                                                
NTHE   = number of angle theta grids in Gauss-Legendre                          
         quadrature (polar coordinates). (12 is reasonable)                     
                                                                                
NPHI   = number of angle phi grids in Gauss-Legendre                            
         quadrature.  NPHI should be double NTHE so points                      
         are spherically distributed. (24 is reasonable)                        
                                                                                
The number of angular points will be NTHE*NPHI.  The values                     
shown give a gradient accuracy near the default OPTTOL of                       
0.00010, while NTHE=24 NPHI=48 approaches OPTTOL=0.00001,                       
and "army grade" is NTHE=36 NPHI=72.                        

NOTE 6: EMSL vs. Built-In Gaussian Basis Sets

I am pleased to report there appears to be no difference running Gaussian with the built-in 6-31G(d,p) and using the EMSL Basis Set Exchange 6-31G(d,p) set (this fact was not obvious at the beginning of this test), but ONLY with the 5D and 7F keywords (specifying the number of angular momentum functions to use for the d and f shells) added (the EMSL basis sets will produce the same results either way. Gaussian’s behavior with its internal basis sets DOES change).

By that, I mean the following for Argon with the B3LYP and B5LYP (B3LYP alt.) functionals.

NOTE: Those lines with 5D 7F show identical energies for the B3LYP and B5LYP pairs. The others, not so much.

B3LYP
B3LYP
B5LYP
B5LYP
Internal 6-31G(d,p)
EMSL 6-31G(d,p)
Internal 6-31G(d,p)
EMSL 6-31G(d,p)
grid=coarse
-527.51705491
-527.51322582
-527.44745782
-527.44362696
grid=coarse, 5D 7F
-527.51322582
-527.51322582
-527.44362696
-527.44362696
grid=fine
-527.51714180
-527.51331287
-527.44754491
-527.44371422
grid=fine, 5D 7F
-527.51331287
-527.51331287
-527.44371422
-527.44371422
grid=ultrafine
-527.51714191
-527.51331298
-527.44754502
-527.44371433
grid=ultrafine, 5D 7F
-527.51331298
-527.51331298
-527.44371433
-527.44371433

NOTE 7: The Optimizers Affect The Final Energies

At the tail end of this energy comparison analysis came the identification of the quality of the optimization itself affecting the final energy differences. While the criteria for optimization in CRYSTALXX is very much like that in Gaussian as far as format is concerned, the reaching of an energetic minimum is different enough to produce energies differences of 10^-5 Hartree or more. My solution to this was to hammer on both the energy and geometry convergence criteria in CRYSTALXX, using:

TOLDEE (SCF and Optimization): 14
TOLDEG: 0.000001
TOLDEX: 0.000001

Nearly ridiculous convergence criteria and a massive waste of computing resources if you’re doing anything but trying to reproduce certain types of calculations (or if you’ve a molecule with +10 freely-rotatable but weakly interacting methyl groups). Your familiar-to-Gaussian-users convergence criteria will look like the following in CRYSTALXX:

 GRADIENT NORM     0.000001  GRADIENT THRESHOLD     0.500000

 MAX GRADIENT      0.000001  THRESHOLD              0.000002 CONVERGED YES
 RMS GRADIENT      0.000001  THRESHOLD              0.000001 CONVERGED YES
 MAX DISPLAC.      0.000000  THRESHOLD              0.000008 CONVERGED YES
 RMS DISPLAC.      0.000000  THRESHOLD              0.000005 CONVERGED YES

My practice with this phenomenon came from optimization attempts of Cl2 (one of the more difficult structures to get into agreement with the two codes early on). While Gaussian will generally take any number of starting geometries and produce the same result, CRYSTAL optimization is found to be very sensitive to the starting geometry, with closer initial Cl-Cl distances producing better agreements with Gaussian.

As a point of larger discussion, it is well known that one of Gaussian’s great benefits over several other codes is the quality of the convergers – you may not like the answer, but Gaussian is, generally, very good at finding minima. Where you have problems, you either have lots of keywords to adjust or lots of behind-the-curtain operations Gaussian does to attempt to find better geometries. Generally, CRYSTAL and Gaussian settled on the same structures. For some cases, the two disagreed on geometry, energy, or both when optimizing dimers (granted, the first row transition metals can be a tough block to make dimers out of), leaving one to “swap out” the optimized geometries from both programs to see if they, at least, agreed on the minimum from code A being an identifiable minimum in code B (which was generally, but not always, the case).

NOTE 8: Test(able) Structures And Assorted Convergence Problems

Finally, it should be stated that the energy analysis was performed to test if the basis sets were correctly converted, NOT to test the programs. I spent as much time as I thought reasonable on this analysis but ran into a few cases that tested my knowledge of keyword combinations and, more generally, tried my patience.

The test structures can be broken into three categories:

1. Full Shell (Noble and Noble-ish) Elements

That’s Ar, Be, Ca, He, Mg, Ne, and Zn.

2. Homodimers As Forced Singlets

That’s H2, Li2, B2, C2, N2, O2, F2, Na2, Al2, Si2, P2, S2, Cl2, K2, Sc2, Ti2, V2, Cr2, Mn2, Fe2, Co2, Ni2, and Cu2.

The dimers and singlets combination grew out of an early frustration when trying to get doublets to be well-behaved in CRYSTAL09. For instance, I could not get CRYSTAL09 to give me an UHF energy for the single Flourine doublet.

Dimers made several combinations easy (H2,F2,Cl2,N2,C2), one easier (Al2), and three less easy (O2,S2,B2). You say to yourself “O2 is a ground-state triplet. Why run the singlet?” My answer is “I didn’t want to deal with unpaired-ness as part of the survey (else would have run a bunch of doublets). And a singlet is a singlet (I thought), so the comparison for the sake of comparing energies is still valid.”

It should be obvious that dimerization in all of the non-full shell cases simplifies life by allowing you to always define a system with a RHF wavefunction (no unpaired electrons, even if they really, really want to be). This approximation in all cases has less to do with a lacking working knowledge of transition metals (but, hey, it has been a while) than it does with an interest in computational expediency. If CRYSTAL and Gaussian can be made to produce identical structures, I believe the basis set conversion even if I don’t believe the reasonability of the optimized structure (which is to say, I did spend significant time getting Gaussian and CRYSTAL to produce the same structure, but didn’t spend any time the best geometry from sets of optimizations).

3. Hydrides For Some Non-Ideal Homodimer Optimizations

That’s AlH3, BH3, CoH3, H2O, H2S, KH, MnH5, NaH, NiH2, VH3.

The production of energetic minima among transition metal homodimers is complicated in the two codes by the presence of multiple minima for these species (we’re talking lots of ways to combine electrons). O2 and S2 Hartree-Fock calculations proved to be annoyingly problematic despite several efforts. The energy difference between the low-spin (singlet) and high-spin (triplet) cases produced too-small numbers in CRYSTAL09 compared to Gaussian. Boron is just naturally poorly-behaved, Aluminum less so. Manganese and nickel were a serious fight to get RHF values to agree. Na2 and K2 weren’t bad, but I thought the agreement could get better (hence NaH and KH). Same for V2 (in the form of VH3).

For a selection of cases, the homodimers are reported (to show how badly they behave), but the appropriately valence-satisfied hydrides for these elements are also reported (where it is shown that the energies between CRYSTAL and Gaussian look great).

NOTE 9: What’s Good Enough?

As too much text above explains, getting CRYSTALXX and GaussianXX to agree to too many significant digits by DFT is more work than it’s worth. Getting Hartree-Fock (esp. RHF) to agree to within narrow tolerances is not a problem provided you really beat on the energy criteria and structure optimizations. A summary of the energy differences between Gaussian09 and CRYSTAL09 for RHF and “best case” DFT are provided below. RHF is my guide here to prove that the basis set conversion was successful. The DFT results show how “very high quality” Gaussian09 and “very high quality” CRYSTAL09 still differ in their final energies.

Atom, Molecule
Best Keyword
RHF Difference
With 6-31G(d,p)
Best Keyword Match
DFT Difference
With 6-31G(d,p)
Notes
Al2
0.0000000959
-0.0000021180
Difference Per Atom
AlH3
0.0000000044
-0.0001532824
Hydride Alternative Optmization
Ar
0.0000000000
0.0000079653
Single atom
B2
0.0160814822
-0.0119799981
Difference Per Atom
BH3
0.0000000002
-0.0000043200
Hydride Alternative Optmization
Be
0.0000000000
-0.0000015870
Single atom
C2
0.0000000385
-0.0000230890
Difference Per Atom
Ca
0.0000000003
0.0000134887
Single atom
Cl2
0.0000000945
-0.0000013374
Difference Per Atom
Co2
0.0004687257
-0.0000485513
Difference Per Atom
CoH3
0.0000000269
-0.0003096507
Hydride Alternative Optmization
Cr2
-0.0000001317
-0.0000701267
Difference Per Atom
Cu2
-0.0000043954
0.0000462382
Difference Per Atom
F2
0.0000000586
0.0000000730
Difference Per Atom
Fe2
0.0000001773
-0.0000175537
Difference Per Atom
H2
0.0000000025
0.0000000010
Difference Per Atom
He
0.0000000000
0.0000000000
Single atom
K2
-0.0000019804
-0.0010458054
Difference Per Atom
KH
-0.0000000021
-0.0000958239
Hydride Alternative Optmization
Li2
0.0000000001
-0.0006904112
Difference Per Atom
Mg
-0.0000000003
-0.0000009333
Single atom
Mn2
-0.0002591557
-0.0554301772
Difference Per Atom
MnH5
0.0000000241
0.0000023412
Hydride Alternative Optmization
N2
0.0000000098
-0.0000055645
Difference Per Atom
Na2
-0.0000001262
-0.0003885180
Difference Per Atom
NaH
-0.0000000007
-0.0000262128
Hydride Alternative Optmization
Ne
0.0000000003
-0.0000007236
Single atom
Ni2
-0.0000101151
-0.0020160551
Difference Per Atom
NiH2
0.0000000050
-0.0000066828
Hydride Alternative Optmization
O2
0.2506265617
-0.0353640801
Difference Per Atom
H2O
0.0000000004
0.0000010523
Hydride Alternative Optmization
P2
-0.0000000409
-0.0006573436
Difference Per Atom
S2
0.1401697163
-0.0174734608
Difference Per Atom
H2S
0.0000000072
-0.0002853645
Hydride Alternative Optmization
Sc2
0.0000002473
-0.0000234407
Difference Per Atom
Si2
-0.0000000110
-0.0000390207
Difference Per Atom
Ti2
0.0000005480
-0.0000421595
Difference Per Atom
V2
-0.0757905400
-0.0000554233
Difference Per Atom
VH3
0.0000000100
–0.0000089300
Hydride Alternative Optmization
Zn
-0.0000000034
-0.0000013193
Single atom

NOTE 10: Keywords

As discussed in NOTE 4 above, you need to specify several parameters to make Gaussian and CRYSTAL agree. In the interest of complete overkill, I decided I wanted to know how the keyword combinations change the final energies from the runs. To that end, the summarized energies from all of the runs performed for the analysis is a bit exhaustive and full of lots of identical data (which is a good thing). These keywords are summarized below.

Parse The RHF Calculations As Follows:

H2__rhf__631Gdp__BOHRANGS__NOBIPOLA__10sTOLINTEG__TOLDEP__GAUSS98

As is a habit, all of the files are named with the relevant keyword combinations in the filenames themselves for ease of sorting.

H2
rhf
631Gdp
BOHRANGS
NOBIPOLA
10sTOLINTEG
TOLDEP
GAUSS98

Additional for the DFT calculations:

DefGRID__BOHRANGS__NOBIPOLA__20sTOLINTEG__TOLDEP__GAUSS98

Differ by the specification of the grid.

DefGRID
LGRID
XLGRID
XXLGRID

You will note that, very generally, the same energies are produced for many of the varied keyword combinations. That said, some difference throughout exist. I will not dwell on the differences here (well, only slightly), only remark that keyword choices affect final energies when trying to perform program comparisons, and differences in keywords may alter relative energies when using two different input files for the same structure. As you might expect, when in doubt, use identical keyword sets.

Just to explain what’s going on in each Excel tab (Excel file can be downloaded at the link at the bottom of this post), here’s a colorized sample case for H2.

2014nov30_testinglabels

* RED Set – RHF CRYSTAL runs with varied keyword combinations (filenames and energies)

* GREEN Set – RHF Gaussian09 runs with, in order, the internal basis set, internal + 5D 7F, EMSL basis set, and EMSL basis set + 5D 7F

* RED and GREEN bordered – the energies compared for the relative energies of the two programs.

* Gaussian – CRYSTAL Difference Using Boxed Values – Should be Obvious

* Difference Per Atom Using Boxed Values – For the homodimers, the difference divided by 2

* BLUE Set – CRYSTAL09 B3LYP/6-31G(d,p) Energies with difference keyword sets

* BLUE Background – Gaussian09’s B3LYP/6-31G(d,p) calculations with the internal 6-31G(d,p) Basis Set

* YELLOW Background – Gaussian09’s B3LYP/6-31G(d,p) calculations with the EMSL 6-31G(d,p) Basis Set

* ORANGE Set – Gaussian Alternative B3LYP/6-31G(d,p) (B5LYP) calculations with the internal 6-31G(d,p) Basis Set

* BLACK Set – Gaussian Alternative B3LYP/6-31G(d,p) (B5LYP) calculations with the EMSL 6-31G(d,p) Basis Set

* Gaussian-CRYSTAL Difference – The B3LYP/6-31G(d,p) Energy Differences For the “B5LYP” EMSL 6-31G(d,p) Cases (best comparisons). The bordered CRYSTAL09 keyword set (XLGRID__NOBIPOLA__20sTOLINTEG__TOLDEP__GAUSS98) is used.

* LIGHT GREEN Background – These calculations don’t include the GAUSS98 keyword, which only produces a formatted GAUSSIAN.DAT file. You’d think the presence of absence of this keyword would mean nothing, so I consider this a control case for keyword sensitivity.

NOTE 11: Some Lessons Learned (Briefly) From Some Small Systems

1. CRYSTAL is much more sensitive to the starting geometry than Gaussian when it comes to finding a stable minimum. Simply changing an interatomic distance by a tenth of an Angstrom is enough to cause a failed optimization to work (and vice versa).

2. Generally, both programs settle on the same minimum. This is easy when the systems are well-behaved (hence the hydrides). For several of the metal systems, the two programs consistently disagreed on the minimum energy geometry (which is not unexpected in some ways).

3. DFT vs. RHF and the addition of END – You might assume that the replacement of B3LYP with RHF in a CRYSTAL input file would look something like:

B3LYP
END

RHF
END

You would, in fact, be wrong. Including this END statement for RHF reads as a hard END for the program. I spent far too long wondering why all of my parameters were being ignored in the RHF runs until I happened to delete the END after RHF, after which life became much simpler. Careful with your calls!

4. CRYSTAL can produce multiple minima for the same starting geometry with different keyword choices. This is not too surprising, as many keyword combinations can interact to result in different early sampling of forces and energies. That said, this is also shown to be element-specific. In the Excel file, Tabs with a “-” at the beginning contain RHF results that show differences (10ths to 1000ths of Hartrees) among the various RHF keyword choices. NiH2 6-31G optimizations, as just one example, group into two structures with a 0.46 Hartree difference in energy that differ by Ni-H bond lengths of 0.006 Angstroms.

For those causally reading, 0.46 Hartree is about 1207 kJ/mol, which is a completely insane amount. This is true, but the program terminated normally. Sadly, normal mode analyses failed for both cases with the same keyword sets (no additional modification to get things to normal mode properly) and, because my concern was only testing the energies to confirm that the basis sets were properly converted, I have not pursued any of these problem cases further.

Can this energy difference issue in the RHF series be dealt with? Certainly. Swapping geometries from one optimization into another input file with… conflicting keyword sets will often produce the original geometry. That said, if you were simply going into the optimizations with these small structures and did not know you were facing the possibility of local minima around a global minimum, you’d risk missing the ridiculous 0.46 Hartree of energy.

The RHF optimization variations in keyword combinations for Co2 6-31G and 6-31G(d,p), Ni2 6-31G and 6-31G(d,p), and NiH2 6-31G and 6-31G(d,p) are marked accordingly. Academically interesting but not pursued further.

5. Boron, Oxygen, Sulfur, Vanadium – Vanadium was far and away the worst dimer to deal with in RHF calculations, to the point where this post would have gone up a week sooner had it been more well-behaved. While the hydride (VH3) is well behaved, V2 settles on one of two minima and CRYSTAL and Gaussian seem to have a very difficult time deciding what that minimum is. One optimization attempt produced a CRYSTAL result consistent with Gaussian, while all others produced an alternative minimum (with the difference obvious in the bond lengths).

My goal in the analysis was NOT to employ multiple convergence keywords/tools to force structures into agreement, as I wanted to find out what different keyword combinations did to affect the final energies and geometries. I suspect B2, O2, S2, and V2 could be made to agree between CRYSTAL and Gaussian. That said, efforts with ONLY the keyword sets used for all of the other comparisons in the element series reveal that CRYSTAL and Gaussian differ in the optimized geometries for these four cases in ways that they do not differ for any other element sets.

Performing the same calculations on the hydrides produces excellent agreement between the two codes (and are my tests to believe that the basis set conversion was successful). Worse still (at least for the continuity of the RHF-centric presentation above), the V2 DFT energies between CRYSTAL and Gaussian are nearly identical (among the best for the larger elements) while the RHF values are far from agreement despite several geometry-swapping attempts (CRYSTAL and Gaussian see two different electronic states and see starting geometries as higher-energy versions of those two different states. A tricky problem to tackle generally).




And, Finally…

The Files

The 6-31G Basis Sets can be downloaded here: 2014dec30_631G_CRYSTAL_Basis_Sets.txt

The 6-31G(d) Basis Sets can be downloaded here: 2014dec30_631Gd_CRYSTAL_Basis_Sets.txt

The 6-31G(d,p) Basis Sets can be downloaded here: 2014dec30_631Gdp_CRYSTAL_Basis_Sets.txt

For those wanting to perform their own tests, all of the input and output files from ALL of the runs are provided here (55 MB zip file): 2014dec30_Crystal_Basis_Sets_Run_Files.zip

For those who want to see the numbers for all of the tests, the excel file containing all of the data can be downloaded here: 2014dec30_Crystal_Basis_Sets_Run_results.xlsx.zip


The 6-31G Gaussian-Type Basis Sets

In order and in CRYSTAL format below. For those wondering, you generate the 6-31G set by taking the extra group of coefficients off the back-end of the 6-31G(d,p) basis sets. Compare any element from the two groups and you’ll see the difference.

NOTE: If making similar modifications to other basis sets with added polarization or diffuse functions, you need to change the number of shells after the element in the first row of each element when you delete the bottom shell (so, for H, “1 3″ for 6-31G(d,p) becomes “1 2″ for 6-31G. If you’ve a problem with a CRYSTAL run with a home-converted basis set, check that first).

1  2      
0 0 3 1.0 1.0
  1.8731136960E+01   3.3494604340E-02    
  2.8253943650E+00   2.3472695350E-01    
  6.4012169230E-01   8.1375732620E-01    
0 0 1 0.0 1.0
  1.6127775880E-01   1.0000000000E+00    

2  2    
0 0 3 2.0 1.0
  3.8421634000E+01   2.3766000000E-02
  5.7780300000E+00   1.5467900000E-01
  1.2417740000E+00   4.6963000000E-01
0 0 1 0.0 1.0
  2.9796400000E-01   1.0000000000E+00
  
3  3      
0 0 6 2.0 1.0
  6.4241892000E+02   2.1426000000E-03
  9.6798515000E+01   1.6208900000E-02
  2.2091121000E+01   7.7315600000E-02
  6.2010703000E+00   2.4578600000E-01
  1.9351177000E+00   4.7018900000E-01
  6.3673580000E-01   3.4547080000E-01
0 1 3 1.0 1.0
  2.3249184000E+00  -3.5091700000E-02   8.9415000000E-03
  6.3243060000E-01  -1.9123280000E-01   1.4100950000E-01
  7.9053400000E-02   1.0839878000E+00   9.4536370000E-01
0 1 1 0.0 1.0
  3.5962000000E-02   1.0000000000E+00   1.0000000000E+00

4  3      
0 0 6 2.0 1.0
  1.2645857000E+03   1.9448000000E-03
  1.8993681000E+02   1.4835100000E-02
  4.3159089000E+01   7.2090600000E-02
  1.2098663000E+01   2.3715420000E-01
  3.8063232000E+00   4.6919870000E-01
  1.2728903000E+00   3.5652020000E-01
0 1 3 2.0 1.0
  3.1964631000E+00  -1.1264870000E-01   5.5980200000E-02
  7.4781330000E-01  -2.2950640000E-01   2.6155060000E-01
  2.1996630000E-01   1.1869167000E+00   7.9397230000E-01
0 1 1 0.0 1.0
  8.2309900000E-02   1.0000000000E+00   1.0000000000E+00

5  3      
0 0 6 2.0 1.0
  2.0688823000E+03   1.8663000000E-03
  3.1064957000E+02   1.4251500000E-02
  7.0683033000E+01   6.9551600000E-02
  1.9861080000E+01   2.3257290000E-01
  6.2993048000E+00   4.6707870000E-01
  2.1270270000E+00   3.6343140000E-01
0 1 3 3.0 1.0
  4.7279710000E+00  -1.3039380000E-01   7.4597600000E-02
  1.1903377000E+00  -1.3078890000E-01   3.0784670000E-01
  3.5941170000E-01   1.1309444000E+00   7.4345680000E-01
0 1 1 0.0 1.0
  1.2675120000E-01   1.0000000000E+00   1.0000000000E+00

6  3      
0 0 6 2.0 1.0
  3.0475248800E+03   1.8347371300E-03    
  4.5736951800E+02   1.4037322800E-02    
  1.0394868500E+02   6.8842622200E-02    
  2.9210155300E+01   2.3218444300E-01    
  9.2866629600E+00   4.6794134800E-01    
  3.1639269600E+00   3.6231198500E-01    
0 1 3 4.0 1.0
  7.8682723500E+00  -1.1933242000E-01   6.8999066600E-02  
  1.8812885400E+00  -1.6085415200E-01   3.1642396100E-01  
  5.4424925800E-01   1.1434564400E+00   7.4430829100E-01  
0 1 1 0.0 1.0
  1.6871447820E-01   1.0000000000E+00   1.0000000000E+00  

7  3      
0 0 6 2.0 1.0
  4.1735110000E+03   1.8348000000E-03    
  6.2745790000E+02   1.3995000000E-02    
  1.4290210000E+02   6.8587000000E-02    
  4.0234330000E+01   2.3224100000E-01    
  1.2820210000E+01   4.6907000000E-01    
  4.3904370000E+00   3.6045500000E-01    
0 1 3 5.0 1.0
  1.1626358000E+01  -1.1496100000E-01   6.7580000000E-02  
  2.7162800000E+00  -1.6911800000E-01   3.2390700000E-01  
  7.7221800000E-01   1.1458520000E+00   7.4089500000E-01  
0 1 1 0.0 1.0
  2.1203130000E-01   1.0000000000E+00   1.0000000000E+00  

8  3      
0 0 6 2.0 1.0
  5.4846717000E+03   1.8311000000E-03    
  8.2523495000E+02   1.3950100000E-02    
  1.8804696000E+02   6.8445100000E-02    
  5.2964500000E+01   2.3271430000E-01    
  1.6897570000E+01   4.7019300000E-01    
  5.7996353000E+00   3.5852090000E-01    
0 1 3 6.0 1.0
  1.5539616000E+01  -1.1077750000E-01   7.0874300000E-02  
  3.5999336000E+00  -1.4802630000E-01   3.3975280000E-01  
  1.0137618000E+00   1.1307670000E+00   7.2715860000E-01  
0 1 1 0.0 1.0
  2.7000580000E-01   1.0000000000E+00   1.0000000000E+00  

9  3      
0 0 6 2.0 1.0
  7.0017130900E+03   1.8196169000E-03
  1.0513660900E+03   1.3916079600E-02
  2.3928569000E+02   6.8405324500E-02
  6.7397445300E+01   2.3318576000E-01
  2.1519957300E+01   4.7126743900E-01
  7.4031013000E+00   3.5661854600E-01
0 1 3 7.0 1.0
  2.0847952800E+01  -1.0850697500E-01   7.1628724300E-02
  4.8083083400E+00  -1.4645165800E-01   3.4591210300E-01
  1.3440698600E+00   1.1286885800E+00   7.2246995700E-01
0 1 1 0.0 1.0
  3.5815139300E-01   1.0000000000E+00   1.0000000000E+00

10  3    
0 0 6 2.0 1.0
  8.4258515300E+03   1.8843481000E-03
  1.2685194000E+03   1.4336899400E-02
  2.8962141400E+02   7.0109623300E-02
  8.1859004000E+01   2.3737326600E-01
  2.6251507900E+01   4.7300712600E-01
  9.0947205100E+00   3.4840124100E-01
0 1 3 8.0 1.0
  2.6532131000E+01  -1.0711828700E-01   7.1909588500E-02
  6.1017550100E+00  -1.4616382100E-01   3.4951337200E-01
  1.6962715300E+00   1.1277735000E+00   7.1994051200E-01
0 1 1 0.0 1.0
  4.4581870000E-01   1.0000000000E+00   1.0000000000E+00

11  4
0 0 6 2.0 1.0
  9.9932000000E+03   1.9377000000E-03
  1.4998900000E+03   1.4807000000E-02
  3.4195100000E+02   7.2706000000E-02
  9.4679700000E+01   2.5262900000E-01
  2.9734500000E+01   4.9324200000E-01
  1.0006300000E+01   3.1316900000E-01
0 1 6 8.0 1.0
  1.5096300000E+02  -3.5421000000E-03   5.0017000000E-03      
  3.5587800000E+01  -4.3959000000E-02   3.5511000000E-02      
  1.1168300000E+01  -1.0975210000E-01   1.4282500000E-01      
  3.9020100000E+00   1.8739800000E-01   3.3862000000E-01      
  1.3817700000E+00   6.4669900000E-01   4.5157900000E-01      
  4.6638200000E-01   3.0605800000E-01   2.7327100000E-01      
0 1 3 1.0 1.0
  4.9796600000E-01  -2.4850300000E-01  -2.3023000000E-02      
  8.4353000000E-02  -1.3170400000E-01   9.5035900000E-01      
  6.6635000000E-02   1.2335200000E+00   5.9858000000E-02      
0 1 1 0.0 1.0
  2.5954400000E-02   1.0000000000E+00   1.0000000000E+00      

12  4 
0 0 6 2.0 1.0
  1.1722800000E+04   1.9778000000E-03         
  1.7599300000E+03   1.5114000000E-02         
  4.0084600000E+02   7.3911000000E-02         
  1.1280700000E+02   2.4919100000E-01         
  3.5999700000E+01   4.8792800000E-01         
  1.2182800000E+01   3.1966200000E-01         
0 1 6 8.0 1.0
  1.8918000000E+02  -3.2372000000E-03   4.9281000000E-03      
  4.5211900000E+01  -4.1008000000E-02   3.4989000000E-02      
  1.4356300000E+01  -1.1260000000E-01   1.4072500000E-01      
  5.1388600000E+00   1.4863300000E-01   3.3364200000E-01      
  1.9065200000E+00   6.1649700000E-01   4.4494000000E-01      
  7.0588700000E-01   3.6482900000E-01   2.6925400000E-01      
0 1 3 2.0 1.0
  9.2934000000E-01  -2.1229000000E-01  -2.2419000000E-02      
  2.6903500000E-01  -1.0798500000E-01   1.9227000000E-01      
  1.1737900000E-01   1.1758400000E+00   8.4618100000E-01      
0 1 1 0.0 1.0
  4.2106100000E-02   1.0000000000E+00   1.0000000000E+00      
  
13  4
0 0 6 2.0 1.0
  1.3983100000E+04   1.9426700000E-03         
  2.0987500000E+03   1.4859900000E-02         
  4.7770500000E+02   7.2849400000E-02         
  1.3436000000E+02   2.4683000000E-01         
  4.2870900000E+01   4.8725800000E-01         
  1.4518900000E+01   3.2349600000E-01         
0 1 6 8.0 1.0
  2.3966800000E+02  -2.9261900000E-03   4.6028500000E-03      
  5.7441900000E+01  -3.7408000000E-02   3.3199000000E-02      
  1.8285900000E+01  -1.1448700000E-01   1.3628200000E-01      
  6.5991400000E+00   1.1563500000E-01   3.3047600000E-01      
  2.4904900000E+00   6.1259500000E-01   4.4914600000E-01      
  9.4454000000E-01   3.9379900000E-01   2.6570400000E-01      
0 1 3 3.0 1.0
  1.2779000000E+00  -2.2760600000E-01  -1.7513000000E-02      
  3.9759000000E-01   1.4458300000E-03   2.4453300000E-01      
  1.6009500000E-01   1.0927900000E+00   8.0493400000E-01      
0 1 1 0.0 1.0
  5.5657700000E-02   1.0000000000E+00   1.0000000000E+00      
  
14  4
0 0 6 2.0 1.0
  1.6115900000E+04   1.9594800000E-03         
  2.4255800000E+03   1.4928800000E-02         
  5.5386700000E+02   7.2847800000E-02         
  1.5634000000E+02   2.4613000000E-01         
  5.0068300000E+01   4.8591400000E-01         
  1.7017800000E+01   3.2500200000E-01         
0 1 6 8.0 1.0
  2.9271800000E+02  -2.7809400000E-03   4.4382600000E-03      
  6.9873100000E+01  -3.5714600000E-02   3.2667900000E-02      
  2.2336300000E+01  -1.1498500000E-01   1.3472100000E-01      
  8.1503900000E+00   9.3563400000E-02   3.2867800000E-01      
  3.1345800000E+00   6.0301700000E-01   4.4964000000E-01      
  1.2254300000E+00   4.1895900000E-01   2.6137200000E-01      
0 1 3 4.0 1.0
  1.7273800000E+00  -2.4463000000E-01  -1.7795100000E-02      
  5.7292200000E-01   4.3157200000E-03   2.5353900000E-01      
  2.2219200000E-01   1.0981800000E+00   8.0066900000E-01      
0 1 1 0.0 1.0
  7.7836900000E-02   1.0000000000E+00   1.0000000000E+00      

15  4
0 0 6 2.0 1.0
  1.9413300000E+04   1.8516000000E-03         
  2.9094200000E+03   1.4206200000E-02         
  6.6136400000E+02   6.9999500000E-02         
  1.8575900000E+02   2.4007900000E-01         
  5.9194300000E+01   4.8476200000E-01         
  2.0031000000E+01   3.3520000000E-01         
0 1 6 8.0 1.0
  3.3947800000E+02  -2.7821700000E-03   4.5646200000E-03      
  8.1010100000E+01  -3.6049900000E-02   3.3693600000E-02      
  2.5878000000E+01  -1.1663100000E-01   1.3975500000E-01      
  9.4522100000E+00   9.6832800000E-02   3.3936200000E-01      
  3.6656600000E+00   6.1441800000E-01   4.5092100000E-01      
  1.4674600000E+00   4.0379800000E-01   2.3858600000E-01      
0 1 3 5.0 1.0
  2.1562300000E+00  -2.5292300000E-01  -1.7765300000E-02      
  7.4899700000E-01   3.2851700000E-02   2.7405800000E-01      
  2.8314500000E-01   1.0812500000E+00   7.8542100000E-01      
0 1 1 0.0 1.0
  9.9831700000E-02   1.0000000000E+00   1.0000000000E+00      
  
16  4
0 0 6 2.0 1.0
  2.1917100000E+04   1.8690000000E-03         
  3.3014900000E+03   1.4230000000E-02         
  7.5414600000E+02   6.9696000000E-02         
  2.1271100000E+02   2.3848700000E-01         
  6.7989600000E+01   4.8330700000E-01         
  2.3051500000E+01   3.3807400000E-01         
0 1 6 8.0 1.0
  4.2373500000E+02  -2.3767000000E-03   4.0610000000E-03      
  1.0071000000E+02  -3.1693000000E-02   3.0681000000E-02      
  3.2159900000E+01  -1.1331700000E-01   1.3045200000E-01      
  1.1807900000E+01   5.6090000000E-02   3.2720500000E-01      
  4.6311000000E+00   5.9225500000E-01   4.5285100000E-01      
  1.8702500000E+00   4.5500600000E-01   2.5604200000E-01      
0 1 3 6.0 1.0
  2.6158400000E+00  -2.5037400000E-01  -1.4511000000E-02      
  9.2216700000E-01   6.6957000000E-02   3.1026300000E-01      
  3.4128700000E-01   1.0545100000E+00   7.5448300000E-01      
0 1 1 0.0 1.0
  1.1716700000E-01   1.0000000000E+00   1.0000000000E+00      

17  4
0 0 6 2.0 1.0
  2.5180100000E+04   1.8330000000E-03         
  3.7803500000E+03   1.4034000000E-02         
  8.6047400000E+02   6.9097000000E-02         
  2.4214500000E+02   2.3745200000E-01         
  7.7334900000E+01   4.8303400000E-01         
  2.6247000000E+01   3.3985600000E-01         
0 1 6 8.0 1.0
  4.9176500000E+02  -2.2974000000E-03   3.9894000000E-03      
  1.1698400000E+02  -3.0714000000E-02   3.0318000000E-02      
  3.7415300000E+01  -1.1252800000E-01   1.2988000000E-01      
  1.3783400000E+01   4.5016000000E-02   3.2795100000E-01      
  5.4521500000E+00   5.8935300000E-01   4.5352700000E-01      
  2.2258800000E+00   4.6520600000E-01   2.5215400000E-01      
0 1 3 7.0 1.0
  3.1864900000E+00  -2.5183000000E-01  -1.4299000000E-02      
  1.1442700000E+00   6.1589000000E-02   3.2357200000E-01      
  4.2037700000E-01   1.0601800000E+00   7.4350700000E-01      
0 1 1 0.0 1.0
  1.4265700000E-01   1.0000000000E+00   1.0000000000E+00      
  
18  4
0 0 6 2.0 1.0
  2.8348300000E+04   1.8252600000E-03         
  4.2576200000E+03   1.3968600000E-02         
  9.6985700000E+02   6.8707300000E-02         
  2.7326300000E+02   2.3620400000E-01         
  8.7369500000E+01   4.8221400000E-01         
  2.9686700000E+01   3.4204300000E-01         
0 1 6 8.0 1.0
  5.7589100000E+02  -2.1597200000E-03   3.8066500000E-03      
  1.3681600000E+02  -2.9077500000E-02   2.9230500000E-02      
  4.3809800000E+01  -1.1082700000E-01   1.2646700000E-01      
  1.6209400000E+01   2.7699900000E-02   3.2351000000E-01      
  6.4608400000E+00   5.7761300000E-01   4.5489600000E-01      
  2.6511400000E+00   4.8868800000E-01   2.5663000000E-01      
0 1 3 8.0 1.0
  3.8602800000E+00  -2.5559200000E-01  -1.5919700000E-02      
  1.4137300000E+00   3.7806600000E-02   3.2464600000E-01      
  5.1664600000E-01   1.0805600000E+00   7.4399000000E-01      
0 1 1 0.0 1.0
  1.7388800000E-01   1.0000000000E+00   1.0000000000E+00      

19  5
0 0 6 2.0 1.0
  3.1594420000E+04   1.8280100000E-03         
  4.7443300000E+03   1.3994030000E-02         
  1.0804190000E+03   6.8871290000E-02         
  3.0423380000E+02   2.3697600000E-01         
  9.7245860000E+01   4.8290400000E-01         
  3.3024950000E+01   3.4047950000E-01         
0 1 6 8.0 1.0
  6.2276250000E+02  -2.5029760000E-03   4.0946370000E-03      
  1.4788390000E+02  -3.3155500000E-02   3.1451990000E-02      
  4.7327350000E+01  -1.2263870000E-01   1.3515580000E-01      
  1.7514950000E+01   5.3536430000E-02   3.3905000000E-01      
  6.9227220000E+00   6.1938600000E-01   4.6294550000E-01      
  2.7682770000E+00   4.3458780000E-01   2.2426380000E-01      
0 1 6 8.0 1.0
  1.1848020000E+01   1.2776890000E-02  -1.2213770000E-02      
  4.0792110000E+00   2.0987670000E-01  -6.9005370000E-03      
  1.7634810000E+00  -3.0952740000E-03   2.0074660000E-01      
  7.8892700000E-01  -5.5938840000E-01   4.2813320000E-01      
  3.5038700000E-01  -5.1347600000E-01   3.9701560000E-01      
  1.4634400000E-01  -6.5980350000E-02   1.1047180000E-01      
0 1 3 1.0 1.0
  7.1680100000E-01  -5.2377720000E-02   3.1643000000E-02      
  2.3374100000E-01  -2.7985030000E-01  -4.0461600000E-02      
  3.8675000000E-02   1.1415470000E+00   1.0120290000E+00      
0 1 1 0.0 1.0
  1.6521000000E-02   1.0000000000E+00   1.0000000000E+00      
  
20  5
0 0 6 2.0 1.0
  3.5264860000E+04   1.8135010000E-03         
  5.2955030000E+03   1.3884930000E-02         
  1.2060200000E+03   6.8361620000E-02         
  3.3968390000E+02   2.3561880000E-01         
  1.0862640000E+02   4.8206390000E-01         
  3.6921030000E+01   3.4298190000E-01         
0 1 6 8.0 1.0
  7.0630960000E+02   2.4482250000E-03   4.0203710000E-03      
  1.6781870000E+02   3.2415040000E-02   3.1006010000E-02      
  5.3825580000E+01   1.2262190000E-01   1.3372790000E-01      
  2.0016380000E+01  -4.3169650000E-02   3.3679830000E-01      
  7.9702790000E+00  -6.1269950000E-01   4.6312810000E-01      
  3.2120590000E+00  -4.4875400000E-01   2.2575320000E-01      
0 1 6 8.0 1.0
  1.4195180000E+01   1.0845000000E-02  -1.2896210000E-02      
  4.8808280000E+00   2.0883330000E-01  -1.0251980000E-02      
  2.1603900000E+00   3.1503380000E-02   1.9597810000E-01      
  9.8789900000E-01  -5.5265180000E-01   4.3579330000E-01      
  4.4951700000E-01  -5.4379970000E-01   3.9964520000E-01      
  1.8738700000E-01  -6.6693420000E-02   9.7136360000E-02      
0 1 3 1.0 1.0
  1.0322710000E+00  -4.4397200000E-02  -4.2986210000E-01      
  3.8117100000E-01  -3.2845630000E-01   6.9358290000E-03      
  6.5131000000E-02   1.1630100000E+00   9.7059330000E-01      
0 1 1 0.0 1.0
  2.6010000000E-02   1.0000000000E+00   1.0000000000E+00      

21  7
0 0 6 2.0 1.00
  3.9088980000E+04   1.8032630000E-03   
  5.8697920000E+03   1.3807690000E-02   
  1.3369100000E+03   6.8003960000E-02   
  3.7660310000E+02   2.3470990000E-01   
  1.2046790000E+02   4.8156900000E-01   
  4.0980320000E+01   3.4456520000E-01   
0 1 6 8.0 1.0
  7.8628520000E+02   2.4518630000E-03   4.0395300000E-03
  1.8688700000E+02   3.2595790000E-02   3.1225700000E-02
  6.0009350000E+01   1.2382420000E-01   1.3498330000E-01
  2.2258830000E+01  -4.3598900000E-02   3.4247930000E-01
  8.8851490000E+00  -6.1771810000E-01   4.6231130000E-01
  3.6092110000E+00  -4.4328230000E-01   2.1775240000E-01
0 1 6 8.0 1.0
  2.9843550000E+01  -2.5863020000E-03  -6.0966520000E-03
  9.5423830000E+00   7.1884240000E-02  -2.6288840000E-02
  4.0567900000E+00   2.5032600000E-01   5.0910010000E-02
  1.7047030000E+00  -2.9910030000E-01   3.7980970000E-01
  7.0623400000E-01  -7.4468180000E-01   5.1708830000E-01
  2.7953600000E-01  -1.7997760000E-01   1.8297720000E-01
0 1 3 2.0 1.0
  1.0656090000E+00   6.4829780000E-02  -2.9384400000E-01
  4.2593300000E-01   3.2537560000E-01   9.2353230000E-02
  7.6320000000E-02  -1.1708060000E+00   9.8479300000E-01
0 1 1 0.0 1.0
  2.9594000000E-02   1.0000000000E+00   1.0000000000E+00
0 3 3 1.0 1.0
  1.1147010000E+01   8.7476720000E-02   
  2.8210430000E+00   3.7956350000E-01   
  8.1962000000E-01   7.1803930000E-01   
0 3 1 0.0 1.0
  2.2146800000E-01   1.0000000000E+00   

22  7  
0 0 6 2.0 1.00
  4.3152950000E+04   1.7918720000E-03   
  6.4795710000E+03   1.3723920000E-02   
  1.4756750000E+03   6.7628300000E-02   
  4.1569910000E+02   2.3376420000E-01   
  1.3300060000E+02   4.8106960000E-01   
  4.5272220000E+01   3.4622800000E-01   
0 1 6 8.0 1.0   
  8.7468260000E+02   2.4310080000E-03   4.0176790000E-03
  2.0797850000E+02   3.2330270000E-02   3.1139660000E-02
  6.6879180000E+01   1.2425200000E-01   1.3490770000E-01
  2.4873470000E+01  -3.9039050000E-02   3.4316720000E-01
  9.9684410000E+00  -6.1717890000E-01   4.6257600000E-01
  4.0638260000E+00  -4.4730970000E-01   2.1546030000E-01
0 1 6 8.0 1.0   
  3.3643630000E+01  -2.9403580000E-03  -6.3116200000E-03
  1.0875650000E+01   7.1631030000E-02  -2.6976380000E-02
  4.6282250000E+00   2.5289150000E-01   5.3168470000E-02
  1.9501260000E+00  -2.9664010000E-01   3.8455490000E-01
  8.0945200000E-01  -7.4322150000E-01   5.1276620000E-01
  3.2047400000E-01  -1.8535200000E-01   1.8111350000E-01
0 1 3 2.0 1.0   
  1.2241480000E+00   6.3514650000E-02  -2.1120700000E-01
  4.8426300000E-01   3.1514040000E-01   7.7719980000E-02
  8.4096000000E-02  -1.1625950000E+00   9.8982140000E-01
0 1 1 0.0 1.0   
  3.2036000000E-02   1.0000000000E+00   1.0000000000E+00
0 3 3 2.0 1.0   
  1.3690850000E+01   8.5894180000E-02   
  3.5131540000E+00   3.7846710000E-01   
  1.0404340000E+00   7.1612390000E-01   
0 3 1 0.0 1.0   
  2.8696200000E-01   1.0000000000E+00   

23  7
0 0 6 2.0 1.00   
  4.7354330000E+04   1.7845130000E-03   
  7.1107870000E+03   1.3667540000E-02   
  1.6195910000E+03   6.7361220000E-02   
  4.5633790000E+02   2.3305520000E-01   
  1.4606060000E+02   4.8063160000E-01   
  4.9757910000E+01   3.4748020000E-01   
0 1 6 8.0 1.0   
  9.6814840000E+02   2.4105990000E-03   3.9950050000E-03
  2.3028210000E+02   3.2072430000E-02   3.1040610000E-02
  7.4145910000E+01   1.2459420000E-01   1.3477470000E-01
  2.7641070000E+01  -3.4821770000E-02   3.4372790000E-01
  1.1114750000E+01  -6.1673740000E-01   4.6287590000E-01
  4.5431130000E+00  -4.5098440000E-01   2.1355470000E-01
0 1 6 8.0 1.0   
  3.7640500000E+01  -3.2331990000E-03  -6.4940560000E-03
  1.2282380000E+01   7.1307440000E-02  -2.7534530000E-02
  5.2333660000E+00   2.5438200000E-01   5.5162840000E-02
  2.2089500000E+00  -2.9338870000E-01   3.8796720000E-01
  9.1788000000E-01  -7.4156950000E-01   5.0902580000E-01
  3.6341200000E-01  -1.9094100000E-01   1.8038400000E-01
0 1 3 2.0 1.0   
  1.3927810000E+00   6.1397030000E-02  -1.8912650000E-01
  5.4391300000E-01   3.0611300000E-01   8.0054530000E-02
  9.1476000000E-02  -1.1548900000E+00   9.8773990000E-01
0 1 1 0.0 1.0   
  3.4312000000E-02   1.0000000000E+00   1.0000000000E+00
0 3 3 3.0 1.0   
  1.6050250000E+01   8.5998990000E-02   
  4.1600630000E+00   3.8029960000E-01   
  1.2432650000E+00   7.1276590000E-01   
0 3 1 0.0 1.0   
  3.4427700000E-01   1.0000000000E+00   

24  7
0 0 6 2.0 1.00   
  5.1789810000E+04   1.7761820000E-03   
  7.7768490000E+03   1.3604760000E-02   
  1.7713850000E+03   6.7069250000E-02   
  4.9915880000E+02   2.3231040000E-01   
  1.5979820000E+02   4.8024100000E-01   
  5.4470210000E+01   3.4876530000E-01   
0 1 6 8.0 1.0   
  1.0643280000E+03   2.3996690000E-03   3.9869970000E-03
  2.5321380000E+02   3.1948860000E-02   3.1046620000E-02
  8.1609240000E+01   1.2508680000E-01   1.3505180000E-01
  3.0481930000E+01  -3.2218660000E-02   3.4488650000E-01
  1.2294390000E+01  -6.1722840000E-01   4.6285710000E-01
  5.0377220000E+00  -4.5259360000E-01   2.1104260000E-01
0 1 6 8.0 1.0   
  4.1562910000E+01  -3.4542160000E-03  -6.7224970000E-03
  1.3676270000E+01   7.2184280000E-02  -2.8064710000E-02
  5.8443900000E+00   2.5448200000E-01   5.8200280000E-02
  2.4716090000E+00  -2.9345340000E-01   3.9169880000E-01
  1.0283080000E+00  -7.3854550000E-01   5.0478230000E-01
  4.0725000000E-01  -1.9471570000E-01   1.7902900000E-01
0 1 3 2.0 1.0   
  1.5714640000E+00   5.8922190000E-02  -1.9301000000E-01
  6.0558000000E-01   2.9760550000E-01   9.6056200000E-02
  9.8561000000E-02  -1.1475060000E+00   9.8176090000E-01
0 1 1 0.0 1.0   
  3.6459000000E-02   1.0000000000E+00   1.0000000000E+00
0 3 3 4.0 1.0   
  1.8419300000E+01   8.6508160000E-02   
  4.8126610000E+00   3.8266990000E-01   
  1.4464470000E+00   7.0937720000E-01   
0 3 1 0.0 1.0   
  4.0041300000E-01   1.0000000000E+00   

25  7
0 0 6 2.0 1.00   
  5.6347140000E+04   1.7715800000E-03   
  8.4609430000E+03   1.3570810000E-02   
  1.9273250000E+03   6.6906050000E-02   
  5.4323430000E+02   2.3185410000E-01   
  1.7399050000E+02   4.7990460000E-01   
  5.9360050000E+01   3.4957370000E-01   
0 1 6 8.0 1.0   
  1.1654120000E+03   2.3887510000E-03   3.9773180000E-03
  2.7732760000E+02   3.1817080000E-02   3.1031120000E-02
  8.9472780000E+01   1.2546700000E-01   1.3518940000E-01
  3.3482560000E+01  -2.9554310000E-02   3.4573870000E-01
  1.3540370000E+01  -6.1751600000E-01   4.6292050000E-01
  5.5579720000E+00  -4.5444580000E-01   2.0905920000E-01
0 1 6 8.0 1.0   
  4.5835320000E+01  -3.6658560000E-03  -6.8875780000E-03
  1.5187770000E+01   7.2319710000E-02  -2.8468160000E-02
  6.5007100000E+00   2.5444860000E-01   6.0318320000E-02
  2.7515830000E+00  -2.9103800000E-01   3.9389610000E-01
  1.1454040000E+00  -7.3598600000E-01   5.0137690000E-01
  4.5368700000E-01  -1.9976170000E-01   1.7922640000E-01
0 1 3 2.0 1.0   
  1.7579990000E+00   5.6285720000E-02  -5.0350240000E-01
  6.6702200000E-01   2.8974910000E-01   2.3450110000E-01
  1.0512900000E-01  -1.1406530000E+00   9.1412570000E-01
0 1 1 0.0 1.0   
  3.8418000000E-02   1.0000000000E+00   1.0000000000E+00
0 3 3 5.0 1.0   
  2.0943550000E+01   8.6727020000E-02   
  5.5104860000E+00   3.8418830000E-01   
  1.6650380000E+00   7.0690710000E-01   
0 3 1 0.0 1.0   
  4.6173300000E-01   1.0000000000E+00   

26  7
0 0 6 2.0 1.00   
  6.1132620000E+04   1.7661110000E-03   
  9.1793420000E+03   1.3530380000E-02   
  2.0908570000E+03   6.6731280000E-02   
  5.8924790000E+02   2.3148230000E-01   
  1.8875430000E+02   4.7970580000E-01   
  6.4446290000E+01   3.5019760000E-01   
0 1 6 8.0 1.0   
  1.2599800000E+03   2.4380140000E-03   4.0280190000E-03
  2.9987610000E+02   3.2240480000E-02   3.1446470000E-02
  9.6849170000E+01   1.2657240000E-01   1.3683170000E-01
  3.6310200000E+01  -3.1399020000E-02   3.4872360000E-01
  1.4729960000E+01  -6.2075930000E-01   4.6179310000E-01
  6.0660750000E+00  -4.5029140000E-01   2.0430580000E-01
0 1 6 8.0 1.0   
  5.0434850000E+01  -3.8732560000E-03  -7.0171280000E-03
  1.6839290000E+01   7.1965980000E-02  -2.8776600000E-02
  7.1920860000E+00   2.5565910000E-01   6.1813830000E-02
  3.0534200000E+00  -2.8828370000E-01   3.9549460000E-01
  1.2736430000E+00  -7.3428220000E-01   4.9890590000E-01
  5.0409100000E-01  -2.0493530000E-01   1.7912510000E-01
0 1 3 2.0 1.0   
  1.9503160000E+00   5.6948690000E-02  -4.5937960000E-01
  7.3672100000E-01   2.8829150000E-01   2.8521390000E-01
  1.1417700000E-01  -1.1381590000E+00   9.0764850000E-01
0 1 1 0.0 1.0   
  4.1148000000E-02   1.0000000000E+00   1.0000000000E+00
0 3 3 6.0 1.0   
  2.3149940000E+01   8.8769350000E-02   
  6.1223680000E+00   3.8963190000E-01   
  1.8466010000E+00   7.0148160000E-01   
0 3 1 0.0 1.0   
  5.0436100000E-01   1.0000000000E+00   

27  7
0 0 6 2.0 1.00   
  6.6148990000E+04   1.7597870000E-03   
  9.9330770000E+03   1.3481620000E-02   
  2.2628160000E+03   6.6493420000E-02   
  6.3791540000E+02   2.3079390000E-01   
  2.0441220000E+02   4.7929190000E-01   
  6.9825380000E+01   3.5140970000E-01   
0 1 6 8.0 1.0   
  1.3788410000E+03   2.3762760000E-03   3.9714880000E-03
  3.2826940000E+02   3.1674500000E-02   3.1081740000E-02
  1.0609460000E+02   1.2628880000E-01   1.3574390000E-01
  3.9832750000E+01  -2.5845520000E-02   3.4768270000E-01
  1.6186220000E+01  -6.1834910000E-01   4.6263400000E-01
  6.6677880000E+00  -4.5670080000E-01   2.0516320000E-01
0 1 6 8.0 1.0   
  5.4523550000E+01  -3.9930040000E-03  -7.2907720000E-03
  1.8297830000E+01   7.4096630000E-02  -2.9260270000E-02
  7.8673480000E+00   2.5420000000E-01   6.5641500000E-02
  3.3405340000E+00  -2.9216570000E-01   4.0006520000E-01
  1.3937560000E+00  -7.3187030000E-01   4.9502360000E-01
  5.5132600000E-01  -2.0407840000E-01   1.7582400000E-01
0 1 3 2.0 1.0   
  2.1519470000E+00   5.3798430000E-02  -2.1654960000E-01
  8.1106300000E-01   2.7599710000E-01   1.2404880000E-01
  1.2101700000E-01  -1.1296920000E+00   9.7240640000E-01
0 1 1 0.0 1.0   
  4.3037000000E-02   1.0000000000E+00   1.0000000000E+00
0 3 3 7.0 1.0   
  2.5593060000E+01   9.0047480000E-02   
  6.8009900000E+00   3.9317030000E-01   
  2.0516470000E+00   6.9768440000E-01   
0 3 1 0.0 1.0   
  5.5567100000E-01   1.0000000000E+00   

28  7
0 0 6 2.0 1.00   
  7.1396350000E+04   1.7530030000E-03   
  1.0720840000E+04   1.3431220000E-02   
  2.4421290000E+03   6.6270410000E-02   
  6.8842650000E+02   2.3025080000E-01   
  2.2061530000E+02   4.7901860000E-01   
  7.5393730000E+01   3.5234440000E-01   
0 1 6 8.0 1.0   
  1.4925320000E+03   2.3707140000E-03   3.9675540000E-03
  3.5540130000E+02   3.1605660000E-02   3.1094790000E-02
  1.1495340000E+02   1.2663350000E-01   1.3595170000E-01
  4.3220430000E+01  -2.4170370000E-02   3.4851360000E-01
  1.7597100000E+01  -6.1877750000E-01   4.6254980000E-01
  7.2577650000E+00  -4.5767700000E-01   2.0351860000E-01
0 1 6 8.0 1.0   
  5.9352610000E+01  -4.1620020000E-03  -7.4214520000E-03
  2.0021810000E+01   7.4251110000E-02  -2.9534100000E-02
  8.6145610000E+00   2.5413600000E-01   6.7318520000E-02
  3.6605310000E+00  -2.9034770000E-01   4.0166600000E-01
  1.5281110000E+00  -7.3021210000E-01   4.9266230000E-01
  6.0405700000E-01  -2.0760570000E-01   1.7568930000E-01
0 1 3 2.0 1.0   
  2.3792760000E+00   5.1578880000E-02  -1.8876630000E-01
  8.8583900000E-01   2.7076110000E-01   1.0151990000E-01
  1.2852900000E-01  -1.1247700000E+00   9.7909060000E-01
0 1 1 0.0 1.0   
  4.5195000000E-02   1.0000000000E+00   1.0000000000E+00
0 3 3 8.0 1.0   
  2.8191470000E+01   9.0988810000E-02   
  7.5235840000E+00   3.9582080000E-01   
  2.2712280000E+00   6.9471540000E-01   
0 3 1 0.0 1.0   
  6.1160300000E-01   1.0000000000E+00   

29  7
0 0 6 2.0 1.00   
  7.6794380000E+04   1.7481610000E-03   
  1.1530700000E+04   1.3396020000E-02   
  2.6265750000E+03   6.6108850000E-02   
  7.4049030000E+02   2.2982650000E-01   
  2.3735280000E+02   4.7876750000E-01   
  8.1158180000E+01   3.5307390000E-01   
0 1 6 8.0 1.0   
  1.6108140000E+03   2.3640550000E-03   3.9633070000E-03
  3.8363670000E+02   3.1536350000E-02   3.1102230000E-02
  1.2417330000E+02   1.2694520000E-01   1.3613500000E-01
  4.6746780000E+01  -2.2628400000E-02   3.4929140000E-01
  1.9065690000E+01  -6.1920800000E-01   4.6247800000E-01
  7.8715670000E+00  -4.5853930000E-01   2.0201020000E-01
0 1 6 8.0 1.0   
  6.4457320000E+01  -4.3310750000E-03  -7.5237250000E-03
  2.1852120000E+01   7.4123070000E-02  -2.9756870000E-02
  9.4053430000E+00   2.5421080000E-01   6.8496540000E-02
  3.9991680000E+00  -2.8748430000E-01   4.0271410000E-01
  1.6702970000E+00  -7.2914360000E-01   4.9084900000E-01
  6.5962700000E-01  -2.1139510000E-01   1.7592680000E-01
0 1 3 2.0 1.0   
  2.6000880000E+00   5.0275770000E-02  -1.7029110000E-01
  9.6309400000E-01   2.6500400000E-01   9.3101330000E-02
  1.3616100000E-01  -1.1201550000E+00   9.8143360000E-01
0 1 1 0.0 1.0   
  4.7332000000E-02   1.0000000000E+00   1.0000000000E+00
0 3 3 9.0 1.0   
  3.0853410000E+01   9.1999050000E-02   
  8.2649850000E+00   3.9850210000E-01   
  2.4953320000E+00   6.9178970000E-01   
0 3 1 0.0 1.0   
  6.6765800000E-01   1.0000000000E+00   

30  7
0 0 6 2.0 1.00   
  8.2400940000E+04   1.7433290000E-03   
  1.2372550000E+04   1.3359660000E-02   
  2.8183510000E+03   6.5943650000E-02   
  7.9457170000E+02   2.2941510000E-01   
  2.5472320000E+02   4.7854530000E-01   
  8.7138800000E+01   3.5377530000E-01   
0 1 6 8.0 1.0   
  1.7325690000E+03   2.3614590000E-03   3.9631250000E-03
  4.1271490000E+02   3.1501770000E-02   3.1134110000E-02
  1.3367800000E+02   1.2727740000E-01   1.3639310000E-01
  5.0385850000E+01  -2.1459280000E-02   3.5012660000E-01
  2.0583580000E+01  -6.1976520000E-01   4.6231790000E-01
  8.5059400000E+00  -4.5901800000E-01   2.0049950000E-01
0 1 6 8.0 1.0   
  6.9364920000E+01  -4.4400980000E-03  -7.6892620000E-03
  2.3620820000E+01   7.5052530000E-02  -2.9979820000E-02
  1.0184710000E+01   2.5331110000E-01   7.0824110000E-02
  4.3340820000E+00  -2.8818970000E-01   4.0461410000E-01
  1.8109180000E+00  -7.2670520000E-01   4.8823250000E-01
  7.1484100000E-01  -2.1334390000E-01   1.7519700000E-01
0 1 3 2.0 1.0   
  2.8238420000E+00   4.8985430000E-02  -1.5867630000E-01
  1.0395430000E+00   2.5927930000E-01   8.3793270000E-02
  1.4326400000E-01  -1.1157110000E+00   9.8405470000E-01
0 1 1 0.0 1.0   
  4.9296000000E-02   1.0000000000E+00   1.0000000000E+00
0 3 3 10.0 1.0   
  3.3707640000E+01   9.2626480000E-02   
  9.0611060000E+00   4.0029800000E-01   
  2.7383830000E+00   6.8966080000E-01   
0 3 1 0.0 1.0   
  7.3029400000E-01   1.0000000000E+00   


The 6-31G(d,p) Gaussian-Type Basis Sets

In order and in CRYSTAL format below:

1  3      
0 0 3 1.0 1.0
  1.8731136960E+01   3.3494604340E-02    
  2.8253943650E+00   2.3472695350E-01    
  6.4012169230E-01   8.1375732620E-01    
0 0 1 0.0 1.0
  1.6127775880E-01   1.0000000000E+00    
0 2 1 0.0 1.0
  1.1000000000E+00   1.0000000000E+00    

2  3    
0 0 3 2.0 1.0
  3.8421634000E+01   2.3766000000E-02
  5.7780300000E+00   1.5467900000E-01
  1.2417740000E+00   4.6963000000E-01
0 0 1 0.0 1.0
  2.9796400000E-01   1.0000000000E+00
0 2 1 0.0 1.0
  1.1000000000E+00   1.0000000000E+00
  
3  4      
0 0 6 2.0 1.0
  6.4241892000E+02   2.1426000000E-03
  9.6798515000E+01   1.6208900000E-02
  2.2091121000E+01   7.7315600000E-02
  6.2010703000E+00   2.4578600000E-01
  1.9351177000E+00   4.7018900000E-01
  6.3673580000E-01   3.4547080000E-01
0 1 3 1.0 1.0
  2.3249184000E+00  -3.5091700000E-02   8.9415000000E-03
  6.3243060000E-01  -1.9123280000E-01   1.4100950000E-01
  7.9053400000E-02   1.0839878000E+00   9.4536370000E-01
0 1 1 0.0 1.0
  3.5962000000E-02   1.0000000000E+00   1.0000000000E+00
0 3 1 0.0 1.0
  2.0000000000E-01   1.0000000000E+00

4  4      
0 0 6 2.0 1.0
  1.2645857000E+03   1.9448000000E-03
  1.8993681000E+02   1.4835100000E-02
  4.3159089000E+01   7.2090600000E-02
  1.2098663000E+01   2.3715420000E-01
  3.8063232000E+00   4.6919870000E-01
  1.2728903000E+00   3.5652020000E-01
0 1 3 2.0 1.0
  3.1964631000E+00  -1.1264870000E-01   5.5980200000E-02
  7.4781330000E-01  -2.2950640000E-01   2.6155060000E-01
  2.1996630000E-01   1.1869167000E+00   7.9397230000E-01
0 1 1 0.0 1.0
  8.2309900000E-02   1.0000000000E+00   1.0000000000E+00
0 3 1 0.0 1.0
  4.0000000000E-01   1.0000000000E+00

5  4      
0 0 6 2.0 1.0
  2.0688823000E+03   1.8663000000E-03
  3.1064957000E+02   1.4251500000E-02
  7.0683033000E+01   6.9551600000E-02
  1.9861080000E+01   2.3257290000E-01
  6.2993048000E+00   4.6707870000E-01
  2.1270270000E+00   3.6343140000E-01
0 1 3 3.0 1.0
  4.7279710000E+00  -1.3039380000E-01   7.4597600000E-02
  1.1903377000E+00  -1.3078890000E-01   3.0784670000E-01
  3.5941170000E-01   1.1309444000E+00   7.4345680000E-01
0 1 1 0.0 1.0
  1.2675120000E-01   1.0000000000E+00   1.0000000000E+00
0 3 1 0.0 1.0
  6.0000000000E-01   1.0000000000E+00

6  4      
0 0 6 2.0 1.0
  3.0475248800E+03   1.8347371300E-03    
  4.5736951800E+02   1.4037322800E-02    
  1.0394868500E+02   6.8842622200E-02    
  2.9210155300E+01   2.3218444300E-01    
  9.2866629600E+00   4.6794134800E-01    
  3.1639269600E+00   3.6231198500E-01    
0 1 3 4.0 1.0
  7.8682723500E+00  -1.1933242000E-01   6.8999066600E-02  
  1.8812885400E+00  -1.6085415200E-01   3.1642396100E-01  
  5.4424925800E-01   1.1434564400E+00   7.4430829100E-01  
0 1 1 0.0 1.0
  1.6871447820E-01   1.0000000000E+00   1.0000000000E+00  
0 3 1 0.0 1.0
  8.0000000000E-01   1.0000000000E+00    

7  4      
0 0 6 2.0 1.0
  4.1735110000E+03   1.8348000000E-03    
  6.2745790000E+02   1.3995000000E-02    
  1.4290210000E+02   6.8587000000E-02    
  4.0234330000E+01   2.3224100000E-01    
  1.2820210000E+01   4.6907000000E-01    
  4.3904370000E+00   3.6045500000E-01    
0 1 3 5.0 1.0
  1.1626358000E+01  -1.1496100000E-01   6.7580000000E-02  
  2.7162800000E+00  -1.6911800000E-01   3.2390700000E-01  
  7.7221800000E-01   1.1458520000E+00   7.4089500000E-01  
0 1 1 0.0 1.0
  2.1203130000E-01   1.0000000000E+00   1.0000000000E+00  
0 3 1 0.0 1.0
  8.0000000000E-01   1.0000000000E+00    

8  4      
0 0 6 2.0 1.0
  5.4846717000E+03   1.8311000000E-03    
  8.2523495000E+02   1.3950100000E-02    
  1.8804696000E+02   6.8445100000E-02    
  5.2964500000E+01   2.3271430000E-01    
  1.6897570000E+01   4.7019300000E-01    
  5.7996353000E+00   3.5852090000E-01    
0 1 3 6.0 1.0
  1.5539616000E+01  -1.1077750000E-01   7.0874300000E-02  
  3.5999336000E+00  -1.4802630000E-01   3.3975280000E-01  
  1.0137618000E+00   1.1307670000E+00   7.2715860000E-01  
0 1 1 0.0 1.0
  2.7000580000E-01   1.0000000000E+00   1.0000000000E+00  
0 3 1 0.0 1.0
  8.0000000000E-01   1.0000000000E+00    

9  4      
0 0 6 2.0 1.0
  7.0017130900E+03   1.8196169000E-03
  1.0513660900E+03   1.3916079600E-02
  2.3928569000E+02   6.8405324500E-02
  6.7397445300E+01   2.3318576000E-01
  2.1519957300E+01   4.7126743900E-01
  7.4031013000E+00   3.5661854600E-01
0 1 3 7.0 1.0
  2.0847952800E+01  -1.0850697500E-01   7.1628724300E-02
  4.8083083400E+00  -1.4645165800E-01   3.4591210300E-01
  1.3440698600E+00   1.1286885800E+00   7.2246995700E-01
0 1 1 0.0 1.0
  3.5815139300E-01   1.0000000000E+00   1.0000000000E+00
0 3 1 0.0 1.0
  8.0000000000E-01   1.0000000000E+00

10  4    
0 0 6 2.0 1.0
  8.4258515300E+03   1.8843481000E-03
  1.2685194000E+03   1.4336899400E-02
  2.8962141400E+02   7.0109623300E-02
  8.1859004000E+01   2.3737326600E-01
  2.6251507900E+01   4.7300712600E-01
  9.0947205100E+00   3.4840124100E-01
0 1 3 8.0 1.0
  2.6532131000E+01  -1.0711828700E-01   7.1909588500E-02
  6.1017550100E+00  -1.4616382100E-01   3.4951337200E-01
  1.6962715300E+00   1.1277735000E+00   7.1994051200E-01
0 1 1 0.0 1.0
  4.4581870000E-01   1.0000000000E+00   1.0000000000E+00
0 3 1 0.0 1.0
  8.0000000000E-01   1.0000000000E+00

11  5
0 0 6 2.0 1.0
  9.9932000000E+03   1.9377000000E-03
  1.4998900000E+03   1.4807000000E-02
  3.4195100000E+02   7.2706000000E-02
  9.4679700000E+01   2.5262900000E-01
  2.9734500000E+01   4.9324200000E-01
  1.0006300000E+01   3.1316900000E-01
0 1 6 8.0 1.0
  1.5096300000E+02  -3.5421000000E-03   5.0017000000E-03      
  3.5587800000E+01  -4.3959000000E-02   3.5511000000E-02      
  1.1168300000E+01  -1.0975210000E-01   1.4282500000E-01      
  3.9020100000E+00   1.8739800000E-01   3.3862000000E-01      
  1.3817700000E+00   6.4669900000E-01   4.5157900000E-01      
  4.6638200000E-01   3.0605800000E-01   2.7327100000E-01      
0 1 3 1.0 1.0
  4.9796600000E-01  -2.4850300000E-01  -2.3023000000E-02      
  8.4353000000E-02  -1.3170400000E-01   9.5035900000E-01      
  6.6635000000E-02   1.2335200000E+00   5.9858000000E-02      
0 1 1 0.0 1.0
  2.5954400000E-02   1.0000000000E+00   1.0000000000E+00      
0 3 1 0.0 1.0
  1.7500000000E-01   1.0000000000E+00         

12  5 
0 0 6 2.0 1.0
  1.1722800000E+04   1.9778000000E-03         
  1.7599300000E+03   1.5114000000E-02         
  4.0084600000E+02   7.3911000000E-02         
  1.1280700000E+02   2.4919100000E-01         
  3.5999700000E+01   4.8792800000E-01         
  1.2182800000E+01   3.1966200000E-01         
0 1 6 8.0 1.0
  1.8918000000E+02  -3.2372000000E-03   4.9281000000E-03      
  4.5211900000E+01  -4.1008000000E-02   3.4989000000E-02      
  1.4356300000E+01  -1.1260000000E-01   1.4072500000E-01      
  5.1388600000E+00   1.4863300000E-01   3.3364200000E-01      
  1.9065200000E+00   6.1649700000E-01   4.4494000000E-01      
  7.0588700000E-01   3.6482900000E-01   2.6925400000E-01      
0 1 3 2.0 1.0
  9.2934000000E-01  -2.1229000000E-01  -2.2419000000E-02      
  2.6903500000E-01  -1.0798500000E-01   1.9227000000E-01      
  1.1737900000E-01   1.1758400000E+00   8.4618100000E-01      
0 1 1 0.0 1.0
  4.2106100000E-02   1.0000000000E+00   1.0000000000E+00      
0 3 1 0.0 1.0
  1.7500000000E-01   1.0000000000E+00         
  
13  5
0 0 6 2.0 1.0
  1.3983100000E+04   1.9426700000E-03         
  2.0987500000E+03   1.4859900000E-02         
  4.7770500000E+02   7.2849400000E-02         
  1.3436000000E+02   2.4683000000E-01         
  4.2870900000E+01   4.8725800000E-01         
  1.4518900000E+01   3.2349600000E-01         
0 1 6 8.0 1.0
  2.3966800000E+02  -2.9261900000E-03   4.6028500000E-03      
  5.7441900000E+01  -3.7408000000E-02   3.3199000000E-02      
  1.8285900000E+01  -1.1448700000E-01   1.3628200000E-01      
  6.5991400000E+00   1.1563500000E-01   3.3047600000E-01      
  2.4904900000E+00   6.1259500000E-01   4.4914600000E-01      
  9.4454000000E-01   3.9379900000E-01   2.6570400000E-01      
0 1 3 3.0 1.0
  1.2779000000E+00  -2.2760600000E-01  -1.7513000000E-02      
  3.9759000000E-01   1.4458300000E-03   2.4453300000E-01      
  1.6009500000E-01   1.0927900000E+00   8.0493400000E-01      
0 1 1 0.0 1.0
  5.5657700000E-02   1.0000000000E+00   1.0000000000E+00      
0 3 1 0.0 1.0
  3.2500000000E-01   1.0000000000E+00         
  
14  5
0 0 6 2.0 1.0
  1.6115900000E+04   1.9594800000E-03         
  2.4255800000E+03   1.4928800000E-02         
  5.5386700000E+02   7.2847800000E-02         
  1.5634000000E+02   2.4613000000E-01         
  5.0068300000E+01   4.8591400000E-01         
  1.7017800000E+01   3.2500200000E-01         
0 1 6 8.0 1.0
  2.9271800000E+02  -2.7809400000E-03   4.4382600000E-03      
  6.9873100000E+01  -3.5714600000E-02   3.2667900000E-02      
  2.2336300000E+01  -1.1498500000E-01   1.3472100000E-01      
  8.1503900000E+00   9.3563400000E-02   3.2867800000E-01      
  3.1345800000E+00   6.0301700000E-01   4.4964000000E-01      
  1.2254300000E+00   4.1895900000E-01   2.6137200000E-01      
0 1 3 4.0 1.0
  1.7273800000E+00  -2.4463000000E-01  -1.7795100000E-02      
  5.7292200000E-01   4.3157200000E-03   2.5353900000E-01      
  2.2219200000E-01   1.0981800000E+00   8.0066900000E-01      
0 1 1 0.0 1.0
  7.7836900000E-02   1.0000000000E+00   1.0000000000E+00      
0 3 1 0.0 1.0
  4.5000000000E-01   1.0000000000E+00         

15  5
0 0 6 2.0 1.0
  1.9413300000E+04   1.8516000000E-03         
  2.9094200000E+03   1.4206200000E-02         
  6.6136400000E+02   6.9999500000E-02         
  1.8575900000E+02   2.4007900000E-01         
  5.9194300000E+01   4.8476200000E-01         
  2.0031000000E+01   3.3520000000E-01         
0 1 6 8.0 1.0
  3.3947800000E+02  -2.7821700000E-03   4.5646200000E-03      
  8.1010100000E+01  -3.6049900000E-02   3.3693600000E-02      
  2.5878000000E+01  -1.1663100000E-01   1.3975500000E-01      
  9.4522100000E+00   9.6832800000E-02   3.3936200000E-01      
  3.6656600000E+00   6.1441800000E-01   4.5092100000E-01      
  1.4674600000E+00   4.0379800000E-01   2.3858600000E-01      
0 1 3 5.0 1.0
  2.1562300000E+00  -2.5292300000E-01  -1.7765300000E-02      
  7.4899700000E-01   3.2851700000E-02   2.7405800000E-01      
  2.8314500000E-01   1.0812500000E+00   7.8542100000E-01      
0 1 1 0.0 1.0
  9.9831700000E-02   1.0000000000E+00   1.0000000000E+00      
0 3 1 0.0 1.0
  5.5000000000E-01   1.0000000000E+00         
  
16  5
0 0 6 2.0 1.0
  2.1917100000E+04   1.8690000000E-03         
  3.3014900000E+03   1.4230000000E-02         
  7.5414600000E+02   6.9696000000E-02         
  2.1271100000E+02   2.3848700000E-01         
  6.7989600000E+01   4.8330700000E-01         
  2.3051500000E+01   3.3807400000E-01         
0 1 6 8.0 1.0
  4.2373500000E+02  -2.3767000000E-03   4.0610000000E-03      
  1.0071000000E+02  -3.1693000000E-02   3.0681000000E-02      
  3.2159900000E+01  -1.1331700000E-01   1.3045200000E-01      
  1.1807900000E+01   5.6090000000E-02   3.2720500000E-01      
  4.6311000000E+00   5.9225500000E-01   4.5285100000E-01      
  1.8702500000E+00   4.5500600000E-01   2.5604200000E-01      
0 1 3 6.0 1.0
  2.6158400000E+00  -2.5037400000E-01  -1.4511000000E-02      
  9.2216700000E-01   6.6957000000E-02   3.1026300000E-01      
  3.4128700000E-01   1.0545100000E+00   7.5448300000E-01      
0 1 1 0.0 1.0
  1.1716700000E-01   1.0000000000E+00   1.0000000000E+00      
0 3 1 0.0 1.0
  6.5000000000E-01   1.0000000000E+00         

17  5
0 0 6 2.0 1.0
  2.5180100000E+04   1.8330000000E-03         
  3.7803500000E+03   1.4034000000E-02         
  8.6047400000E+02   6.9097000000E-02         
  2.4214500000E+02   2.3745200000E-01         
  7.7334900000E+01   4.8303400000E-01         
  2.6247000000E+01   3.3985600000E-01         
0 1 6 8.0 1.0
  4.9176500000E+02  -2.2974000000E-03   3.9894000000E-03      
  1.1698400000E+02  -3.0714000000E-02   3.0318000000E-02      
  3.7415300000E+01  -1.1252800000E-01   1.2988000000E-01      
  1.3783400000E+01   4.5016000000E-02   3.2795100000E-01      
  5.4521500000E+00   5.8935300000E-01   4.5352700000E-01      
  2.2258800000E+00   4.6520600000E-01   2.5215400000E-01      
0 1 3 7.0 1.0
  3.1864900000E+00  -2.5183000000E-01  -1.4299000000E-02      
  1.1442700000E+00   6.1589000000E-02   3.2357200000E-01      
  4.2037700000E-01   1.0601800000E+00   7.4350700000E-01      
0 1 1 0.0 1.0
  1.4265700000E-01   1.0000000000E+00   1.0000000000E+00      
0 3 1 0.0 1.0
  7.5000000000E-01   1.0000000000E+00         
  
18  5
0 0 6 2.0 1.0
  2.8348300000E+04   1.8252600000E-03         
  4.2576200000E+03   1.3968600000E-02         
  9.6985700000E+02   6.8707300000E-02         
  2.7326300000E+02   2.3620400000E-01         
  8.7369500000E+01   4.8221400000E-01         
  2.9686700000E+01   3.4204300000E-01         
0 1 6 8.0 1.0
  5.7589100000E+02  -2.1597200000E-03   3.8066500000E-03      
  1.3681600000E+02  -2.9077500000E-02   2.9230500000E-02      
  4.3809800000E+01  -1.1082700000E-01   1.2646700000E-01      
  1.6209400000E+01   2.7699900000E-02   3.2351000000E-01      
  6.4608400000E+00   5.7761300000E-01   4.5489600000E-01      
  2.6511400000E+00   4.8868800000E-01   2.5663000000E-01      
0 1 3 8.0 1.0
  3.8602800000E+00  -2.5559200000E-01  -1.5919700000E-02      
  1.4137300000E+00   3.7806600000E-02   3.2464600000E-01      
  5.1664600000E-01   1.0805600000E+00   7.4399000000E-01      
0 1 1 0.0 1.0
  1.7388800000E-01   1.0000000000E+00   1.0000000000E+00      
0 3 1 0.0 1.0
  8.5000000000E-01   1.0000000000E+00         

19  6
0 0 6 2.0 1.0
  3.1594420000E+04   1.8280100000E-03         
  4.7443300000E+03   1.3994030000E-02         
  1.0804190000E+03   6.8871290000E-02         
  3.0423380000E+02   2.3697600000E-01         
  9.7245860000E+01   4.8290400000E-01         
  3.3024950000E+01   3.4047950000E-01         
0 1 6 8.0 1.0
  6.2276250000E+02  -2.5029760000E-03   4.0946370000E-03      
  1.4788390000E+02  -3.3155500000E-02   3.1451990000E-02      
  4.7327350000E+01  -1.2263870000E-01   1.3515580000E-01      
  1.7514950000E+01   5.3536430000E-02   3.3905000000E-01      
  6.9227220000E+00   6.1938600000E-01   4.6294550000E-01      
  2.7682770000E+00   4.3458780000E-01   2.2426380000E-01      
0 1 6 8.0 1.0
  1.1848020000E+01   1.2776890000E-02  -1.2213770000E-02      
  4.0792110000E+00   2.0987670000E-01  -6.9005370000E-03      
  1.7634810000E+00  -3.0952740000E-03   2.0074660000E-01      
  7.8892700000E-01  -5.5938840000E-01   4.2813320000E-01      
  3.5038700000E-01  -5.1347600000E-01   3.9701560000E-01      
  1.4634400000E-01  -6.5980350000E-02   1.1047180000E-01      
0 1 3 1.0 1.0
  7.1680100000E-01  -5.2377720000E-02   3.1643000000E-02      
  2.3374100000E-01  -2.7985030000E-01  -4.0461600000E-02      
  3.8675000000E-02   1.1415470000E+00   1.0120290000E+00      
0 1 1 0.0 1.0
  1.6521000000E-02   1.0000000000E+00   1.0000000000E+00      
0 3 1 0.0 1.0
  2.0000000000E-01   1.0000000000E+00         
  
20  6
0 0 6 2.0 1.0
  3.5264860000E+04   1.8135010000E-03         
  5.2955030000E+03   1.3884930000E-02         
  1.2060200000E+03   6.8361620000E-02         
  3.3968390000E+02   2.3561880000E-01         
  1.0862640000E+02   4.8206390000E-01         
  3.6921030000E+01   3.4298190000E-01         
0 1 6 8.0 1.0
  7.0630960000E+02   2.4482250000E-03   4.0203710000E-03      
  1.6781870000E+02   3.2415040000E-02   3.1006010000E-02      
  5.3825580000E+01   1.2262190000E-01   1.3372790000E-01      
  2.0016380000E+01  -4.3169650000E-02   3.3679830000E-01      
  7.9702790000E+00  -6.1269950000E-01   4.6312810000E-01      
  3.2120590000E+00  -4.4875400000E-01   2.2575320000E-01      
0 1 6 8.0 1.0
  1.4195180000E+01   1.0845000000E-02  -1.2896210000E-02      
  4.8808280000E+00   2.0883330000E-01  -1.0251980000E-02      
  2.1603900000E+00   3.1503380000E-02   1.9597810000E-01      
  9.8789900000E-01  -5.5265180000E-01   4.3579330000E-01      
  4.4951700000E-01  -5.4379970000E-01   3.9964520000E-01      
  1.8738700000E-01  -6.6693420000E-02   9.7136360000E-02      
0 1 3 1.0 1.0
  1.0322710000E+00  -4.4397200000E-02  -4.2986210000E-01      
  3.8117100000E-01  -3.2845630000E-01   6.9358290000E-03      
  6.5131000000E-02   1.1630100000E+00   9.7059330000E-01      
0 1 1 0.0 1.0
  2.6010000000E-02   1.0000000000E+00   1.0000000000E+00      
0 3 1 0.0 1.0
  2.0000000000E-01   1.0000000000E+00         

21  8
0 0 6 2.0 1.00
  3.9088980000E+04   1.8032630000E-03   
  5.8697920000E+03   1.3807690000E-02   
  1.3369100000E+03   6.8003960000E-02   
  3.7660310000E+02   2.3470990000E-01   
  1.2046790000E+02   4.8156900000E-01   
  4.0980320000E+01   3.4456520000E-01   
0 1 6 8.0 1.0
  7.8628520000E+02   2.4518630000E-03   4.0395300000E-03
  1.8688700000E+02   3.2595790000E-02   3.1225700000E-02
  6.0009350000E+01   1.2382420000E-01   1.3498330000E-01
  2.2258830000E+01  -4.3598900000E-02   3.4247930000E-01
  8.8851490000E+00  -6.1771810000E-01   4.6231130000E-01
  3.6092110000E+00  -4.4328230000E-01   2.1775240000E-01
0 1 6 8.0 1.0
  2.9843550000E+01  -2.5863020000E-03  -6.0966520000E-03
  9.5423830000E+00   7.1884240000E-02  -2.6288840000E-02
  4.0567900000E+00   2.5032600000E-01   5.0910010000E-02
  1.7047030000E+00  -2.9910030000E-01   3.7980970000E-01
  7.0623400000E-01  -7.4468180000E-01   5.1708830000E-01
  2.7953600000E-01  -1.7997760000E-01   1.8297720000E-01
0 1 3 2.0 1.0
  1.0656090000E+00   6.4829780000E-02  -2.9384400000E-01
  4.2593300000E-01   3.2537560000E-01   9.2353230000E-02
  7.6320000000E-02  -1.1708060000E+00   9.8479300000E-01
0 1 1 0.0 1.0
  2.9594000000E-02   1.0000000000E+00   1.0000000000E+00
0 3 3 1.0 1.0
  1.1147010000E+01   8.7476720000E-02   
  2.8210430000E+00   3.7956350000E-01   
  8.1962000000E-01   7.1803930000E-01   
0 3 1 0.0 1.0
  2.2146800000E-01   1.0000000000E+00   
0 4 1 0.0 1.0
  8.0000000000E-01   1.0000000000E+00   

22  8  
0 0 6 2.0 1.00
  4.3152950000E+04   1.7918720000E-03   
  6.4795710000E+03   1.3723920000E-02   
  1.4756750000E+03   6.7628300000E-02   
  4.1569910000E+02   2.3376420000E-01   
  1.3300060000E+02   4.8106960000E-01   
  4.5272220000E+01   3.4622800000E-01   
0 1 6 8.0 1.0   
  8.7468260000E+02   2.4310080000E-03   4.0176790000E-03
  2.0797850000E+02   3.2330270000E-02   3.1139660000E-02
  6.6879180000E+01   1.2425200000E-01   1.3490770000E-01
  2.4873470000E+01  -3.9039050000E-02   3.4316720000E-01
  9.9684410000E+00  -6.1717890000E-01   4.6257600000E-01
  4.0638260000E+00  -4.4730970000E-01   2.1546030000E-01
0 1 6 8.0 1.0   
  3.3643630000E+01  -2.9403580000E-03  -6.3116200000E-03
  1.0875650000E+01   7.1631030000E-02  -2.6976380000E-02
  4.6282250000E+00   2.5289150000E-01   5.3168470000E-02
  1.9501260000E+00  -2.9664010000E-01   3.8455490000E-01
  8.0945200000E-01  -7.4322150000E-01   5.1276620000E-01
  3.2047400000E-01  -1.8535200000E-01   1.8111350000E-01
0 1 3 2.0 1.0   
  1.2241480000E+00   6.3514650000E-02  -2.1120700000E-01
  4.8426300000E-01   3.1514040000E-01   7.7719980000E-02
  8.4096000000E-02  -1.1625950000E+00   9.8982140000E-01
0 1 1 0.0 1.0   
  3.2036000000E-02   1.0000000000E+00   1.0000000000E+00
0 3 3 2.0 1.0   
  1.3690850000E+01   8.5894180000E-02   
  3.5131540000E+00   3.7846710000E-01   
  1.0404340000E+00   7.1612390000E-01   
0 3 1 0.0 1.0   
  2.8696200000E-01   1.0000000000E+00   
0 4 1 0.0 1.0   
  8.0000000000E-01   1.0000000000E+00   

23  8
0 0 6 2.0 1.00   
  4.7354330000E+04   1.7845130000E-03   
  7.1107870000E+03   1.3667540000E-02   
  1.6195910000E+03   6.7361220000E-02   
  4.5633790000E+02   2.3305520000E-01   
  1.4606060000E+02   4.8063160000E-01   
  4.9757910000E+01   3.4748020000E-01   
0 1 6 8.0 1.0   
  9.6814840000E+02   2.4105990000E-03   3.9950050000E-03
  2.3028210000E+02   3.2072430000E-02   3.1040610000E-02
  7.4145910000E+01   1.2459420000E-01   1.3477470000E-01
  2.7641070000E+01  -3.4821770000E-02   3.4372790000E-01
  1.1114750000E+01  -6.1673740000E-01   4.6287590000E-01
  4.5431130000E+00  -4.5098440000E-01   2.1355470000E-01
0 1 6 8.0 1.0   
  3.7640500000E+01  -3.2331990000E-03  -6.4940560000E-03
  1.2282380000E+01   7.1307440000E-02  -2.7534530000E-02
  5.2333660000E+00   2.5438200000E-01   5.5162840000E-02
  2.2089500000E+00  -2.9338870000E-01   3.8796720000E-01
  9.1788000000E-01  -7.4156950000E-01   5.0902580000E-01
  3.6341200000E-01  -1.9094100000E-01   1.8038400000E-01
0 1 3 2.0 1.0   
  1.3927810000E+00   6.1397030000E-02  -1.8912650000E-01
  5.4391300000E-01   3.0611300000E-01   8.0054530000E-02
  9.1476000000E-02  -1.1548900000E+00   9.8773990000E-01
0 1 1 0.0 1.0   
  3.4312000000E-02   1.0000000000E+00   1.0000000000E+00
0 3 3 3.0 1.0   
  1.6050250000E+01   8.5998990000E-02   
  4.1600630000E+00   3.8029960000E-01   
  1.2432650000E+00   7.1276590000E-01   
0 3 1 0.0 1.0   
  3.4427700000E-01   1.0000000000E+00   
0 4 1 0.0 1.0   
  8.0000000000E-01   1.0000000000E+00   

24  8
0 0 6 2.0 1.00   
  5.1789810000E+04   1.7761820000E-03   
  7.7768490000E+03   1.3604760000E-02   
  1.7713850000E+03   6.7069250000E-02   
  4.9915880000E+02   2.3231040000E-01   
  1.5979820000E+02   4.8024100000E-01   
  5.4470210000E+01   3.4876530000E-01   
0 1 6 8.0 1.0   
  1.0643280000E+03   2.3996690000E-03   3.9869970000E-03
  2.5321380000E+02   3.1948860000E-02   3.1046620000E-02
  8.1609240000E+01   1.2508680000E-01   1.3505180000E-01
  3.0481930000E+01  -3.2218660000E-02   3.4488650000E-01
  1.2294390000E+01  -6.1722840000E-01   4.6285710000E-01
  5.0377220000E+00  -4.5259360000E-01   2.1104260000E-01
0 1 6 8.0 1.0   
  4.1562910000E+01  -3.4542160000E-03  -6.7224970000E-03
  1.3676270000E+01   7.2184280000E-02  -2.8064710000E-02
  5.8443900000E+00   2.5448200000E-01   5.8200280000E-02
  2.4716090000E+00  -2.9345340000E-01   3.9169880000E-01
  1.0283080000E+00  -7.3854550000E-01   5.0478230000E-01
  4.0725000000E-01  -1.9471570000E-01   1.7902900000E-01
0 1 3 2.0 1.0   
  1.5714640000E+00   5.8922190000E-02  -1.9301000000E-01
  6.0558000000E-01   2.9760550000E-01   9.6056200000E-02
  9.8561000000E-02  -1.1475060000E+00   9.8176090000E-01
0 1 1 0.0 1.0   
  3.6459000000E-02   1.0000000000E+00   1.0000000000E+00
0 3 3 4.0 1.0   
  1.8419300000E+01   8.6508160000E-02   
  4.8126610000E+00   3.8266990000E-01   
  1.4464470000E+00   7.0937720000E-01   
0 3 1 0.0 1.0   
  4.0041300000E-01   1.0000000000E+00   
0 4 1 0.0 1.0   
  8.0000000000E-01   1.0000000000E+00   

25  8
0 0 6 2.0 1.00   
  5.6347140000E+04   1.7715800000E-03   
  8.4609430000E+03   1.3570810000E-02   
  1.9273250000E+03   6.6906050000E-02   
  5.4323430000E+02   2.3185410000E-01   
  1.7399050000E+02   4.7990460000E-01   
  5.9360050000E+01   3.4957370000E-01   
0 1 6 8.0 1.0   
  1.1654120000E+03   2.3887510000E-03   3.9773180000E-03
  2.7732760000E+02   3.1817080000E-02   3.1031120000E-02
  8.9472780000E+01   1.2546700000E-01   1.3518940000E-01
  3.3482560000E+01  -2.9554310000E-02   3.4573870000E-01
  1.3540370000E+01  -6.1751600000E-01   4.6292050000E-01
  5.5579720000E+00  -4.5444580000E-01   2.0905920000E-01
0 1 6 8.0 1.0   
  4.5835320000E+01  -3.6658560000E-03  -6.8875780000E-03
  1.5187770000E+01   7.2319710000E-02  -2.8468160000E-02
  6.5007100000E+00   2.5444860000E-01   6.0318320000E-02
  2.7515830000E+00  -2.9103800000E-01   3.9389610000E-01
  1.1454040000E+00  -7.3598600000E-01   5.0137690000E-01
  4.5368700000E-01  -1.9976170000E-01   1.7922640000E-01
0 1 3 2.0 1.0   
  1.7579990000E+00   5.6285720000E-02  -5.0350240000E-01
  6.6702200000E-01   2.8974910000E-01   2.3450110000E-01
  1.0512900000E-01  -1.1406530000E+00   9.1412570000E-01
0 1 1 0.0 1.0   
  3.8418000000E-02   1.0000000000E+00   1.0000000000E+00
0 3 3 5.0 1.0   
  2.0943550000E+01   8.6727020000E-02   
  5.5104860000E+00   3.8418830000E-01   
  1.6650380000E+00   7.0690710000E-01   
0 3 1 0.0 1.0   
  4.6173300000E-01   1.0000000000E+00   
0 4 1 0.0 1.0   
  8.0000000000E-01   1.0000000000E+00   

26  8
0 0 6 2.0 1.00   
  6.1132620000E+04   1.7661110000E-03   
  9.1793420000E+03   1.3530380000E-02   
  2.0908570000E+03   6.6731280000E-02   
  5.8924790000E+02   2.3148230000E-01   
  1.8875430000E+02   4.7970580000E-01   
  6.4446290000E+01   3.5019760000E-01   
0 1 6 8.0 1.0   
  1.2599800000E+03   2.4380140000E-03   4.0280190000E-03
  2.9987610000E+02   3.2240480000E-02   3.1446470000E-02
  9.6849170000E+01   1.2657240000E-01   1.3683170000E-01
  3.6310200000E+01  -3.1399020000E-02   3.4872360000E-01
  1.4729960000E+01  -6.2075930000E-01   4.6179310000E-01
  6.0660750000E+00  -4.5029140000E-01   2.0430580000E-01
0 1 6 8.0 1.0   
  5.0434850000E+01  -3.8732560000E-03  -7.0171280000E-03
  1.6839290000E+01   7.1965980000E-02  -2.8776600000E-02
  7.1920860000E+00   2.5565910000E-01   6.1813830000E-02
  3.0534200000E+00  -2.8828370000E-01   3.9549460000E-01
  1.2736430000E+00  -7.3428220000E-01   4.9890590000E-01
  5.0409100000E-01  -2.0493530000E-01   1.7912510000E-01
0 1 3 2.0 1.0   
  1.9503160000E+00   5.6948690000E-02  -4.5937960000E-01
  7.3672100000E-01   2.8829150000E-01   2.8521390000E-01
  1.1417700000E-01  -1.1381590000E+00   9.0764850000E-01
0 1 1 0.0 1.0   
  4.1148000000E-02   1.0000000000E+00   1.0000000000E+00
0 3 3 6.0 1.0   
  2.3149940000E+01   8.8769350000E-02   
  6.1223680000E+00   3.8963190000E-01   
  1.8466010000E+00   7.0148160000E-01   
0 3 1 0.0 1.0   
  5.0436100000E-01   1.0000000000E+00   
0 4 1 0.0 1.0   
  8.0000000000E-01   1.0000000000E+00   

27  8
0 0 6 2.0 1.00   
  6.6148990000E+04   1.7597870000E-03   
  9.9330770000E+03   1.3481620000E-02   
  2.2628160000E+03   6.6493420000E-02   
  6.3791540000E+02   2.3079390000E-01   
  2.0441220000E+02   4.7929190000E-01   
  6.9825380000E+01   3.5140970000E-01   
0 1 6 8.0 1.0   
  1.3788410000E+03   2.3762760000E-03   3.9714880000E-03
  3.2826940000E+02   3.1674500000E-02   3.1081740000E-02
  1.0609460000E+02   1.2628880000E-01   1.3574390000E-01
  3.9832750000E+01  -2.5845520000E-02   3.4768270000E-01
  1.6186220000E+01  -6.1834910000E-01   4.6263400000E-01
  6.6677880000E+00  -4.5670080000E-01   2.0516320000E-01
0 1 6 8.0 1.0   
  5.4523550000E+01  -3.9930040000E-03  -7.2907720000E-03
  1.8297830000E+01   7.4096630000E-02  -2.9260270000E-02
  7.8673480000E+00   2.5420000000E-01   6.5641500000E-02
  3.3405340000E+00  -2.9216570000E-01   4.0006520000E-01
  1.3937560000E+00  -7.3187030000E-01   4.9502360000E-01
  5.5132600000E-01  -2.0407840000E-01   1.7582400000E-01
0 1 3 2.0 1.0   
  2.1519470000E+00   5.3798430000E-02  -2.1654960000E-01
  8.1106300000E-01   2.7599710000E-01   1.2404880000E-01
  1.2101700000E-01  -1.1296920000E+00   9.7240640000E-01
0 1 1 0.0 1.0   
  4.3037000000E-02   1.0000000000E+00   1.0000000000E+00
0 3 3 7.0 1.0   
  2.5593060000E+01   9.0047480000E-02   
  6.8009900000E+00   3.9317030000E-01   
  2.0516470000E+00   6.9768440000E-01   
0 3 1 0.0 1.0   
  5.5567100000E-01   1.0000000000E+00   
0 4 1 0.0 1.0   
  8.0000000000E-01   1.0000000000E+00   

28  8
0 0 6 2.0 1.00   
  7.1396350000E+04   1.7530030000E-03   
  1.0720840000E+04   1.3431220000E-02   
  2.4421290000E+03   6.6270410000E-02   
  6.8842650000E+02   2.3025080000E-01   
  2.2061530000E+02   4.7901860000E-01   
  7.5393730000E+01   3.5234440000E-01   
0 1 6 8.0 1.0   
  1.4925320000E+03   2.3707140000E-03   3.9675540000E-03
  3.5540130000E+02   3.1605660000E-02   3.1094790000E-02
  1.1495340000E+02   1.2663350000E-01   1.3595170000E-01
  4.3220430000E+01  -2.4170370000E-02   3.4851360000E-01
  1.7597100000E+01  -6.1877750000E-01   4.6254980000E-01
  7.2577650000E+00  -4.5767700000E-01   2.0351860000E-01
0 1 6 8.0 1.0   
  5.9352610000E+01  -4.1620020000E-03  -7.4214520000E-03
  2.0021810000E+01   7.4251110000E-02  -2.9534100000E-02
  8.6145610000E+00   2.5413600000E-01   6.7318520000E-02
  3.6605310000E+00  -2.9034770000E-01   4.0166600000E-01
  1.5281110000E+00  -7.3021210000E-01   4.9266230000E-01
  6.0405700000E-01  -2.0760570000E-01   1.7568930000E-01
0 1 3 2.0 1.0   
  2.3792760000E+00   5.1578880000E-02  -1.8876630000E-01
  8.8583900000E-01   2.7076110000E-01   1.0151990000E-01
  1.2852900000E-01  -1.1247700000E+00   9.7909060000E-01
0 1 1 0.0 1.0   
  4.5195000000E-02   1.0000000000E+00   1.0000000000E+00
0 3 3 8.0 1.0   
  2.8191470000E+01   9.0988810000E-02   
  7.5235840000E+00   3.9582080000E-01   
  2.2712280000E+00   6.9471540000E-01   
0 3 1 0.0 1.0   
  6.1160300000E-01   1.0000000000E+00   
0 4 1 0.0 1.0   
  8.0000000000E-01   1.0000000000E+00   

29  8
0 0 6 2.0 1.00   
  7.6794380000E+04   1.7481610000E-03   
  1.1530700000E+04   1.3396020000E-02   
  2.6265750000E+03   6.6108850000E-02   
  7.4049030000E+02   2.2982650000E-01   
  2.3735280000E+02   4.7876750000E-01   
  8.1158180000E+01   3.5307390000E-01   
0 1 6 8.0 1.0   
  1.6108140000E+03   2.3640550000E-03   3.9633070000E-03
  3.8363670000E+02   3.1536350000E-02   3.1102230000E-02
  1.2417330000E+02   1.2694520000E-01   1.3613500000E-01
  4.6746780000E+01  -2.2628400000E-02   3.4929140000E-01
  1.9065690000E+01  -6.1920800000E-01   4.6247800000E-01
  7.8715670000E+00  -4.5853930000E-01   2.0201020000E-01
0 1 6 8.0 1.0   
  6.4457320000E+01  -4.3310750000E-03  -7.5237250000E-03
  2.1852120000E+01   7.4123070000E-02  -2.9756870000E-02
  9.4053430000E+00   2.5421080000E-01   6.8496540000E-02
  3.9991680000E+00  -2.8748430000E-01   4.0271410000E-01
  1.6702970000E+00  -7.2914360000E-01   4.9084900000E-01
  6.5962700000E-01  -2.1139510000E-01   1.7592680000E-01
0 1 3 2.0 1.0   
  2.6000880000E+00   5.0275770000E-02  -1.7029110000E-01
  9.6309400000E-01   2.6500400000E-01   9.3101330000E-02
  1.3616100000E-01  -1.1201550000E+00   9.8143360000E-01
0 1 1 0.0 1.0   
  4.7332000000E-02   1.0000000000E+00   1.0000000000E+00
0 3 3 9.0 1.0   
  3.0853410000E+01   9.1999050000E-02   
  8.2649850000E+00   3.9850210000E-01   
  2.4953320000E+00   6.9178970000E-01   
0 3 1 0.0 1.0   
  6.6765800000E-01   1.0000000000E+00   
0 4 1 0.0 1.0   
  8.0000000000E-01   1.0000000000E+00   

30  8
0 0 6 2.0 1.00   
  8.2400940000E+04   1.7433290000E-03   
  1.2372550000E+04   1.3359660000E-02   
  2.8183510000E+03   6.5943650000E-02   
  7.9457170000E+02   2.2941510000E-01   
  2.5472320000E+02   4.7854530000E-01   
  8.7138800000E+01   3.5377530000E-01   
0 1 6 8.0 1.0   
  1.7325690000E+03   2.3614590000E-03   3.9631250000E-03
  4.1271490000E+02   3.1501770000E-02   3.1134110000E-02
  1.3367800000E+02   1.2727740000E-01   1.3639310000E-01
  5.0385850000E+01  -2.1459280000E-02   3.5012660000E-01
  2.0583580000E+01  -6.1976520000E-01   4.6231790000E-01
  8.5059400000E+00  -4.5901800000E-01   2.0049950000E-01
0 1 6 8.0 1.0   
  6.9364920000E+01  -4.4400980000E-03  -7.6892620000E-03
  2.3620820000E+01   7.5052530000E-02  -2.9979820000E-02
  1.0184710000E+01   2.5331110000E-01   7.0824110000E-02
  4.3340820000E+00  -2.8818970000E-01   4.0461410000E-01
  1.8109180000E+00  -7.2670520000E-01   4.8823250000E-01
  7.1484100000E-01  -2.1334390000E-01   1.7519700000E-01
0 1 3 2.0 1.0   
  2.8238420000E+00   4.8985430000E-02  -1.5867630000E-01
  1.0395430000E+00   2.5927930000E-01   8.3793270000E-02
  1.4326400000E-01  -1.1157110000E+00   9.8405470000E-01
0 1 1 0.0 1.0   
  4.9296000000E-02   1.0000000000E+00   1.0000000000E+00
0 3 3 10.0 1.0   
  3.3707640000E+01   9.2626480000E-02   
  9.0611060000E+00   4.0029800000E-01   
  2.7383830000E+00   6.8966080000E-01   
0 3 1 0.0 1.0   
  7.3029400000E-01   1.0000000000E+00   
0 4 1 0.0 1.0   
  8.0000000000E-01   1.0000000000E+00   


The 6-31G(d) Gaussian-Type Basis Sets

Use the 6-31G Hydrogen result and the 6-31G(d,p) “Other Atoms” result. Simple!


References

1. EMSL Basis Set Exchange: “The Role of Databases in Support of Computational Chemistry Calculations.” Feller, D., J. Comp. Chem., 17(13), 1571-1586, 1996.

2. “Basis Set Exchange: A Community Database for Computational Sciences.” Schuchardt, K.L., Didier, B.T., Elsethagen, T., Sun, L., Gurumoorthi, V., Chase, J., Li, J., and Windus, T.L. J. Chem. Inf. Model., 47(3), 1045-1052, 2007, doi:10.1021/ci600510j.

3. From EMSL: H – He: W.J. Hehre, R. Ditchfield and J.A. Pople, J. Chem. Phys. 56; Li – Ne: 2257 (1972). Note: Li and B come from J.D. Dill and J.A. Pople, J. Chem. Phys. 62, 2921 (1975); He is reportedly an unpublished basis set taken from Gaussian.

4. From EMSL: Na – Ar: M.M. Francl, W.J. Petro, W.J. Hehre, J.S. Binkley, M.S. Gordon, D.J. DeFrees and J.A. Pople, J. Chem. Phys. 77, 3654 (1982); Ne is reportedly an unpublished basis set taken from Gaussian.

5. From EMSL: K – Zn: V. Rassolov, J.A. Pople, M. Ratner and T.L. Windus, J. Chem. Phys. 109, 1223 (1998)

6. CRYSTAL09: R. Dovesi, R. Orlando, B. Civalleri, C. Roetti, V.R. Saunders, C.M. Zicovich-Wilson CRYSTAL: a computational tool for the ab initio study of the electronic properties of crystals Z. Kristallogr.220, 571–573 (2005).

7. CRYSTAL09: R. Dovesi, V.R. Saunders, C. Roetti, R. Orlando, C. M. Zicovich-Wilson, F. Pascale, B. Cival- leri, K. Doll, N.M. Harrison, I.J. Bush, Ph. D’Arco, M. Llunell CRYSTAL09 User’s Manual, University of Torino, Torino, 2009.

8. Gaussian09: Gaussian 09, Revision D.01, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, T. Keith, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, O. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, and D. J. Fox, Gaussian, Inc., Wallingford CT, 2013.

9. B3LYP: A.D. Becke, J.Chem.Phys. 98 (1993) 5648-5652.

10. B3LYP: C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785-789.

11. B3LYP: S.H. Vosko, L. Wilk, M. Nusair, Can. J. Phys. 58 (1980) 1200-1211.

12. B3LYP: P.J. Stephens, F.J. Devlin, C.F. Chabalowski, M.J. Frisch, J. Phys. Chem. 98 (1994) 11623-11627.

For The Windows-Specific: Sed For Windows And A .bat File To Get Gaussian09 Files Working With aClimax

Wednesday, September 3rd, 2014

Provided you’ve installed Sed For Windows and know its proper path, the .bat file below should make all the modifications you need to your Gaussian09 .out files (in differently-named files at that) to get them properly loading in aClimax (see the previous post for all the details). A few simple steps:

1. Download and install Sed for Windows. Currently available at: gnuwin32.sourceforge.net/packages/sed.htm

2. Find its location on your machine. Under XP (where I’m using aClimax), this should be C:\Program Files\GnuWin32\bin

3. Copy + paste the text below into Notepad and save that as “aClimax_converter.bat” or something. NOTE: The quotes are IMPORTANT! You risk saving the file as an aClimax_converter.bat.txt file otherwise. The pause is optional. If there’s something wrong with the conversion, keeping the pause will let you see the error. If, by some miracle, your Sed is installed elsewhere, change the PATH statement below. The .aclimaxconversion_step1 file will be deleted (just there for doing sequential Sed’ing in case additional modifications are needed in the future).

PATH=C:\Program Files\GnuWin32\bin;
sed.exe "s/  Atom  AN/ Atom AN /g" %1 > %1.aclimaxconversion_step1
sed.exe "s/ Atom   / Atom/g" %1.aclimaxconversion_step1 > %1.aClimaxable.out
del %1.aclimaxconversion_step1
pause

4. If the path is right, just drag + drop your .out files onto the .bat file (with a shortcut to the .bat file, or place a copy of the file in your working directory).

5. Finally, try opening one of the .aClimaxeable.out files in aClimax and report back if you’ve any problems.

Generating Molecular Orbitals (And Visualizing Assorted Properties) With The Gaussian09 cubegen Utility

Saturday, June 7th, 2014

To begin, this post owes its existence to the efforts of Dr. Douglas Fox at Gaussian, Inc., who provided me with an alternative explanation of how the cubegen utility works. After much wailing and gnashing of teeth, I intend on taking Dr. Fox’s advice and asking Gaussian Support for assistance earlier in my endeavors. What follows below, I hope, will save you some significant frustration (and, given how little there is online that really describes the extra workings of cubegen in a clear and example’ed way, it is my expectation that this page appeared early in your search list).

What I wanted out of cubegen that I couldn’t figure out how to get:

The situation was simple. I wanted my molecule centered and bound within an arbitrarily-sized box (X,Z,Y) for making images and doing additional post-processing. Specifically, I wanted to be able to take many different molecules (from hydrogen gas to big biomolecules) defined within the same-sized box for layering and presentation (different boxes for each, but all the same size).

I am assuming for this that you’re using cubegen from a terminal (not within GaussView or the like) to produce .cub/.cube files for use in some kind of rendering-capable program (like VESTA or VMD) and that cubegen and formchk are in your PATH (either properly placed or by running the Gaussian install script). I’ll be demonstrating usage with benzene (C6H6) and the benzene cation (C6H6+).

1. The Checkpoint File

To extract any kind of data for making .cub/.cube files, you need a checkpoint file (.chk) from your run. This is performed by adding a %chk=FILENAME.chk line to the top of the input file (which, if you’re a Gaussian user, you likely already know). If you want additional properties cube’d, check the Gaussian Tech Document, specifically looking at the Pop keyword for most of the properties you’d want visualized (this data gets placed into the .chk file for .cub/.cube generation after the run). For the standard molecular orbitals, they’re already saved in the .chk file (or their coefficients, anyway).

For benzene.gjf:

%chk=benzene.chk
# b3lyp/6-31G(d,p)

Benzene

0 1
 C                  1.20809735    0.69749533   -0.00000000
 C                  0.00000000    1.39499067   -0.00000000
 C                 -1.20809735    0.69749533   -0.00000000
 C                 -1.20809735   -0.69749533   -0.00000000
 C                  0.00000000   -1.39499067   -0.00000000
 C                  1.20809735   -0.69749533   -0.00000000
 H                  2.16038781    1.24730049   -0.00000000
 H                  0.00000000    2.49460097   -0.00000000
 H                 -2.16038781    1.24730049   -0.00000000
 H                 -2.16038781   -1.24730049   -0.00000000
 H                  0.00000000   -2.49460097   -0.00000000
 H                  2.16038781   -1.24730049   -0.00000000

For benzenecation.gjf:

%chk=benzenecation.chk
# b3lyp/6-31G(d,p)

Benzene cation

1 2
 C                  1.20809735    0.69749533   -0.00000000
 C                  0.00000000    1.39499067   -0.00000000
 C                 -1.20809735    0.69749533   -0.00000000
 C                 -1.20809735   -0.69749533   -0.00000000
 C                  0.00000000   -1.39499067   -0.00000000
 C                  1.20809735   -0.69749533   -0.00000000
 H                  2.16038781    1.24730049   -0.00000000
 H                  0.00000000    2.49460097   -0.00000000
 H                 -2.16038781    1.24730049   -0.00000000
 H                 -2.16038781   -1.24730049   -0.00000000
 H                  0.00000000   -2.49460097   -0.00000000
 H                  2.16038781   -1.24730049   -0.00000000

2. Convert The .chk To .fchk With formchk

As per the Gaussian Tech Doc:

formchk converts the data in a Gaussian checkpoint file into a formatted form which is suitable for input into a variety of visualization software.

Basically, making the .chk file something that cubegen can manipulate to generate .cub/.cube files of orbitals, densities, electrostatic potentials, etc. This run is simple for most users (for the rest, see formchk).

formchk benzene.chk benzene.fchk
formchk benzenecation.chk benzenecation.fchk

3. Using cubegen

And now the fun begins. A typical cubegen run looks like the following:

cubegen 0 MO=HOMO benzene.fchk benzene_HOMO.cub 0 h

cubegen – run cubegen
0 – an old memory flag (must be there, but not important)
MO=HOMO – generate the highest occupied molecular orbital
benzene.fchk – the .fchk file
benzene_HOMO.cub – the generated .cub file
0 – use the default grid point specification (80*80*80 points total in the whole cube file)
h – write out the .cub file with headers

The output you find summarized in VESTA is below for this case.

DEFAULT:
OpenGL version: 2.1 INTEL-8.26.34
Video configuration: Intel HD Graphics 4000 OpenGL Engine
Maximum supported width and height of the viewport: 16384 x 16384
OpenGL depth buffer bit: 16

/Users/damianallis/benzene_HOMO_default_0.cub
====================================================================================
Title Benzene MO=HOMO
Dimensions 87 91 65

Lattice parameters

a b c alpha beta gamma
9.39704 9.82909 7.02078 90.0000 90.0000 90.0000

Unit-cell volume = 648.469273 Å^3

Total number of polygons and unique vertices on slices;
(1 0 0): 0 ( 0), 0 ( 0)
(0 1 0): 0 ( 0), 0 ( 0)
(0 0 1): 0 ( 0), 0 ( 0)
====================================================================================

====================================================================================
Title Benzene

Lattice type P
Space group name P 1
Space group number 1
Setting number 1

Lattice parameters

a b c alpha beta gamma
1.00000 1.00000 1.00000 90.0000 90.0000 90.0000

Unit-cell volume = 1.000000 Å^3

Structure parameters

x y z Occ. B Site Sym.
1 C C1 4.65450 6.23638 3.44640 1.000 1.000 1 –
2 C C2 5.86259 5.53889 3.44640 1.000 1.000 1 –
3 C C3 5.86259 4.14389 3.44640 1.000 1.000 1 –
4 C C4 4.65450 3.44640 3.44640 1.000 1.000 1 –
5 C C5 3.44640 4.14389 3.44640 1.000 1.000 1 –
6 C C6 3.44640 5.53889 3.44640 1.000 1.000 1 –
7 H H1 4.65450 7.33599 3.44640 1.000 1.000 1 –
8 H H2 6.81488 6.08869 3.44640 1.000 1.000 1 –
9 H H3 6.81488 3.59409 3.44640 1.000 1.000 1 –
10 H H4 4.65450 2.34679 3.44640 1.000 1.000 1 –
11 H H5 2.49411 3.59409 3.44640 1.000 1.000 1 –
12 H H6 2.49411 6.08869 3.44640 1.000 1.000 1 –
====================================================================================

Number of polygons and unique vertices on isosurface = 16904 (8460)
12 atoms, 12 bonds, 0 polyhedra; CPU time = 39 ms

For the coarse grid (-2) case:

cubegen 0 MO=HOMO benzene.fchk benzene_HOMO_default_m2.cub -2 h

The output you find summarized in VESTA is below for this case.

/Users/damianallis/benzene_HOMO_default_m2.cub
====================================================================================
Title Benzene MO=HOMO
Dimensions 54 56 40

Lattice parameters

a b c alpha beta gamma
9.52518 9.87796 7.05569 90.0000 90.0000 90.0000

Unit-cell volume = 663.865482 Å^3

Total number of polygons and unique vertices on slices;
(1 0 0): 0 ( 0), 0 ( 0)
(0 1 0): 0 ( 0), 0 ( 0)
(0 0 1): 0 ( 0), 0 ( 0)
====================================================================================

====================================================================================
Title Benzene

Lattice type P
Space group name P 1
Space group number 1
Setting number 1

Lattice parameters

a b c alpha beta gamma
1.00000 1.00000 1.00000 90.0000 90.0000 90.0000

Unit-cell volume = 1.000000 Å^3

Structure parameters

x y z Occ. B Site Sym.
1 C C1 4.65450 6.23638 3.44640 1.000 1.000 1 –
2 C C2 5.86259 5.53889 3.44640 1.000 1.000 1 –
3 C C3 5.86259 4.14389 3.44640 1.000 1.000 1 –
4 C C4 4.65450 3.44640 3.44640 1.000 1.000 1 –
5 C C5 3.44640 4.14389 3.44640 1.000 1.000 1 –
6 C C6 3.44640 5.53889 3.44640 1.000 1.000 1 –
7 H H1 4.65450 7.33599 3.44640 1.000 1.000 1 –
8 H H2 6.81488 6.08869 3.44640 1.000 1.000 1 –
9 H H3 6.81488 3.59409 3.44640 1.000 1.000 1 –
10 H H4 4.65450 2.34679 3.44640 1.000 1.000 1 –
11 H H5 2.49411 3.59409 3.44640 1.000 1.000 1 –
12 H H6 2.49411 6.08869 3.44640 1.000 1.000 1 –
====================================================================================

Number of polygons and unique vertices on isosurface = 6516 (3266)
12 atoms, 12 bonds, 0 polyhedra; CPU time = 10 ms

For the medium grid (-3) case:

cubegen 0 MO=HOMO benzene.fchk benzene_HOMO_default_m3.cub -3 h

The output you find summarized in VESTA is below for this case.

/Users/damianallis/benzene_HOMO_default_m3.cub
====================================================================================
Title Benzene MO=HOMO
Dimensions 107 111 79

Lattice parameters

a b c alpha beta gamma
9.43701 9.78980 6.96751 90.0000 90.0000 90.0000

Unit-cell volume = 643.703858 Å^3

Total number of polygons and unique vertices on slices;
(1 0 0): 0 ( 0), 0 ( 0)
(0 1 0): 0 ( 0), 0 ( 0)
(0 0 1): 0 ( 0), 0 ( 0)
====================================================================================

====================================================================================
Title Benzene

Lattice type P
Space group name P 1
Space group number 1
Setting number 1

Lattice parameters

a b c alpha beta gamma
1.00000 1.00000 1.00000 90.0000 90.0000 90.0000

Unit-cell volume = 1.000000 Å^3

Structure parameters

x y z Occ. B Site Sym.
1 C C1 4.65450 6.23638 3.44640 1.000 1.000 1 –
2 C C2 5.86259 5.53889 3.44640 1.000 1.000 1 –
3 C C3 5.86259 4.14389 3.44640 1.000 1.000 1 –
4 C C4 4.65450 3.44640 3.44640 1.000 1.000 1 –
5 C C5 3.44640 4.14389 3.44640 1.000 1.000 1 –
6 C C6 3.44640 5.53889 3.44640 1.000 1.000 1 –
7 H H1 4.65450 7.33599 3.44640 1.000 1.000 1 –
8 H H2 6.81488 6.08869 3.44640 1.000 1.000 1 –
9 H H3 6.81488 3.59409 3.44640 1.000 1.000 1 –
10 H H4 4.65450 2.34679 3.44640 1.000 1.000 1 –
11 H H5 2.49411 3.59409 3.44640 1.000 1.000 1 –
12 H H6 2.49411 6.08869 3.44640 1.000 1.000 1 –
====================================================================================

Number of polygons and unique vertices on isosurface = 25532 (12774)
12 atoms, 12 bonds, 0 polyhedra; CPU time = 51 ms

For the fine grid (-4) case:

cubegen 0 MO=HOMO benzene.fchk benzene_HOMO_default_m4.cub -4 h

The output you find summarized in VESTA is below for this case.

/Users/damianallis/benzene_HOMO_default_m4.cub
====================================================================================
Title Benzene MO=HOMO
Dimensions 212 221 157

Lattice parameters

a b c alpha beta gamma
9.34876 9.74564 6.92337 90.0000 90.0000 90.0000

Unit-cell volume = 630.786281 Å^3

Total number of polygons and unique vertices on slices;
(1 0 0): 0 ( 0), 0 ( 0)
(0 1 0): 0 ( 0), 0 ( 0)
(0 0 1): 0 ( 0), 0 ( 0)
====================================================================================

====================================================================================
Title Benzene

Lattice type P
Space group name P 1
Space group number 1
Setting number 1

Lattice parameters

a b c alpha beta gamma
1.00000 1.00000 1.00000 90.0000 90.0000 90.0000

Unit-cell volume = 1.000000 Å^3

Structure parameters

x y z Occ. B Site Sym.
1 C C1 4.65450 6.23638 3.44640 1.000 1.000 1 –
2 C C2 5.86259 5.53889 3.44640 1.000 1.000 1 –
3 C C3 5.86259 4.14389 3.44640 1.000 1.000 1 –
4 C C4 4.65450 3.44640 3.44640 1.000 1.000 1 –
5 C C5 3.44640 4.14389 3.44640 1.000 1.000 1 –
6 C C6 3.44640 5.53889 3.44640 1.000 1.000 1 –
7 H H1 4.65450 7.33599 3.44640 1.000 1.000 1 –
8 H H2 6.81488 6.08869 3.44640 1.000 1.000 1 –
9 H H3 6.81488 3.59409 3.44640 1.000 1.000 1 –
10 H H4 4.65450 2.34679 3.44640 1.000 1.000 1 –
11 H H5 2.49411 3.59409 3.44640 1.000 1.000 1 –
12 H H6 2.49411 6.08869 3.44640 1.000 1.000 1 –
====================================================================================

Number of polygons and unique vertices on isosurface = 100680 (50348)
12 atoms, 12 bonds, 0 polyhedra; CPU time = 155 ms

These all generate a file containing the highest occupied molecular orbital (or one of the degenerate HOMO’s in this case. Do I have to qualify that this doesn’t mean what 99.5% of the people coming to this page thinks this means?). The box is generated by something in cubegen to be 9.3ish x 9.7ish x 6.9ish Angstroms on a side and containing X points per Angstrom (and you can change the fineness of the grid points). The image below shows the four cases for the benzene HOMO. Click to see larger versions if you want to see the influence of grid fineness on the final image.

benzene_homo_gaussian_defaults_small

Click for a larger view.

Now, then, while the boxes are almost all identical, the same molecule and input gives four slightly different results. Fine for individual images, but not ideal for the obsessive-compulsive image maker. Also, you see how a box simply bounds the molecule, meaning no standardization of size if you needed that standardization for some reason.

   a        b        c       alpha    beta     gamma
 9.39704  9.82909  7.02078  90.0000  90.0000  90.0000 < - default (0)
  9.52518  9.87796  7.05569  90.0000  90.0000  90.0000 <- coarse (-2)
  9.43701  9.78980  6.96751  90.0000  90.0000  90.0000 <- medium (-3)
  9.34876  9.74564  6.92337  90.0000  90.0000  90.0000 <- fine (-4)
 

So, for a specific case - suppose I wanted this orbital in a box exactly 15 x 20 x 25 Angstroms on a side with the molecule offset from the center by -1.0 Angstrom in each direction.

I was pleased to finally discover that cubegen allows for that, although you have to ask Gaussian Support to find out how (until now, that is) and you need to do a little bit of math to get the placement right (or use the excel file I've linked in a .zip file found at 2014june7_cubegen_excel_file.xlsx).

You begin with the following:

cubegen 0 MO=HOMO benzene.fchk benzene_HOMO.cub -1 h

But for -1, Where do the numbers go?

From the Gaussian Tech Doc:

A value of -1 says to read the cube specification from the input stream, according to the following format:

IFlag, X0, Y0, Z0 Output unit number and initial point.
N1, X1, Y1, Z1 Number of points and step-size in the X-direction.
N2, X2, Y2, Z2 Number of points and step-size in the Y-direction.
N3, X3, Y3, Z3 Number of points and step-size in the Z-direction.

IFlag is the output unit number. If IFlag is less than 0, then a formatted file will be produced; otherwise, an unformatted file will be written.

Admittedly, “input stream” made no sense to me upon first and second read. I just knew that the program didn’t do anything when I ran it. Now obvious, this means you input the cube specifications by typing in (or, better, pasting in) the 16 numbers it asks for.

Continuing…

The -1 tells cubegen to “expect more input.” In this case, without explanation first, my input would look as below:

-12  -6.50000  -9.00000 -11.50000
 60   0.25000   0.00000   0.00000
 80   0.00000   0.25000   0.00000
100   0.00000   0.00000   0.25000

Which you just paste into your terminal at the new line (having pressed ENTER after typing out the cubegen line above).

How this works (and note the use of minus signs!):

-[# Atoms] -[Start Point For Box In X] -[Start Point For Box In Y] -[Start Point For Box In Z]
[Number of Points In X]   [Grid Fineness In X]   [Grid Fineness In Y]   [Grid Fineness In Z]
[Number of Points In Y]   [Grid Fineness In X]   [Grid Fineness In Y]   [Grid Fineness In Z]
[Number of Points In Y]   [Grid Fineness In X]   [Grid Fineness In Y]   [Grid Fineness In Z]

Assuming orthogonality in your box, the off-diagonals for the grid fineness matrix are zero.

-[# Atoms] -[Start Point For Box In X] -[Start Point For Box In Y] -[Start Point For Box In Z]
[Number of Points In X]  [Grid Fineness In X]   0.000   0.000
[Number of Points In Y]  0.000   [Grid Fineness In Y]   0.000
[Number of Points In Y]  0.000   0.000   [Grid Fineness In Z]

4. -6.5, -9, -11.5?

You build the box around your molecule in cubegen, which means you combine (1) where you want the molecule positions with (2) the number of grid points along each direction and (3) the fineness of the grid to generate the box. Here, I’m starting my hypothetical box at -6.5 in X, -9 in Y, and -11.5 in Z, then building out my molecule 121*.25 points in X, 161*.25 in Y, 201*.25 in Z. This will produce the intended box size with the molecule technically centered at the origin in the box (0,0,0), but the generation of all 121, 161, and 201 points in X, Y, and Z will result in the box going from -6.5 to 8.5, -9 to 11, and -11.5 to 13.5 (and there’s your asymmetry in the box). Alternatively, you could think of it as generating a box 15 x 20 x 25, then placing the center of the molecule at 6.5, 9, 11.5 (but you don’t specify the box size directly, instead relying on the relative position of the molecule and the fineness of the grid to determine the position (from which you could work back to get the number of points you needed in each direction if you knew the size of the box you wanted. Yes, you might have to re-read that a few times).

I demonstrate this below for a benzene orbital “walk” along X using direct output from VESTA. The rest of the numbers in my matrix above are the same except for the “-[Start Point For The Box In X]” value.

benzene_homo_walk

The benzene walk (numbers show the spacing based on the cubegen input above).

5. Formula For Boxes And Grid Points

You can, in fact, work from the box size you want and relative position of the molecule in that box with some simple math. That looks like the table below:

-(# Atoms)           -(X Position)  -(Y Position)  -(Z Position)
(Box Size / X Mesh)    X Mesh         0.00000        0.00000
(Box Size / Y Mesh)    0.00000        Y Mesh         0.00000
(Box Size / Z Mesh)    0.00000        0.00000        Z Mesh

You specify # Atoms, X Position, Y Position, Z Position, X Mesh, Y Mesh and Z Mesh, then decide on how big your box is going to be. Also, note that X Position, Y Position, Z Position all need to be 1/2 the size of your box if you want the molecule centered. A way to help force this is to force the molecule to have its center of mass shifted to the origin using Symm=COM in your input file.

As mentioned above, a simple excel file for performing this task is provided for download at 2014june7_cubegen_excel_file.xlsx.

6. Lastly, A Procedure For Scripting The Generation Of Many Orbitals

That first stone passed, everything about making custom .cub/.cube files finally made sense. But it lead to another problem. Suppose I want to generate many molecular orbitals. Does one have to paste in the IFlag…Z3 block each time?

Thankfully, this process can be scripted to automation as well, although it’s not just a matter of pasting IFlag…Z3 below each run of cubegen. Doing that produces the following…

Example:

This isn’t a cubegen problem, it’s a Linux issue with the interpretation of stdin. The cubegen script needs to be fed in the matrix in a file (say cubegen.dat if you always want the same .cub/.cube file generated) or via the use of an EOF call.

Cubegen.dat:

cubegen 0 MO=1 benzene.fchk benzene_MO1.cub -1 h < cubegen.dat
 cubegen 0 MO=2 benzene.fchk benzene_MO2.cub -1 h < cubegen.dat
 cubegen 0 MO=3 benzene.fchk benzene_MO3.cub -1 h < cubegen.dat
 ...
 

EOF

cubegen 0 MO=1 benzene.fchk benzene_MO1.cub -1 h << EOF
-12  -6.50000  -9.00000 -11.50000
 60   0.25000   0.00000   0.00000
 80   0.00000   0.25000   0.00000
100   0.00000   0.00000   0.25000
EOF
cubegen 0 MO=2 benzene.fchk benzene_MO2.cub -1 h << EOF
-12  -6.50000  -9.00000 -11.50000
 60   0.25000   0.00000   0.00000
 80   0.00000   0.25000   0.00000
100   0.00000   0.00000   0.25000
EOF
cubegen 0 MO=3 benzene.fchk benzene_MO3.cub -1 h << EOF
-12  -6.50000  -9.00000 -11.50000
 60   0.25000   0.00000   0.00000
 80   0.00000   0.25000   0.00000
100   0.00000   0.00000   0.25000
EOF
...

7. What’s The Deal With The Benzene Cation?

Nothing, except I saw a question in my perusing of cubegen problems and found one related to UHF wavefunctions. How do you render alpha spin orbitals and beta spin orbitals? The answer is you dig into the .log file for the orbital energies and count (to the best of my knowledge).

Benzene (21 alpha/beta-occupied)

 Alpha  occ. eigenvalues -- -10.18955 -10.18928 -10.18928 -10.18872 -10.18872
 Alpha  occ. eigenvalues -- -10.18845  -0.84761  -0.73971  -0.73971  -0.59595
 Alpha  occ. eigenvalues --  -0.59595  -0.51588  -0.45423  -0.43943  -0.41518
 Alpha  occ. eigenvalues --  -0.41518  -0.36090  -0.33862  -0.33862  -0.24750
 Alpha  occ. eigenvalues --  -0.24750
 Alpha virt. eigenvalues --   0.00266   0.00266   0.08636   0.14126   0.14126
 Alpha virt. eigenvalues --   0.16238   0.17957   0.17957   0.18681   0.29989
 Alpha virt. eigenvalues --   0.29989   0.31908   0.31908   0.46637   0.52628
 Alpha virt. eigenvalues --   0.54782   0.55099   0.56222   0.59294   0.60077
 Alpha virt. eigenvalues --   0.60077   0.60084   0.60084   0.62384   0.62384
 Alpha virt. eigenvalues --   0.66653   0.66653   0.74180   0.81178   0.81178
 Alpha virt. eigenvalues --   0.82134   0.83694   0.83694   0.91676   0.93745
 Alpha virt. eigenvalues --   0.93745   0.95812   1.08054   1.08054   1.12992
 Alpha virt. eigenvalues --   1.12992   1.20098   1.26111   1.30051   1.40786
 Alpha virt. eigenvalues --   1.40786   1.42585   1.42585   1.42914   1.42914
 Alpha virt. eigenvalues --   1.74102   1.76078   1.80542   1.87583   1.90680
 Alpha virt. eigenvalues --   1.90680   1.97195   1.97195   1.97924   1.97924
 Alpha virt. eigenvalues --   2.02762   2.07664   2.07664   2.29609   2.29609
 Alpha virt. eigenvalues --   2.34429   2.34429   2.35491   2.39944   2.40328
 Alpha virt. eigenvalues --   2.40328   2.44636   2.44636   2.48731   2.48731
 Alpha virt. eigenvalues --   2.50802   2.58538   2.58538   2.60300   2.65987
 Alpha virt. eigenvalues --   2.75521   2.80103   2.80103   3.03123   3.03123
 Alpha virt. eigenvalues --   3.18490   3.20485   3.21867   3.21867   3.37166
 Alpha virt. eigenvalues --   3.48298   3.48298   3.93339   4.13215   4.16289
 Alpha virt. eigenvalues --   4.16289   4.43754   4.43754   4.82384

RHF wave functions are easy as the alpha and beta spin orbitals are identical (so you just call one).

Benzene Cation (21 alpha occ, 20 beta occ)

 Alpha  occ. eigenvalues --  -10.44746 -10.44745 -10.44690 -10.44689 -10.41307
 Alpha  occ. eigenvalues --  -10.41306  -1.09893  -0.99649  -0.97270  -0.83278
 Alpha  occ. eigenvalues --   -0.83268  -0.74423  -0.68358  -0.67574  -0.65278
 Alpha  occ. eigenvalues --   -0.63494  -0.61047  -0.56837  -0.56618  -0.51141
 Alpha  occ. eigenvalues --   -0.47878
 Alpha virt. eigenvalues --   -0.25225  -0.22671  -0.10624  -0.07758  -0.05310
 Alpha virt. eigenvalues --   -0.04280  -0.01821  -0.00871   0.00401   0.08260
 Alpha virt. eigenvalues --    0.08579   0.09642   0.10056   0.25206   0.29439
 Alpha virt. eigenvalues --    0.31399   0.31852   0.34121   0.36475   0.36906
 Alpha virt. eigenvalues --    0.37451   0.38343   0.38500   0.39459   0.40284
 Alpha virt. eigenvalues --    0.43576   0.45334   0.52549   0.60260   0.60770
 Alpha virt. eigenvalues --    0.61287   0.62929   0.64337   0.70989   0.71650
 Alpha virt. eigenvalues --    0.71731   0.74333   0.85713   0.86949   0.90112
 Alpha virt. eigenvalues --    0.90952   0.98816   1.00856   1.05831   1.15646
 Alpha virt. eigenvalues --    1.17792   1.17972   1.18789   1.20601   1.20854
 Alpha virt. eigenvalues --    1.49713   1.52475   1.57000   1.65756   1.66784
 Alpha virt. eigenvalues --    1.68337   1.73545   1.74011   1.74167   1.74723
 Alpha virt. eigenvalues --    1.80258   1.82880   1.84586   2.04024   2.06015
 Alpha virt. eigenvalues --    2.12117   2.12667   2.14025   2.17682   2.18940
 Alpha virt. eigenvalues --    2.19096   2.22084   2.22451   2.24748   2.25480
 Alpha virt. eigenvalues --    2.28544   2.35165   2.36888   2.39005   2.41062
 Alpha virt. eigenvalues --    2.52629   2.57091   2.57724   2.79730   2.80863
 Alpha virt. eigenvalues --    2.95189   2.99029   2.99731   3.01110   3.14403
 Alpha virt. eigenvalues --    3.25310   3.26537   3.70063   3.88553   3.90763
 Alpha virt. eigenvalues --    3.92953   4.18629   4.20462   4.58339
  Beta  occ. eigenvalues --  -10.44304 -10.44303 -10.44252 -10.44250 -10.41463
  Beta  occ. eigenvalues --  -10.41462  -1.08758  -0.97673  -0.97028  -0.82708
  Beta  occ. eigenvalues --   -0.82377  -0.74165  -0.67883  -0.67164  -0.64793
  Beta  occ. eigenvalues --   -0.63478  -0.57727  -0.56637  -0.56323  -0.47270
  Beta virt. eigenvalues --   -0.41639  -0.21435  -0.21139  -0.10438  -0.05496
  Beta virt. eigenvalues --   -0.05056  -0.04232  -0.01054  -0.00739   0.00754
  Beta virt. eigenvalues --    0.08748   0.08784   0.10027   0.10356   0.25410
  Beta virt. eigenvalues --    0.30875   0.31655   0.33033   0.34430   0.37599
  Beta virt. eigenvalues --    0.38243   0.38423   0.38827   0.38857   0.40471
  Beta virt. eigenvalues --    0.40510   0.45633   0.45687   0.53548   0.60543
  Beta virt. eigenvalues --    0.61003   0.61366   0.63303   0.64325   0.71163
  Beta virt. eigenvalues --    0.71910   0.72371   0.74501   0.86611   0.87153
  Beta virt. eigenvalues --    0.90721   0.90982   0.99163   1.02443   1.07028
  Beta virt. eigenvalues --    1.17547   1.18130   1.19642   1.19672   1.20955
  Beta virt. eigenvalues --    1.21374   1.51458   1.52709   1.57335   1.66396
  Beta virt. eigenvalues --    1.67580   1.68460   1.73895   1.74747   1.75260
  Beta virt. eigenvalues --    1.75568   1.80924   1.84865   1.84936   2.06229
  Beta virt. eigenvalues --    2.06582   2.12479   2.12665   2.14334   2.18350
  Beta virt. eigenvalues --    2.18883   2.19283   2.22289   2.22978   2.25783
  Beta virt. eigenvalues --    2.25938   2.29233   2.36212   2.37068   2.39062
  Beta virt. eigenvalues --    2.42549   2.53376   2.57824   2.57840   2.79980
  Beta virt. eigenvalues --    2.80952   2.95964   2.99101   2.99875   3.01115
  Beta virt. eigenvalues --    3.14561   3.25632   3.26592   3.70353   3.89317
  Beta virt. eigenvalues --    3.92008   3.93146   4.19813   4.20623   4.58989

In the case of UHF wave functions, you specify alpha or beta using AMO= or BMO= when you run cubegen.

Compiling And Running GAMESS-US (1 May 2013(R1)) On 64-bit Ubuntu 12.X/13.X In SMP Mode

Saturday, April 5th, 2014

Author’s Note 1: It is my standard policy to put too much info into guides so that those who are searching for specific problems they come across will find the offending text in their searches. With luck, your “build error” search sent you here.

Author’s Note 2: It’s not as bad as it looks (I’ve included lots of output and error messages for easy searching)!

Author’s Note 3: I won’t be much help for you in diagnosing your errors, but am happy to tweak the text below if something is unclear.

Conventions: I include both the commands you type in your Terminal and some of the output from these commands, the output being where most of the errors appear that I work on in the discussion.

Input is formatted as below:

username – your username (check your prompt)
machinename – your hostname (type hostname or check your prompt)

Text you put in at the (also shown, so you see the directory structure) prompt (copy + paste should be fine)

Text you get out (for checking results and reproducing errors)

Having just recently downloaded the newest version of GAMESS-US (R1 2013), my first few passes at using it under Linux (specifically, Ubuntu 12.04) ran into a few walls that required some straightforward modifications and a little bit of system prep planning. As my first few passes before successful execution are likely the same exact problems you might have run into in your attempts to get GAMESS-US to run (after a successful compilation and linking), I’m posting my problems and solutions here.

Qualifier 1 – My concern at the moment has been to get GAMESS-US to run under 64-bit Ubuntu 12.04 on a multi-core board (ye olde symmetric multiprocessing (which I always called single multi-processor, or SMP)). While some answers may follow in what’s below, this post doesn’t cover MPI-specific builds (nothing through a router, that is). SMP is the only concern (which is to say, I likely won’t have good answers if you send along an MPI-specific question). Also, although I’m VERY interested in trying it, I’ve not yet attempted to build a GPU-capable version (but plan to in the near future).

Qualifier 2 – It is my standard policy to install apps into /opt, and my steps below will reflect that (specifically because there’s a permission issue that needs to be addressed when you first try to build components). You can default to whatever you like, but keep in mind my tweaks when you try to build your local copy.

So, with the qualifiers in mind…

1. Prepping The System (apt-get)

There are few things better than being able to apt-get everything you need to prep your machine for an install, and I’m pleased to report that the (current) process for putting the important files onto Ubuntu 12.X/13.X is easy. Assuming you’re not going the Intel / PGI / MKL route, you can do everything by installing gfortran (compiler, presently installing 4.4) and the blas and atlas math libraries.

username@machinename:~$ sudo apt-get install gfortran libblas-dev libatlas-base-dev

Note: your atlas libraries will be installed in /usr/lib64/atlas/ – this will matter when you run config.

After these finish, run the following to determine your installed gfortran version (will be asked for by the new GAMESS config)

username@machinename:~$ gfortran -dumpversion

GNU Fortran (Ubuntu 4.4.3-4ubuntu5.1) 4.4.3 Copyright (C) 2010 Free Software Foundation, Inc. GNU Fortran comes with NO WARRANTY, to the extent permitted by law. You may redistribute copies of GNU Fortran under the terms of the GNU General Public License. For more information about these matters, see the file named COPYING

4.4 And you’re ready for GAMESS.

2. Downloading GAMESS-US, Placing Into /opt, And Changing Permissions

First, obviously, get the GAMESS source (click on the red text).

After downloading, copy/move gamess-current.tar.gz into /opt

username@machinename:~$ cd ~/Downloads
username@machinename:~/Downloads$ sudo cp gamess-current.tar.gz /opt
username@machinename:~/Downloads$ cd /opt
username@machinename:/opt$ sudo gunzip gamess-cuerent.tar.gz
username@machinename:/opt$ sudo tar xvd gamess-current.tar

gamess/ gamess/gms-files.csh gamess/tools/ ... gamess/misc/count.code gamess/misc/vbdum.src gamess/Makefile.in

At this point, if you go through the config process and get to the point of building ddikick.x, you will get an error when you first try to run ./compddi

username@machinename:/opt/gamess/ddi$ sudo ./compddi >& compddi.log &
[1] 4622 -bash: compddi.log: Permission denied

The problem is with the permission of the entire gamess folder:

drwxr-xr-x  4 root        root              4096 2014-04-04 21:43 . drwxr-xr-x 22 root        root              4096 2013-12-27 16:17 .. drwxr-xr-x 14 1300 504              4096 2014-04-04 21:43 gamess -rw-r--r-- 1 root        root         198481920 2014-04-04 21:42 gamess-current.tar

Which you remedy before running into this error by changing the permissions:

username@machinename:/opt$ sudo chown -R username gamess

The next step is recommended when you run config, so I’m performing the step here to get it out of the way. With the atlas libraries installed, generate two symbolic links.

username@machinename:/opt$ cd /usr/lib64/atlas
username@machinename:/usr/lib64/atlas$ sudo ln -s libf77blas.so.3.0 libf77blas.so
username@machinename:/usr/lib64/atlas$ sudo ln -s libatlas.so.3.0 libatlas.so

And, at this point, you’re ready to run the new (well, new to me) config script that preps your system install.

3. Building GAMESS-US

Back to the GAMESS-US folder.

username@machinename:/usr/lib64/atlas$ cd /opt/gamess
username@machinename:/opt/gamess$ sudo ./config
This script asks a few questions, depending on your computer system, to set up compiler names, libraries, message passing libraries, and so forth. You can quit at any time by pressing control-C, and then . Please open a second window by logging into your target machine, in case this script asks you to 'type' a command to learn something about your system software situation. All such extra questions will use the word 'type' to indicate it is a command for the other window. After the new window is open, please hit to go on.

You can open that second window or blindly assume that what I include below is all you need.

[enter]

GAMESS can compile on the following 32 bit or 64 bit machines: axp64 - Alpha chip, native compiler, running Tru64 or Linux cray-xt - Cray's massively parallel system, running CNL hpux32 - HP PA-RISC chips (old models only), running HP-UX hpux64 - HP Intel or PA-RISC chips, running HP-UX ibm32 - IBM (old models only), running AIX ibm64 - IBM, Power3 chip or newer, running AIX or Linux ibm64-sp - IBM SP parallel system, running AIX ibm-bg - IBM Blue Gene (P or L model), these are 32 bit systems linux32 - Linux (any 32 bit distribution), for x86 (old systems only) linux64 - Linux (any 64 bit distribution), for x86_64 or ia64 chips AMD/Intel chip Linux machines are sold by many companies mac32 - Apple Mac, any chip, running OS X 10.4 or older mac64 - Apple Mac, any chip, running OS X 10.5 or newer sgi32 - Silicon Graphics Inc., MIPS chip only, running Irix sgi64 - Silicon Graphics Inc., MIPS chip only, running Irix sun32 - Sun ultraSPARC chips (old models only), running Solaris sun64 - Sun ultraSPARC or Opteron chips, running Solaris win32 - Windows 32-bit (Windows XP, Vista, 7, Compute Cluster, HPC Edition) win64 - Windows 64-bit (Windows XP, Vista, 7, Compute Cluster, HPC Edition) winazure - Windows Azure Cloud Platform running Windows 64-bit type 'uname -a' to partially clarify your computer's flavor. please enter your target machine name:

We’re doing a linux64 build, so type the following at the prompt:

linux64
Where is the GAMESS software on your system? A typical response might be /u1/mike/gamess, most probably the correct answer is /opt/gamess GAMESS directory? [/opt/gamess]

Who is this mike and where is my folder u1? We’ll get to that in rungms. For now, I’m installing in /opt, so the default directory is fine:

[enter]

Setting up GAMESS compile and link for GMS_TARGET=linux64 GAMESS software is located at GMS_PATH=/opt/gamess Please provide the name of the build locaation. This may be the same location as the GAMESS directory. GAMESS build directory? [/opt/gamess]

Fine as selected.

[enter]

Please provide a version number for the GAMESS executable. This will be used as the middle part of the binary's name, for example: gamess.00.x Version? [00]

Is this important? Maybe, if you plan on building multiple versions of GAMESS-US (you might want a GPU-friendly version, one with a different compiler, one with MPI, etc.). Number as you wish and remember the number when it comes to rungms. That said, the actual linking step seems to really want to produce a 01 version (we’ll get to that). Meantime, default value is fine.

[enter]

Linux offers many choices for FORTRAN compilers, including the GNU compiler set ('g77' in old versions of Linux, or 'gfortran' in current versions), which are included for free in Unix distributions. There are also commercial compilers, namely Intel's 'ifort', Portland Group's 'pgfortran', and Pathscale's 'pathf90'. The last two are not common, and aren't as well tested as the others. type 'rpm -aq | grep gcc' to check on all GNU compilers, including gcc type 'which gfortran' to look for GNU's gfortran (a very good choice), type 'which g77' to look for GNU's g77, type 'which ifort' to look for Intel's compiler, type 'which pgfortran' to look for Portland Group's compiler, type 'which pathf90' to look for Pathscale's compiler. Please enter your choice of FORTRAN:

We’re using gfortran (currently 4.4.3):

gfortran

gfortran is very robust, so this is a wise choice. Please type 'gfortran -dumpversion' or else 'gfortran -v' to detect the version number of your gfortran. This reply should be a string with at least two decimal points, such as 4.1.2 or 4.6.1, or maybe even 4.4.2-12. The reply may be labeled as a 'gcc' version, but it is really your gfortran version. Please enter only the first decimal place, such as 4.1 or 4.6:
4.4

Alas, your version of gfortran does not support REAL*16, so relativistic integrals cannot use quadruple precision. Other than this, everything will work properly. hit to continue to the math library setup.

If this was my biggest concern I’d be a happy quantum chemist. Obviously you can try to install other flavors of gfortran and, possibly, by the time you need the procedure I’m following, a newer version of gfortran will be apt-gotten.

[enter]

Linux distributions do not include a standard math library. There are several reasonable add-on library choices, MKL from Intel for 32 or 64 bit Linux (very fast) ACML from AMD for 32 or 64 bit Linux (free) ATLAS from www.rpmfind.net for 32 or 64 bit Linux (free) and one very unreasonable option, namely 'none', which will use some slow FORTRAN routines supplied with GAMESS. Choosing 'none' will run MP2 jobs 2x slower, or CCSD(T) jobs 5x slower. Some typical places (but not the only ones) to find math libraries are Type 'ls /opt/intel/mkl' to look for MKL Type 'ls /opt/intel/Compiler/mkl' to look for MKL Type 'ls /opt/intel/composerxe/mkl' to look for MKL Type 'ls -d /opt/acml*' to look for ACML Type 'ls -d /usr/local/acml*' to look for ACML Type 'ls /usr/lib64/atlas' to look for Atlas Enter your choice of 'mkl' or 'atlas' or 'acml' or 'none':
atlas

Where is your Atlas math library installed? A likely place is /usr/lib64/atlas Please enter the Atlas subdirectory on your system:

Our location is, in fact, /usr/lib64/atlas, so we type it in accordingly.

NOTE: If you don’t type anything but [enter] below, the script closes (/usr/lib64/atlas is listed as the expected location, but it is not defaulted by the script. You need to type it in.

/usr/lib64/atlas
 
The linking step in GAMESS assumes that a softlink exists within the system's /usr/lib64/atlas from libatlas.so to a specific file like libatlas.so.3.0 from libf77blas.so to a specific file like libf77blas.so.3.0 config can carry on for the moment, but the 'root' user should chdir /usr/lib64/atlas ln -s libf77blas.so.3.0 libf77blas.so ln -s libatlas.so.3.0 libatlas.so prior to the linking of GAMESS to a binary executable. Math library 'atlas' will be taken from /usr/lib64/atlas please hit to compile the GAMESS source code activator

The symbolic linking was performed before the GAMESS steps.

[enter]

gfortran -o /home/username/gamess/tools/actvte.x actvte.f unset echo Source code activator was successfully compiled. please hit to set up your network for Linux clusters.
[enter]

If you have a slow network, like Gigabit Ethernet (GE), or if you have so few nodes you won't run extensively in parallel, or if you have no MPI library installed, or if you want a fail-safe compile/link and easy execution, choose 'sockets' to use good old reliable standard TCP/IP networking. If you have an expensive but fast network like Infiniband (IB), and if you have an MPI library correctly installed, choose 'mpi'. communication library ('sockets' or 'mpi')?

Again, I’m not building an mpi-friendly version, so am using sockets.

sockets

64 bit Linux builds can attach a special LIBCCHEM code for fast MP2 and CCSD(T) runs. The LIBCCHEM code can utilize nVIDIA GPUs, through the CUDA libraries, if GPUs are available. Usage of LIBCCHEM requires installation of HDF5 I/O software as well. GAMESS+LIBCCHEM binaries are unable to run most of GAMESS computations, and are a bit harder to create due to the additional CUDA/HDF5 software. Therefore, the first time you run 'config', the best answer is 'no'! If you decide to try LIBCCHEM later, just run this 'config' again. Do you want to try LIBCCHEM? (yes/no):
no

Your configuration for GAMESS compilation is now in /home/username/gamess/install.info Now, please follow the directions in /home/username/gamess/machines/readme.unix username@machinename:~/gamess$

At this stage, you’re ready to build ddikick.x and continue with the compiling.

4. Build ddikick.x

username@machinename:/opt/gamess$ cd ddi
username@machinename:/opt/gamess/ddi$ sudo ./compddi >& compddi.log &

Will dump output into compddi.log (which will now work with the correct permissions).

username@machinename:/opt/gamess/ddi$ sudo mv ddikick.x ..
username@machinename:/opt/gamess/ddi$ cd ..
username@machinename:/opt/gamess$ sudo ./compall >& compall.log &

Feel free to follow along as compall.log dumps results. You’re also welcome to follow the readme.unix advice:

This takes a while, so go for coffee, or check the SF Giants web page.

Upon completion, the last step is to link the executable.

Now, it used to be the case that you specified the version number in the lked step. So, if you wanted to stick with the 00 version from the config file, you’d type

username@machinename:/opt/gamess$ sudo ./lked gamess 00 >& lked.log &

When you do that at present, you get

[1] 7626 username@machinename:/opt/gamess$ [1]+ Stopped sudo ./lked gamess 00 &>lked.log

This then leads you to use the lked call from the readme.unix file.

username@machinename:/opt/gamess$ sudo ./lked gamess 01 >& lked.log &

Which then produces lked.log and gamess.01.x.

Now, if you run with 00 again, you get a successful linking of gamess.00.x . Not sure why this happens, but the version number isn’t important so long as you specify the right one when you use rungms (so I’ve not diagnosed it further).

At this point, you have a gamess.00.x and/or gamess.01.x executable in your /opt/gamess folder:

30828747 2014-04-04 22:41 gamess.01.x

I’m going to ignore the 00 issue out of the config file and use the gamess.01.x executable.

We’re ready to run calculations and work through the next set of errors you’ll receive if you don’t properly modify files.

5. PATH Setting

First, we copy rungms to our home folder, then add /opt/gamess to the PATH:

username@machinename:/opt/gamess$ cp rungms ~/
username@machinename:/opt/gamess$ cd ~/
username@machinename:~$ nano .bashrc

Add the following to the bottom of .bashrc (or extend your PATH)

PATH=$PATH:/opt/gamess

Quit nano and source.

username@machinename:~$ source .bashrc
[OPTIONAL] username@machinename:~$ echo $PATH
/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:.../opt/gamess:

6. rungms (Probably Why You’re Here)

If you just go blindly into a run, you’ll get the following error:

username@machinename:~$ ./rungms test.inp

----- GAMESS execution script 'rungms' ----- This job is running on host machinename under operating system Linux at Fri Apr 4 22:47:55 EDT 2014 Available scratch disk space (Kbyte units) at beginning of the job is df: `/scr/username': No such file or directory df: no file systems processed GAMESS temporary binary files will be written to /scr/username GAMESS supplementary output files will be written to /home/username/scr Copying input file test.inp to your run's scratch directory... cp test.inp /scr/username/test.F05 cp: cannot create regular file `/scr/username/test.F05': No such file or directory unset echo /u1/mike/gamess/gms-files.csh: No such file or directory.

As is obvious, rungms needs some modifying.

username@machinename:~$ nano rungms

Scroll down until you see the following:

set TARGET=sockets set SCR=/scr/$USER set USERSCR=~$USER/scr set GMSPATH=/u1/mike/gamess

Given that it’s just me on the machine, I tend to simplify this by making SCR and USERSCR the same directory, and I make them both /tmp. If you intend on keeping all of the files, you’ll need to make rungms specific for each run case. My only concerns are .dat and .log, so /tmp dumping is fine. Furthermore, we must change GMSPATH from how the ever-helpful Mike Schmidt (he got me through some early issues when I started my GAMESS-US adventure 15ish years ago. Won’t complain about his continued default-ed presence in the scripts) has it set up at Iowa to how we want it on our own machines (in my case, /opt/gamess)

set TARGET=sockets set SCR=/tmp set USERSCR=/tmp set GMSPATH=/opt/gamess

With these modifications, your next run will be a bit more successful:

username@machinename:~$ ./rungms test.inp

----- GAMESS execution script 'rungms' ----- This job is running on host machinename under operating system Linux at Fri Apr 4 22:51:35 EDT 2014 Available scratch disk space (Kbyte units) at beginning of the job is Filesystem 1K-blocks Used Available Use% Mounted on /dev/sda2 1905222596 249225412 1559217460 14% / GAMESS temporary binary files will be written to /tmp GAMESS supplementary output files will be written to /tmp Copying input file test.inp to your run's scratch directory... cp test.inp /tmp/test.F05 unset echo /opt/gamess/ddikick.x /opt/gamess/gamess.00.x test -ddi 1 1 machinename -scr /tmp Distributed Data Interface kickoff program. Initiating 1 compute processes on 1 nodes to run the following command: /opt/gamess/gamess.00.x test ****************************************************** * GAMESS VERSION = 1 MAY 2013 (R1) * * FROM IOWA STATE UNIVERSITY * * M.W.SCHMIDT, K.K.BALDRIDGE, J.A.BOATZ, S.T.ELBERT, * * M.S.GORDON, J.H.JENSEN, S.KOSEKI, N.MATSUNAGA, * * K.A.NGUYEN, S.J.SU, T.L.WINDUS, * * TOGETHER WITH M.DUPUIS, J.A.MONTGOMERY * * J.COMPUT.CHEM. 14, 1347-1363(1993) * **************** 64 BIT LINUX VERSION **************** ... INPUT CARD> DDI Process 0: shmget returned an error. Error EINVAL: Attempting to create 160525768 bytes of shared memory. Check system limits on the size of SysV shared memory segments. The file ~/gamess/ddi/readme.ddi contains information on how to display the current SystemV memory settings, and how to increase their sizes. Increasing the setting requires the root password, and usually a sytem reboot. DDI Process 0: error code 911 ddikick.x: application process 0 quit unexpectedly. ddikick.x: Fatal error detected. The error is most likely to be in the application, so check for input errors, disk space, memory needs, application bugs, etc. ddikick.x will now clean up all processes, and exit... ddikick.x: Sending kill signal to DDI processes. ddikick.x: Execution terminated due to error(s). unset echo ----- accounting info ----- Files used on the master node machinename were: -rw-r--r-- 1 username username 0 2014-04-04 22:51 /tmp/test.dat -rw-r--r-- 1 username username 1341 2014-04-04 22:51 /tmp/test.F05 ls: No match. ls: No match. ls: No match. Fri Apr 4 22:51:36 EDT 2014 0.0u 0.0s 0:01.08 9.2% 0+0k 0+8io 0pf+0w

Things worked, but with a memory error. This issue is discussed at the Baldridge Group wiki: ocikbapps.uzh.ch/kbwiki/gamess_troubleshooting.html

From the wiki:

If you are sure you are not asking for too much memory in the input file, check that your kernel parameters are not allowing enough memory to be requested. You might have to increase the SHMALL & SHMAX kernel memory values to allow GAMESS to run. (See http://www.pythian.com/news/245/the-mysterious-world-of-shmmax-and-shmall/ for a better explanation.)
For example, on a machine with 4GB of memory, you might add these to /etc/sysctl.conf:
# cat /etc/sysctl.conf | grep shm
kernel.shmmax = 3064372224
kernel.shmall = 748137
Then set the new settings like so:
# sysctl -p
Since they are in /etc/sysctl.conf, they will automatically be set each time the system is booted.

In our case, we modify sysctl.conf with the recommendations from the wiki:

username@machinename:~$ sudo nano /etc/sysctl.conf

Add the following to the bottom of the file:

kernel.shmmax = 3064372224 kernel.shmall = 748137

Save and exit.

username@machinename:~$ sudo sysctl -p

net.ipv4.ip_forward = 1 kernel.shmmax = 3064372224 kernel.shmall = 748137

These memory values will change depending on your system.

Now we empty the /tmp and rerun.

username@machinename:~$ rm /tmp/*
username@machinename:~$ ./rungms test.inp

If your input file is worth it’s salt, you’ll have successfully run your file on a single processor (single core, that is). If you run into additional memory errors, increase kernel.shmmax and kernel.shmall.

Now, onto the SMP part. My first attempt to run games in parallel (on 4 cores using version 00) produced the following error:

username@machinename:~$ rm /tmp/*
username@machinename:~$ ./rungms test.inp 00 4

----- GAMESS execution script 'rungms' ----- This job is running on host machinename under operating system Linux at Fri Apr 4 22:52:52 EDT 2014 Available scratch disk space (Kbyte units) at beginning of the job is Filesystem 1K-blocks Used Available Use% Mounted on /dev/sda2 1905222596 249225416 1559217456 14% / GAMESS temporary binary files will be written to /tmp GAMESS supplementary output files will be written to /tmp Copying input file test.inp to your run's scratch directory... cp test.inp /tmp/test.F05 unset echo I do not know how to run this node in parallel.

I tried a number of stupid things to get the run to work, finally settling on modifying the rungms file properly. To make gamess know how to run the node in parallel, we need only make the following changes to our rungms file.

username@machinename:~$ nano rungms

Scroll down until you find the section below:

# 2. This is an example of how to run on a multi-core SMP enclosure, # where all CPUs (aka COREs) are inside a -single- NODE. # At other locations, you may wish to consider some of the examples # that follow below, after commenting out this ISU specific part. if ($NCPUS > 1) then switch (`hostname`) case se.msg.chem.iastate.edu: case sb.msg.chem.iastate.edu: if ($NCPUS > 2) set NCPUS=4 set NNODES=1

The change is simple. We remove the cases for $NCPUS > 1 in the file and add the hostname of our linux box (and if you don’t know this or it’s not in your prompt, simply type hostname at the prompt first). We’ll disable the two cases listed and add our hostname to the case list.

# 2. This is an example of how to run on a multi-core SMP enclosure, # where all CPUs (aka COREs) are inside a -single- NODE. # At other locations, you may wish to consider some of the examples # that follow below, after commenting out this ISU specific part. if ($NCPUS > 1) then switch (`hostname`) case machinename: # case se.msg.chem.iastate.edu: # case sb.msg.chem.iastate.edu: if ($NCPUS > 2) set NCPUS=4 set NNODES=1

This gives you parallel functionality, but it’s still not using the machine resources (cores) correctly when I ask for anything more than 2 cores (always using only 2 cores).

[minor complaint]
Admittedly, I don’t immediately get the logic of this section as currently coded, as one cannot get more than 2 cores to work in this case given how the if statements are written (so far as I can see now. I will assume I am the one missing something but have not decided to ask about it, instead changing the rungms text to the following). You can check this yourself by running top in another window. This is the most simple modification, and assumes you want to run N number of cores each time. Clearly, you can make this more elegant than it is (my modification, that is). Meantime, I want to run 4 cores on this machine, so I change the section to reflect a 4-core board (and commented out much of this section).
[/complaint]

# 2. This is an example of how to run on a multi-core SMP enclosure, # where all CPUs (aka COREs) are inside a -single- NODE. # At other locations, you may wish to consider some of the examples # that follow below, after commenting out this ISU specific part. if ($NCPUS > 1) then switch (`hostname`) case machinename # case se.msg.chem.iastate.edu: # case sb.msg.chem.iastate.edu: # if ($NCPUS > 2) set NCPUS=2 # set NNODES=1 # set HOSTLIST=(`hostname`:cpus=$NCPUS) # breaksw # case machinename # case br.msg.chem.iastate.edu: if ($NCPUS >= 4) set NCPUS=4 set NNODES=1 set HOSTLIST=(`hostname`:cpus=$NCPUS) breaksw case machinename # case cd.msg.chem.iastate.edu: # case zn.msg.chem.iastate.edu: # case ni.msg.chem.iastate.edu: # case co.msg.chem.iastate.edu: # case pb.msg.chem.iastate.edu: # case bi.msg.chem.iastate.edu: # case po.msg.chem.iastate.edu: # case at.msg.chem.iastate.edu: # case sc.msg.chem.iastate.edu: # if ($NCPUS > 4) set NCPUS=4 # set NNODES=1 # set HOSTLIST=(`hostname`:cpus=$NCPUS) # breaksw # case ga.msg.chem.iastate.edu: # case ge.msg.chem.iastate.edu: # case gd.msg.chem.iastate.edu: # if ($NCPUS > 6) set NCPUS=6 # set NNODES=1 # set HOSTLIST=(`hostname`:cpus=$NCPUS) # breaksw default: echo I do not know how to run this node in parallel. exit 20 endsw endif #

And, with this set of changes, I’m using all 4 cores on the board (but have some significant memory issues when running MP2 calks. But that’s for another post).

The typical user will never be able to do what the GAMESS group has done in making an excellent program that also happens to be free. That said, the need to make changes to the rungms file is something that would be greatly simplified by having N number of rungms scripts for each case instead of a monolithic file that is mostly useless text to users not using one of the system types. This, for instance, would make rungms modification much easier. If I streamline rungms for my specific system, I may post a new file accordingly.

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