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

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

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.

Afrika Bambaataa Via DJ Shadow And Cut Chemist, Westcott Theater, 10 November 2014 – Photo Gallery On LiveHighFive.com And Flickr

December 3rd, 2014

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A bit of a diversion from the usual posting faire, I had the privilege of catching the Syracuse stop of DJ Shadow and Cut Chemist’s Renegades of Rhythm tour from the other side of the security gate (for the first 10 minutes, anyway, then a bunch from the back). 80% performance and 20% history lesson, the set featured selections from Afrika Bambaataa’s own vinyl collection (current in the process of digitization at Cornell Library, where hip hop’s Amen Ra currently graces the campus as a Visiting Scholar).

The extra-special access provided through arrangement between the performers and Gregory Allis of, among other things, Live High Five. From Greg’s post of the event at livehighfive.com:

DJ Shadow and Cut Chemist brought their touring ethnomusicology lesson to a respectable and excited crowd on a cold Tuesday in Syracuse, NY a few weeks back. After catching the show in Austin during the tour’s first leg, it was pretty much mandatory to follow up with a second helping of tunes cultivated from Afrika Bambaataa’s personal stash. It isn’t often that the longtime friends pair up and bring their skills on the road, but it’s always a spectacle when they do!

A few things need to be said: 1) Hip Hop = DJ’s, MC’s, Breakdancing, and Graffiti, 2) DJ Shadow and Cut Chemist incorporated all those elements into the performance and tour, 3) Afrika Bambaataa deserves every ounce of recognition he has coming to him, and 4) the beginning of Boogie Down Production’s “South Bronx” is one of the hardest things on Earth.

For the full set, off to flickr -> flickr.com/photos/somewhereville/sets/72157649174784268/

Different X-Axis Values, But The Same X-Axis Units – Getting Excel 2013 (OSX-Specific) To Produce Multiple Scatter Plots On The Same Graph

November 18th, 2014

Posting a workaround to re-introduce a feature for Excel 2013 that I think was removed for some reason and for which information on Excel 2013 (OSX-specific) is impossible to find through google searches. It is my hope that newer versions of Excel don’t have this thoroughly annoying problem (and if there’s an obvious way I don’t know about to make this happen in a single shot, feel free to drop a line).

If you found this page via google, I’m going to assume you were searching for something like the following questions (which I’m including below so that search engines find similar questions):

How do I add:
– data with two different X-axes to a single plot in Excel?
– multiple plots to the same graph in Excel with different X-values but the same X-axis units?
– a second dataset to a plot in Excel with new X-axis values?
– a new dataset with different abscissa values in Excel?
– a secondary X-axis to plot new data on the same graph in Excel?

My Scenario – Overlaying Two Spectra On The Same Graph

This issue came up for me when trying to generate some simple spectral overlays in Excel. The problem proceeds as follows:

1. You’ve two datasets with the same X-axis values.

2. You’ve a third dataset for which the X-axis points have the same units, but different values.

3. You plot this third dataset with Chart… -> Add Data by selecting your X-axis and Y-axis values (just selecting the columns).

4. You don’t get the expected results.

Ideally, Excel would see that the headers for the X-axis columns have the same exact labels in all the datasets and treat the new points (in Step 3) as values to be accounted for within the same range of numbers as the previous plot. If you plot dataset 1 and add dataset 2, there’s no problem (because the X-axis column is identical). Step 3 will set you back an hour or so (assuming this isn’t in the Help Pages, which take too long to load anyway).

The steps below describe a way to recover an old functionality in Excel 2007 that just simply worked without issue.

1. My Working Excel Sheet

To set the stage, my sheet is set up as shown below.

2014nov18_excel_1

Rows 7-3115 and 3122-3498 are hidden for clarity
Col A: cm-1 – my X-axis values, with label
Col B: Exp.: Time=0 – My first dataset
Col C: Exp.: Time=20 – My second dataset; uses the same X-axis values as Col B (cm-1)
Col F: cm-1 – my X-axis values for a new dataset (in G,H), scalable using Cell J2
Col G: Theory – my calculated values
Col H: Theory (Scaled) – my calculated values in Col G, scalable using Cell J5
Col J Rows 1,2: X Scaling – used to scale the values of the calculated data along the X-axis (actual values in Col E)
Col J Rows 4,5: Y Scaling – used to scale the values of the calculated data along the Y-axis (Col H)

To explain briefly (for the non-spectroscopists), your calculated X-axis (energy, here in wavenumbers) and Y-axis (intensity) values are/can be adjusted for better agreement with experiment. In this case, I’m applying a global scalar to the X-axis (Cell J2 – make the plot wider or narrower) and Y-axis (Cel J5 – make the plot taller or shorter) values. These values will be adjusted to taste in the final images. I’m going into a little more detail than one would otherwise need because how you make your data fit properly will depend on how you change the source data (and not doing it properly will lead to a fitting problem. You’ll see shortly).

2. First + Second Plottings

After plotting the first dataset (Col A + Col B) as a Scatter Plot and doing some cleaning up, you get the image below.

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To add the data in Col C (which we see already uses the same X-axis values as Col B), you simply go to Chart -> Add Data, select Col C, and you should get the image below (20 min data in green):

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3. Where The Trouble Starts

To this new plot we want to add the Theory results. You’ll note that the experimental X-axis values differ in their increments from the theoretical data. But X-axis values are X-axis values, right?

Go to Chart -> Add Data, then select the new X/Y data you want to include in the plot. When adding the data, you should see the following.

2014nov18_excel_4

Not cool. Instead of reading Col F as new X-axis values with the same units (with Excel 2007 did just fine), Excel 2013 sees this as a new dataset using the original X-axis values in Col A. The Theory plot in Col H (red) looks like it worked, but you’ll see shortly that the defaulting to the X-axis values in Col A has resulted in very poor agreement with experiment (and it’s the wrong X-axis values, so this is no surprise).

First off, the cm-1 (black) values are bogus, so delete that dataset to beautify the plot. That image is below.

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4. Partial Fix (Nearly The Same As The Full Fix)

We clean up the spectrum by right-clicking on the plot and choosing Select Data… (shown below)

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This will take you to a Select Data Source window where one of the Series will be selected. Click on the dataset you want to change the X-axis column for (here, Theory (Scaled)). You will see next to the obvious red arrow that the X values: column is reading $A$2:$A$3501. You’ll note that Col A has no data in cell A3501 (that’s bad enough).

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Now, for the Partial Fix, double-click on the content of X values: to select it all, and then click on the column you want the X-axis values to be (for me, Col F). X values: will become the following:

2014nov18_excel_8

If you do this and hit OK, you’ll see the plot below, which is just what you expected from a well-behaved Excel program.

2014nov18_excel_9

Your X-axis is as it should be, even if the peak intensities for the theory are too high. That you can remedy by changing Cell J5 (results below).

2014nov18_excel_10

That is much better, but you can see that the most prominent peaks (around 1600 cm-1) are calculated too high. This is why there’s a scaling factor in Cell J2. If you change the value of Cell J2 to, say, 0.973, you produce the following plot:

2014nov18_excel_10

Which, as you can see, is exactly the same as the previous plot. Our X-axis scaling factor had no affect.

5. And Now, The Full Fix

We selected the new X-axis column (Col F) correctly, but Excel won’t give us our proper scaling unless we specifically define the range of cells used for the X-axis values. So, we go back to Select Data… (right click) and put the actual cell numbers in. At the obvious red arrow below…

2014nov18_excel_12

Change the $F:$F to our actual range, $F$2:$F$3501

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Hit OK. If you didn’t change your J2 value back to 1, you should see that your plot slid right into place (granted, the theory doesn’t line up all that well anyway, but that’s a problem for a different post).

2014nov18_excel_14

And that’s it. May this post spare you the time wasted searching for a solution to a problem that didn’t previously exist.

“Stu’s Last Lesson” – Sky & Telescope’s Focal Point For December, 2014

October 23rd, 2014

As posted on the CNY Observers website (direct link).

Greetings fellow astrophiles,

2014oct23_stuDr. Stuart Forster (a.k.a. STU – full caps) was one of the THE fixtures in the CNY amateur astronomy scene and his name still comes up regularly, often as part of some pearl of wisdom being imparted to new observers and seasoned members alike (I’ll leave you to read the top of the Stuventory page for more info about STU and to check out links to some of his images on the Syracuse Astronomical Society website). The trials and tribulations of Ryan Goodson and myself to handle the massive equipment collection we’ve come to refer to as the “Stuventory” is olde hat to local observers who’ve kept track of the process from a far. The sorting, documenting, and distribution of the Stuventory has taught us both about how very unique the hobby of amateur astronomy can be when you step beyond the 1×7 mm binoculars in your head and effort the collection of more and more photons.

To that end, and to prod others to recognize the complexities of sorting through the mound of gear inhabiting their basements, garages, and domes by those who follow when the unexpected happens, I am honored to have an article on the topic, “Stu’s Last Lesson,” included as the December 2014 Focal Point in Sky & Telescope magazine.

2014oct23_stuslastlesson

The article can be distilled to a single, all-encompassing message – Imagine you not being around to help your family unload your astro gear, then take steps to simplify their lives. Think about all the boxes, hex wrenches, leftover focusers and brackets from your modifications to other scopes, eyepieces (eyepieces!), cables, controllers, everything, and organize it all, either in a notebook or with a bunch of pics and notes on your smartphone.

If you read the article and have other ideas on how to help organize your equipment, by all means let others know (post a comment here, write a letter to the editor with your ideas, start a cloudynights.com thread, etc.). In the meantime, I hope the article gives you the impetus to block out a Saturday afternoon listening to astronomy.fm as you commit your astronomical obsession to pen and paper (or keyboard and monitor). Better still, I’m pleased that readers of Sky & Telescope (of which he had the full collection back to 1964) will learn a little bit about one of CNY’s great amateur astronomers.

Obligatory

  • CNYO

  • Sol. Sys. Amb.

  • Ubuntu 4 Nano

  • NMT Review

  • N-Fact. Collab.

  • Pres. Asn. CNY

  • T R P Nanosys

  • Nano Gallery

  • nano gallery
  • Aerial Photos

    More @ flickr.com

    Syracuse Scenes

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