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

Tuesday, December 30th, 2014

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

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

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

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

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

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

Note 1: Trust But Verify; RHF

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

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

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

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

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

NOTE 2: B3LYP vs. B3LYP

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

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

You can interpret this as:

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

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

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

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

NOTE 3: A Slight Aside For The Gaussian User

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

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

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

H2 optimization and normal mode analysis

0 1
H 0.000 0.000 0.000
H 1.000 0.000 0.000

Produces:

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

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

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

H2 optimization

0 1
H 0.000 0.000 0.000
H 1.000 0.000 0.000

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

H2 normal mode analysis

0 1

Produces:

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

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

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

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

> Gaussian 98 - CRYSTAL03 energy 


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


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

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

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

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

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

The CRYSTAL input is as follows:

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

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

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

Neopentane                                                                      

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

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

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

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

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

Then do the following for Gaussian:

# 5D 7F

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

NOTE 5: DFT Calculations Are A Completely Different Matter

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

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

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

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

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

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

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

2014dec3_gaussianshells

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

Gaussian Specifications:

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

CRYSTAL Specifications:

Again, a few pre-defined grids are available.

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

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

In GAMESS, you specify the components.

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

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

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

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

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

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

NOTE 7: The Optimizers Affect The Final Energies

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

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

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

 GRADIENT NORM     0.000001  GRADIENT THRESHOLD     0.500000

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

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

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

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

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

The test structures can be broken into three categories:

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

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

2. Homodimers As Forced Singlets

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

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

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

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

3. Hydrides For Some Non-Ideal Homodimer Optimizations

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

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

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

NOTE 9: What’s Good Enough?

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

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

NOTE 10: Keywords

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

Parse The RHF Calculations As Follows:

H2__rhf__631Gdp__BOHRANGS__NOBIPOLA__10sTOLINTEG__TOLDEP__GAUSS98

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

H2
rhf
631Gdp
BOHRANGS
NOBIPOLA
10sTOLINTEG
TOLDEP
GAUSS98

Additional for the DFT calculations:

DefGRID__BOHRANGS__NOBIPOLA__20sTOLINTEG__TOLDEP__GAUSS98

Differ by the specification of the grid.

DefGRID
LGRID
XLGRID
XXLGRID

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

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

2014nov30_testinglabels

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

B3LYP
END

RHF
END

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

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

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

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

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

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

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

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




And, Finally…

The Files

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

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

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

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

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


The 6-31G Gaussian-Type Basis Sets

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


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

In order and in CRYSTAL format below:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


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

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


References

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

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

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

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

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

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

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

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

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

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

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

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

Isotopically-Labeled Solid-State Vibrational Mode Energies And Intensities In Crystal09 – A Simple How-To

Wednesday, November 21st, 2012

The generation of isotopically-substituted molecular crystal spectra has become a point of interest, which means blog post. To be clear, this is for cases where isotopic substitution does not affect the crystal geometry – the crystal cell does not change significantly upon deuteration (and for those who believe isotopic substitution never leads to significant changes in the solid, I refer you Zhou, Kye, and Harbison’s article on Isotopomeric Polymprphism and their work on 4-methylpyridine pentachlorophenol, which changes dramatically upon deuteration. I beat on this point because blindly assuming of the crystal cell geometry in such cases will produce spectra noticeably different than measured. It’s NOT the calculation’s fault!).

The generation of isotopically-substituted spectra and intensities in Crystal09 is trivial provided that you KEEP THE FREQINFO.DAT FILE. In fact, you need keep ONLY the FREQINFO.DAT to generate these spectra, which greatly reduces file transfer loads and allows for the scripted calculation of new vibrational spectra and thermodynamic data post-frequency calculation.

As my example system, I’m using the dispersion-corrected crystal cell of alpha-HMX (I have it handy, it’s a small system, and having anything about HMX on your website is proven to increase traffic) at the B3LYP/6-31G(d,p) level of theory. Original input file (the one where the original normal mode analysis is performed) is below:

Test - alpha-HMX 6-31Gdp set DFT/B3LYP FREQ
CRYSTAL
0 0 0
43
15.14 23.89 5.913 124.3
14
6      1.016493675797E-01 -4.109909899348E-02 -3.351438244488E-03
6     -6.539109813231E-02 -6.180633576707E-02 -1.110575784790E-02
1      9.149797846691E-02 -4.382919469310E-02 -1.860042940246E-01
1      1.558888705857E-01 -6.829708099502E-02  4.595161229829E-02
1     -5.138242817334E-02 -5.844587273099E-02 -1.920922064181E-01
1     -9.781600273101E-02 -1.015710562102E-01  2.063738273292E-02
7      1.992579327285E-02 -5.951921578598E-02  1.040704228546E-01
7      1.232154652110E-01  1.634305404407E-02  5.951841980010E-02
7      2.220759010770E-02 -7.142100857312E-02  3.299259852838E-01
7      2.054067942916E-01  2.817244373261E-02  1.473285310628E-01
8     -4.761487685316E-02 -8.656669456613E-02  4.192568497756E-01
8      9.327421157186E-02 -6.479426971916E-02  4.286363161888E-01
8      2.563441491059E-01 -1.128705054032E-02  1.760581823035E-01
8      2.225071782791E-01  7.736574474011E-02  1.903699942346E-01
FREQCALC
INTENS
END
END
8 4
0 0 6 2.0 1.0
 5484.671700         0.1831100000E-02
 825.2349500         0.1395010000E-01
 188.0469600         0.6844510000E-01
 52.96450000         0.2327143000    
 16.89757000         0.4701930000    
 5.799635300         0.3585209000  
0 1 3 6.0 1.0
 15.53961600        -0.1107775000         0.7087430000E-01
 3.599933600        -0.1480263000         0.3397528000    
 1.013761800          1.130767000         0.7271586000    
0 1 1 0.0 1.0
 0.2700058000          1.000000000          1.000000000
0 3 1 0.0 1.0
 0.800000000          1.00000000    
7 4
0 0 6 2.0 1.0
       4173.51100         0.183480000E-02
       627.457900         0.139950000E-01
       142.902100         0.685870000E-01
       40.2343300         0.232241000    
       12.8202100         0.469070000    
       4.39043700         0.360455000    
0 1 3 5.0 1.0
       11.6263580        -0.114961000         0.675800000E-01
       2.71628000        -0.169118000         0.323907000    
      0.772218000          1.14585200         0.740895000    
0 1 1 0.0 1.0
      0.212031300          1.00000000          1.00000000    
0 3 1 0.0 1.0
 0.800000000          1.00000000    
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
END
DFT
B3LYP
XLGRID
END
EXCHSIZE
10654700
BIPOSIZE
10654700
TOLINTEG
8 8 8 8 16
SCFDIR
MAXCYCLE
100
TOLDEE
11
GRIMME
1.05 20. 25.
4
1 0.14 1.001
6 1.75 1.452 
7 1.23 1.397
8 0.70 1.342
SHRINK
8 8
LEVSHIFT
5 0
FMIXING
50
END
END

Upon completion of this run, you need only the FREQINFO.DAT file, the last set of coordinates from the .OUT file (for atom counting purposes) and an input file which is modified from the original only in the specification of the ISOTOPES section and which includes a RESTART.

Question – how does one deal with isotopically-labeling atoms when it breaks the space group symmetry? If I isotopically label Atom 1 in the asymmetric unit, what happens to the other N symmetry-related atoms?

Answer – Crystal09, in its infinite wisdom, does not consider the asymmetric unit in the isotopic substitution scheme. If you’ve 14 atoms in the asymmetric unit (the symmetry-unique atoms you provide in the input file)…

14
6      1.016493675797E-01 -4.109909899348E-02 -3.351438244488E-03
6     -6.539109813231E-02 -6.180633576707E-02 -1.110575784790E-02
...
8      2.563441491059E-01 -1.128705054032E-02  1.760581823035E-01
8      2.225071782791E-01  7.736574474011E-02  1.903699942346E-01

and 56 atoms in the full unit cell…

ATOMS IN THE ASYMMETRIC UNIT   14 - ATOMS IN THE UNIT CELL:   56
     ATOM              X/A                 Y/B                 Z/C    
 *******************************************************************************
   1 T   6 C    -1.460999048177E-01  1.393970283287E-01  6.390170683069E-02
   2 F   6 C     1.393970283287E-01 -1.460999048177E-01 -5.719883034171E-02
   3 F   6 C     3.071988303417E-01  1.860982931693E-01  1.106029716713E-01
   4 F   6 C     1.860982931693E-01  3.071988303417E-01  3.960999048177E-01
...
  53 T   8 O     4.522856069554E-02  3.355114277736E-01  1.095029287847E-01
  54 F   8 O     3.355114277736E-01  4.522856069554E-02 -4.902429172538E-01
  55 F   8 O    -2.597570827462E-01  1.404970712153E-01 -8.551142777356E-02
  56 F   8 O     1.404970712153E-01 -2.597570827462E-01  2.047714393045E-01

your ISOTOPES section relies on the numbering of the atoms in the “56 atom” list.

The input file below will calculate an isotopically-labeled vibrational spectrum for 8 of the hydrogen atoms that ends up breaking the unit cell symmetry (which will be more obvious from the produced mode energies). Again, the atom numbers come from the “ATOMS IN THE ASYMMETRIC UNIT” part of the original optimization by which you performed the original normal mode analysis (hopefully).

Test - alpha-HMX 6-31Gdp set DFT/B3LYP FREQ - Isotopic Substitution
CRYSTAL
0 0 0
43
15.14 23.89 5.913 124.3
14
6      1.016493675797E-01 -4.109909899348E-02 -3.351438244488E-03
6     -6.539109813231E-02 -6.180633576707E-02 -1.110575784790E-02
1      9.149797846691E-02 -4.382919469310E-02 -1.860042940246E-01
1      1.558888705857E-01 -6.829708099502E-02  4.595161229829E-02
1     -5.138242817334E-02 -5.844587273099E-02 -1.920922064181E-01
1     -9.781600273101E-02 -1.015710562102E-01  2.063738273292E-02
7      1.992579327285E-02 -5.951921578598E-02  1.040704228546E-01
7      1.232154652110E-01  1.634305404407E-02  5.951841980010E-02
7      2.220759010770E-02 -7.142100857312E-02  3.299259852838E-01
7      2.054067942916E-01  2.817244373261E-02  1.473285310628E-01
8     -4.761487685316E-02 -8.656669456613E-02  4.192568497756E-01
8      9.327421157186E-02 -6.479426971916E-02  4.286363161888E-01
8      2.563441491059E-01 -1.128705054032E-02  1.760581823035E-01
8      2.225071782791E-01  7.736574474011E-02  1.903699942346E-01
FREQCALC
RESTART
ISOTOPES
8
9  2
10 2
11 2
13 2
14 2
15 2
16 2
18 2
INTENS
END
END
8 4
0 0 6 2.0 1.0
 5484.671700         0.1831100000E-02
 825.2349500         0.1395010000E-01
 188.0469600         0.6844510000E-01
 52.96450000         0.2327143000    
 16.89757000         0.4701930000    
 5.799635300         0.3585209000  
0 1 3 6.0 1.0
 15.53961600        -0.1107775000         0.7087430000E-01
 3.599933600        -0.1480263000         0.3397528000    
 1.013761800          1.130767000         0.7271586000    
0 1 1 0.0 1.0
 0.2700058000          1.000000000          1.000000000
0 3 1 0.0 1.0
 0.800000000          1.00000000    
7 4
0 0 6 2.0 1.0
       4173.51100         0.183480000E-02
       627.457900         0.139950000E-01
       142.902100         0.685870000E-01
       40.2343300         0.232241000    
       12.8202100         0.469070000    
       4.39043700         0.360455000    
0 1 3 5.0 1.0
       11.6263580        -0.114961000         0.675800000E-01
       2.71628000        -0.169118000         0.323907000    
      0.772218000          1.14585200         0.740895000    
0 1 1 0.0 1.0
      0.212031300          1.00000000          1.00000000    
0 3 1 0.0 1.0
 0.800000000          1.00000000    
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
END
DFT
B3LYP
XLGRID
END
EXCHSIZE
10654700
BIPOSIZE
10654700
TOLINTEG
8 8 8 8 16
SCFDIR
MAXCYCLE
100
TOLDEE
11
GRIMME
1.05 20. 25.
4
1 0.14 1.001
6 1.75 1.452 
7 1.23 1.397
8 0.70 1.342
SHRINK
8 8
LEVSHIFT
5 0
FMIXING
50
END
END

The difference is in the FREQCALC section, which calls RESTART (to use the FREQINFO.DAT file), ISOTOPES (obvious), the total number of atoms that are having their isotopes changed (8), then the list, containing the atom number and the new mass (here, 2 for deuterium).

The proof is in the high-frequency region, where the last 16 modes (H-atom motion) in the non-deuterated form…

 HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH

    MODES         EIGV          FREQUENCIES     IRREP  IR   INTENS    RAMAN
             (HARTREE**2)   (CM**-1)     (THZ)             (KM/MOL)
...
  153- 153    0.2003E-03   3106.1384   93.1197  (A2 )   I (     0.00)   A
  154- 154    0.2003E-03   3106.5054   93.1307  (B1 )   A (     0.02)   A
  155- 155    0.2004E-03   3106.5586   93.1323  (A1 )   A (     0.23)   A
  156- 156    0.2004E-03   3106.8420   93.1408  (B2 )   A (     0.48)   A
  157- 157    0.2017E-03   3117.1664   93.4503  (B2 )   A (     1.13)   A
  158- 158    0.2018E-03   3117.4901   93.4600  (B1 )   A (     2.33)   A
  159- 159    0.2021E-03   3120.2876   93.5439  (A1 )   A (   115.24)   A
  160- 160    0.2022E-03   3120.7805   93.5586  (A2 )   I (     0.00)   A
  161- 161    0.2131E-03   3203.6552   96.0432  (A1 )   A (    44.59)   A
  162- 162    0.2131E-03   3203.6581   96.0433  (B2 )   A (   115.98)   A
  163- 163    0.2132E-03   3204.6505   96.0730  (B1 )   A (    15.30)   A
  164- 164    0.2132E-03   3204.8874   96.0801  (A2 )   I (     0.00)   A
  165- 165    0.2157E-03   3223.4669   96.6371  (A1 )   A (    44.98)   A
  166- 166    0.2157E-03   3223.5803   96.6405  (B2 )   A (    27.02)   A
  167- 167    0.2158E-03   3223.8536   96.6487  (B1 )   A (    35.26)   A
  168- 168    0.2158E-03   3224.3355   96.6631  (A2 )   I (     0.00)   A

change to the following last 16 modes (H/D-atom motion) upon deuteration. Note the mode energies split and the mode symmetries go from (A1,A2,B1,B2) to (A). Also note your IR mode intensities change, giving you the complete picture upon isotopic substitution.

 HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH

    MODES         EIGV          FREQUENCIES     IRREP  IR   INTENS    RAMAN
             (HARTREE**2)   (CM**-1)     (THZ)             (KM/MOL)
...
  153- 153    0.1074E-03   2274.8942   68.1996  (A  )   A (     1.07)   A
  154- 154    0.1075E-03   2275.5949   68.2206  (A  )   A (     3.75)   A
  155- 155    0.1075E-03   2275.7008   68.2238  (A  )   A (     2.93)   A
  156- 156    0.1099E-03   2300.7446   68.9746  (A  )   A (     4.68)   A
  157- 157    0.1148E-03   2351.7846   70.5047  (A  )   A (    11.32)   A
  158- 158    0.1183E-03   2387.0269   71.5613  (A  )   A (    36.17)   A
  159- 159    0.1183E-03   2387.2610   71.5683  (A  )   A (    16.04)   A
  160- 160    0.1184E-03   2387.6687   71.5805  (A  )   A (     3.73)   A
  161- 161    0.2006E-03   3108.6223   93.1942  (A  )   A (     0.93)   A
  162- 162    0.2009E-03   3110.5061   93.2506  (A  )   A (    12.43)   A
  163- 163    0.2009E-03   3110.7567   93.2581  (A  )   A (    13.67)   A
  164- 164    0.2039E-03   3134.0133   93.9554  (A  )   A (    40.48)   A
  165- 165    0.2147E-03   3215.5160   96.3987  (A  )   A (    19.38)   A
  166- 166    0.2157E-03   3223.4291   96.6360  (A  )   A (    35.29)   A
  167- 167    0.2157E-03   3223.5925   96.6409  (A  )   A (    29.50)   A
  168- 168    0.2158E-03   3223.8729   96.6493  (A  )   A (     8.37)   A

Running (Only) A Single-Point Energy Calculation In Crystal06/09, Proper Input Format For Long-Range Dispersion Contributions In Crystal09, And Removing The MPICH2 Content From The Output File In Pcrystal

Saturday, May 29th, 2010

Now enjoying the benefits of dispersion-corrected solid-state density functional theory (and a proper MPICH2 implementation for infrared intensity calculations, although this now a problem for reasons to be addressed in an upcoming post) in Crystal09, three issues in recent calculations caused me to think hard enough about keyword formats and job runs that I have opted to post briefly about what to do in case google and bing are your preferred methods of manual searching.

1. How To Run Only A Single-Point Energy Calculation In Crystal06/Crystal09

This had never come up before and, by the time I needed to find an input file to see what do to, the first google search provided Civalleri’s Total Energy Calculation page that currently has broken links to .zip files. There is quite a bit about the different geometry optimization approaches in the manual, but a search for “single-point” provides no information about what to do for only single-point energy calculations.

The solution, it should be obvious after, is simply to not include the geometry optimization section in the input file. What would otherwise be the following (with arbitrary geometry optimization-like info between [COORDINATES] and [BASIS SETS]…

[COORDINATES]
OPTGEOM
TOLDEG
0.000005
TOLDEX
0.000020
END
END
[BASIS SETS]

becomes…

[COORDINATES]
[BASIS SETS]

One problem solved by simply not having any optimization parameters (again, makes sense and is now google-able).

2. Proper GRIMME Input Format For Long-Range Dispersion Contributions In Crystal09

This is another example where one’s first efforts in translating the manual into calculations may lead to considerable confusion until the proper format is finally identified (by which time you’ve run many pruned-down input tests).

GRIMME
1.05 20. 25.
1.05 20. 25. s6 (scaling factor) d (steepness) Rcut (cutoff radius)
5
1  0.14 1.001 Hydrogen Conventional Atomic number , C6 , Rvdw
6  1.75 1.452 Carbon Conventional Atomic number , C6 , Rvdw
7  1.23 1.397 Nitrogen Conventional Atomic number , C6 , Rvdw
8  0.70 1.342 Oxygen Conventional Atomic number , C6 , Rvdw
17 5.07 1.639 Chlorine Conventional Atomic number , C6 ,'Rvdw

I’m not even sure where the final ,’Rvdw comes from. Your .out file may terminate with the following error (or something similar)…

rank 7 in job 8  korterquad_51438   caused collective abort of all ranks
  exit status of rank 7: killed by signal 9

And the ERROR.peN file with any content will show the following, clearly pointing to a GRIMME-specific error…

 ERROR **** GRIMME_INPUT **** ELEMENT NOT DEFINED:           1

The problem is the additional content within the manual pages for the GRIMME keyword that require pruning (or, at least, some identifier to show what is and what is not needed). The proper GRIMME section above is properly provided in the INPUT file as…

GRIMME
1.05 20. 25.
5
1  0.14 1.001
6  1.75 1.452
7  1.23 1.397
8  0.70 1.342
17 5.07 1.639

Where (see page 88 of the Crystal09 manual)…

GRIMME <- keyword is called
1.05 20. 25. <- scaling factor, steepness, cutoff distance
5 <- number of elements in the list (not the total number of atoms)
1  0.14 1.001 <- atomic number, dispersion coefficient, van der Waals radius
...

When all is properly run, the bottom of your output file will look something like the following:

 CYC  43 ETOT(AU) -5.784662098123E+03 DETOT  1.18E-11 tst  8.17E-15 PX  6.73E-08

 == SCF ENDED - CONVERGENCE ON ENERGY      E(AU) -5.7846620981229E+03 CYCLES  43

 ENERGY EXPRESSION=HARTREE+FOCK EXCH*0.20000+(BECKE  EXCH)*0.80000+LYP    CORR

 TOTAL ENERGY(DFT)(AU)( 43) -5.7846620981229E+03 DE 1.2E-11 tester 8.2E-15
 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT EDFT        TELAPSE     4705.82 TCPU     4651.41

 *******************************************************************************

 GRIMME DISPERSION ENERGY CORRECTION

 SCALE FACTOR (S6):     1.0500

 GRIMME DISPERSION ENERGY (AU) -1.9723347118951E-01
 TOTAL ENERGY + DISP (AU) -5.7848593315941E+03

 *******************************************************************************

The Crystal09 manual refers you to Table 1 of the Stefan Grimme paper, “Semiempirical GGA-type density functional constructed with a long-range dispersion correction” (Journal of Computational Chemistry, Volume 27, Issue 15, Pages 1787 – 1799), which I’ve put together into the proper format below. Be sure to (1) delete the elements in parentheses ( -> get rid of the (H) <- ), (2) remove those atoms you do not need, (3) be sure to change the “number of elements” number for your structure, and (4) get and reference the Grimme paper so you have the proper C6 parameters and van der Waals radii accounted for (you’ll be the right nitwit if I mis-copied something and you ran with it (although I trust my input), and you should have the reference regardless).

( H)   1   0.14 1.001
(Li)   3   1.61 0.825
(Na)  11   5.71 1.144
( K)  19  10.80 1.485
(Rb)  37  24.67 1.628
(Be)   4   1.61 1.408
(Mg)  12   5.71 1.364
(Ca)  20  10.80 1.474
(Sr)  38  24.67 1.606
( B)   5   3.13 1.485
(Al)  13  10.79 1.639
(Ga)  31  16.99 1.650
(In)  49  37.32 1.672
( C)   6   1.75 1.452
(Si)  14   9.23 1.716
(Ge)  32  17.10 1.727
(Sn)  50  38.71 1.804
( N)   7   1.23 1.397
( P)  15   7.84 1.705
(As)  33  16.37 1.760
(Sb)  51  38.44 1.881
( O)   8   0.70 1.342
( S)  16   5.57 1.683
(Se)  34  12.64 1.771
(Te)  52  31.74 1.892
( F)   9   0.75 1.287
(Cl)  17   5.07 1.639
(Br)  35  12.47 1.749
( I)  53  31.50 1.892
(He)   2   0.08 1.012
(Ne)  10   0.63 1.243
(Ar)  18   4.61 1.595
(Kr)  36  12.01 1.727
(Xe)  54  29.99 1.881
Y-Cd      24.67 1.639
Sc-Zn     10.80 1.562

Note that the d-block is identical for each row (so no atom numbers provided).

3. Removing The MPICH2 Content From The Output File In Pcrystal(/09)

This final issue does not occur in Pcrystal(/06) but does in Pcrystal(/09), with the reason being (I assume) the new use of MPICH2 in Pcrystal(/09) instead of MPICH in Pcrystal(/06).  The problem comes from running the following set of commands at the terminal window in MPICH2:

mpiexec -machinefile machine -np N /path/to/Pcrystal &>FILENAME.out &

Embedded within the FILENAME.out file will be all flavors of MPI-specific output, perhaps such as the following (in this case errors, but it happens in proper output as well):

application called MPI_Abort(MPI_COMM_WORLD, 1) - process 4
application called MPI_Abort(MPI_COMM_WORLD, 1) - process 7
rank 7 in job 9  korterquad_51438   caused collective abort of all ranks
 exit status of rank 7: return code 1 
rank 4 in job 9  korterquad_51438   caused collective abort of all ranks
 exit status of rank 4: killed by signal 9 

or…

mpiexec_machine (handle_stdin_input 1089): stdin problem; if pgm is run in background...
mpiexec_machine (handle_stdin_input 1090):     e.g.: mpiexec -n 4 a.out < /dev/null &

The solution is to break up the mpiexec output from the Pcrystal output, performed by directing the mpiexec-specific content to, in this case, /dev/null (because it is not necessary except for diagnostic purposes).

mpiexec -machinefile machine -np N /path/to/Pcrystal < /dev/null &>FILENAME.out &

Which removes all traces of mpi-specific output from FILENAME.out.

Terahertz Spectroscopic Investigation Of S-(+)-Ketamine Hydrochloride And Vibrational Assignment By Density Functional Theory, “Function Follows Functional Follows Formalism”

Sunday, February 21st, 2010

Accepted in the Journal of Physical Chemistry A, with my fingers crossed for pulling off the rare double-header in an upcoming print edition of the journal (having missed it by three intermediate articles with the Cs2B12H12 and HMX papers back in 2006 (you’d keep track, too). A fortuitous overlap of scheduled defense dates between P. Hakey, Ph.D. and M. Hudson, A.B.D.). A brief summary of interesting points from this study is provided below, including what I think is a useful point about how to most easily interpret AND represent solid-state vibrational spectra for publications.

1. AS USUAL, YOU CANNOT USE GAS-PHASE CALCULATIONS TO ASSIGN SOLID-STATE TERAHERTZ SPECTRA. It will take a phenomenal piece of data and one helluvan interpretation to convince me otherwise. As a more subtle point (for those attempting an even worse job of vibrational mode assignment), if the molecule exists in its protonated form in the solid-state, do not use the neutral form for your gas-phase calculation (this is a point that came up as part of an MDMA re-assignment published (and posted here) previously).

2. It is very difficult to find what I would consider to be “complete data sets” for molecules and solids being studied by spectroscopic and computational methods. For many molecular solids, the influences of thermal motion are not important to providing a proper vibrational analysis by solid-state density functional theory methods. Heating a crystal may make spectral lines broader, but phase changes and unusual spectral features do not often result when heating a sample from cryogenic (say, liquid nitrogen) to room temperature. Yes, there are thousands of cases where this is not true, but several fold more cases where it is. We are fortunate to live in a temperature regime where characterization is reasonably straightforward and yet we can modify a system to observe its subtle changes under standard laboratory conditions. The THz spectrum of S-(+)-Ketamine Hydrochloride gets a bit cleaner upon cooling, which makes the assignment easier. As the ultimate goal is to be able to characterize these systems in a person’s pocket instead of their liquid nitrogen thermos, the limited observed change to the spectrum upon cooling is important to note.

3. Crystal06 vs. DMol3 – This paper contains what is hoped to be a level, pragmatic discussion about the strengths and weaknesses of computational tools available to terahertz spectroscopists for use in their efforts to assign spectra. This type of discussion is, as a computational chemist using tools and not developing tools, a touchy subject to present on not because of the finger-pointing of limitations with software, but because the Crystal06 team and Accelrys (through Delley’s initial DMol3 code) clearly are doing things that the vast majority of their users (myself included) could in no way do by themselves. The analysis for the theory-minded terahertz spectroscopist is presented comparing two metrics – speed and functionality (specifically, infra-red intensity prediction). What is observed as the baseline is that both DMol3 and Crystal06 make available density functionals and basis sets that, when used at high levels of theory and rigorous convergence criteria, produce simulated terahertz spectra with vibrational mode energies that are in good (if not very good) agreement with each other. For the terahertz spectroscopist, Crystal06 provides as output (although this is system size- and basis set size-dependent) rigorous infrared intensity predictions for vibrational modes, inseparable from mode energy as “the most important” pieces of information for mode assignments. While DMol3 does not produce infrared intensities (the many previous terahertz papers I’ve worked on employed difference-dipole calculations that are, at best, a guesstimate), DMol3 produces very good mode energy predictions in 1/6th to (I’ve seen it happen) 1/10th the time of a comparable Crystal06 calculation. This is the reason DMol3 has been the go-to program for all of the neutron scattering spectroscopy papers cited on this blog (where intensity is determined by normal mode eigenvectors, which are provided by both (and any self-respecting quantum chemical code) programs).

Now, it should be noted that this difference in functionality has NOTHING to do with formalism. Both codes are excellent for what they are intended to do. To the general assignment-minded spectroscopist (the target audience of the Discussion in the paper), any major problem with Crystal06 likely originates with the time to run calculations (and, quite frankly, the time it takes to run a calculation is the worst possible reason for not running a calculation if you need that data. Don’t blame the theory, blame the deadline). In my past exchanges with George Fitzgerald of Accelrys, the issue of DMol3 infrared intensities came up as a feature request that would greatly improve the (this) user experience and Dr. Fitzgerald is very interested (of course) in making a great code that much better. Neither code will be disappearing from my toolbox anytime soon.

4. The Periodicity Of The Molecular Solid Doesn’t Care What The Space Group Is – One of the more significant problems facing the assignment-minded spectroscopist is the physical description of molecular motion in a vibrational mode. In the simplest motions involving the most weakly interacting molecules, translational and rotational motions are often quite easy to pick out and state as such. When the molecules are very weakly interacting, often the intramolecular vibrational modes are easy to identify as well, as they are largely unchanged from their gas-phase descriptions. In ionic solids or strongly hydrogen-bonded systems, it is often much harder to separate out individual molecular motions from “group modes” involving the in- and out-of-phase motions of multiple molecules. In the unit cells of molecular solids, it can be the case that these group modes appear, by inspection, to be extremely complicated, sometimes too involved to easily describe in the confines of a table in a journal article.

S-(+)-Ketamine Hydrochloride is one such example where a great simplification in vibrational mode description comes from thinking, well, “outside the box.” The image below shows two cells and the surrounding molecules of S-(+)-Ketamine Hydrochloride. As it is difficult to see why the mode descriptions are complex from just an image, assume that I am right in this statement of complexity. Part of this complexity comes from the fact that the two molecules in the unit cell are not strongly interacting, instead packed together by van der Waals and dispersion forces more than anything else. The key to a greatly simplified assignment comes from the realization that the most polar fragments of these molecules are aligned on the edges of the unit cell.

An alternate view of molecular vibrational motion comes from considering not the contents of the defined unit cell but the hydrogen-bonding and ionic bonding arrangement that exists between pairs of molecules between unit cells. The colorized image below shows two distinct chains (red and blue) that, when the predicted vibrational modes are animated, become trivial to characterize as the relative motions of a hydrogen/ionic-bonded chain. Rotational motions appear as spinning motions of the chains, translational motions as either chain sliding motions or chain breathing modes. It appears as a larger macromolecule undergoing very “molecular” vibrations. In optical vibrational spectroscopy, selection rules and the unit cell arrangement do not produce in- and out-of-phase motions of the red and blue chains, as only one “chain” exists in the periodicity of the unit cell. In neutron scattering spectroscopy, these relative motions between red and blue would appear in the phonon region. This same discussion was had, in part, in a previous post on the solid-state terahertz assignment of ephedrine (with a nicer picture).

So, look at the cell contents, then see if there’s more structure than crystal packing would indicate. It greatly simplifies the assignment (which, in turn. greatly simplifies the reader’s digestion of the vibrational motions).

Patrick M. Hakey, Damian G. Allis, Matthew R. Hudson, Wayne Ouellette, and Timothy M. Korter

Department of Chemistry, Syracuse University, Syracuse, New York 13244-4100

Abstract: The terahertz (THz) spectrum of (S)-(+)-ketamine hydrochloride has been investigated from 10 to 100 cm-1 (0.3-3.0 THz) at both liquid-nitrogen (78 K) and room (294 K) temperatures. Complete solid-state density functional theory structural analyses and normal-mode analyses are performed using a single hybrid density functional (B3LYP) and three generalized gradient approximation density functionals (BLYP, PBE, PW91). An assignment of the eight features present in the well-resolved cryogenic spectrum is provided based upon solid-state predictions at a PW91/6-31G(d,p) level of theory. The simulations predict that a total of 13 infrared- active vibrational modes contribute to the THz spectrum with 26.4% of the spectral intensity originating from external lattice vibrations.

pubs.acs.org/journal/jpcafh
www.somewhereville.com/?p=29
www.somewhereville.com/?p=26
www.somewhereville.com/?p=126
en.wikipedia.org/wiki/Density_functional_theory
en.wikipedia.org/wiki/Ketamine
www.crystal.unito.it
accelrys.com/products/materials-studio/quantum-and-catalysis-software.html
en.wikipedia.org/wiki/Time_domain_terahertz_spectroscopy
en.wikipedia.org/wiki/Computational_chemistry
accelrys.com
en.wikipedia.org/wiki/Inelastic_neutron_scattering
en.wikipedia.org/wiki/Vibrational_spectroscopy
www.somewhereville.com/?p=680

The Vibrational Spectrum Of Parabanic Acid By Inelastic Neutron Scattering Spectroscopy And Simulation By Solid-State DFT

Sunday, February 21st, 2010

Available as an ASAP in The Journal of Physical Chemistry A. As a general rule in computational chemistry, the smaller the molecule, the harder it is to get right. As a brief summary, parabanic acid has several interesting properties of significance to computational chemists as both a model for other systems containing similar sub-structures and as a complicated little molecule in its own right.

1. The solid-state spectrum requires solid-state modeling. This should be of no surprise (see the figure below for the difference in solid-state (top) and isolated-molecule (bottom)). This task was undertaken with both DMol3 and Crystal06, with DMol3 calculations responsible for the majority of the analysis of this system (as has always been the case in the neutron studies reported on this site).

2. The agreement in the hydrogen-bonded N-H…O vibrations is, starting from the crystal structure, in poor agreement with experiment. You’ll note the region between 750 and 900 cm-1 is a little too high (and for clarification, the simulated spectrum is in red below). According to the kitchen sink that Matt threw at the structure, the problem is not the same anharmonicity one would acknowledge by Dr. Walnut’s “catalytic handwaving” approach to spectrum assignment (Dr. Walnut does not engage in this behavior, rather endeavors to find it in others where it should not be).

3. The local geometry of the hydrogen-bonding network in this molecular solid leads to notable changes in parabanic acid structure that, in turn, leads to the different behavior of the N-H…O vibrational motions. There is one potentially inflammatory comment in the Conclusions section that results from this identification. The parabanic acid molecule is, at its sub-structure, a set of three constrained peptide linkages that under go subtle but vibrationally-observable changes to their geometry because of crystal packing and intermolecular hydrogen bond formation. This means that the isolated molecule and solid-state forms are different and that peptide groups are influenced by neighboring interactions.

So, why should one care? Suppose one is parameterizing a biomolecular force field (CHARMM, AMBER, GROMOS, etc.) using bond lengths, bond angles, etc., for the amino acid geometry and vibrational data for some aspect of the force constant analysis. The structural data for these force fields often originates with solid-state studies (diffraction results). This means, to those very concerned with structural accuracy, that a geometry we know to be influenced by solid-state interactions is being used as the basis for molecular dynamics calculations that will NOT be used in their solid-state forms. Coupled with the different spectral properties due to intermolecular interactions, the description being used as the basis for the biomolecular force field likely being used in solution (solvent box approaches) is based on data in a phase where the structure and dynamics are altered from their less conformationally-restricted counterpart (in this case, solid-state).

A subtle point, but that’s where applied theoreticians do some of their best work.

Matthew R. Hudson, Damian G. Allis, and Bruce S. Hudson

Department of Chemistry, 1-014 Center for Science and Technology, Syracuse University, Syracuse, New York 13244-4100

Abstract: The incoherent inelastic neutron scattering spectrum of parabanic acid was measured and simulated using solid-state density functional theory (DFT). This molecule was previously the subject of low-temperature X-ray and neutron diffraction studies. While the simulated spectra from several density functionals account for relative intensities and factor group splitting regardless of functional choice, the hydrogen-bending vibrational energies for the out-of-plane modes are poorly described by all methods. The disagreement between calculated and observed out-of-plane hydrogen bending mode energies is examined along with geometry optimization differences of bond lengths, bond angles, and hydrogen-bonding interactions for different functionals. Neutron diffraction suggests nearly symmetric hydrogen atom positions in the crystalline solid for both heavy-atom and N-H bond distances but different hydrogen-bonding angles. The spectroscopic results suggest a significant factor group splitting for the out-of-plane bending motions associated with the hydrogen atoms (N-H) for both the symmetric and asymmetric bending modes, as is also supported by DFT simulations. The differences between the quality of the crystallographic and spectroscopic simulations by isolated-molecule DFT, cluster-based DFT (that account for only the hydrogen-bonding interactions around a single molecule), and solid-state DFT are considered in detail, with parabanic acid serving as an excellent case study due to its small size and the availability of high-quality structure data. These calculations show that hydrogen bonding results in a change in the bond distances and bond angles of parabanic acid from the free molecule values.

pubs.acs.org/doi/abs/10.1021/jp9114095
pubs.acs.org/journal/jpcafh
en.wikipedia.org/wiki/Computational_chemistry
accelrys.com/products/materials-studio/quantum-and-catalysis-software.html
www.crystal.unito.it
en.wikipedia.org/wiki/Anharmonicity
chemistry.syr.edu/faculty/walnut.html
en.wikipedia.org/wiki/Hydrogen_bond
en.wikipedia.org/wiki/Peptide
en.wikipedia.org/wiki/Force_field_%28chemistry%29
www.charmm.org
ambermd.org
gromacs.org
en.wikipedia.org/wiki/Molecular_dynamics

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