CCL:G: GAUSSIAN/GAMESS/MOLPRO/CRYSTAL: different energies

On Wed, Feb 19, 2014 at 11:30 AM, Mike Towler mdt26-.-cam.ac.uk <owner-chemistry(_)ccl.net> wrote:

Sent to CCL by: "Mike Towler" [mdt26*cam.ac.uk]
Hello,

I'm one of the authors of the CASINO program - a widely-used quantum Monte
Carlo code: http://vallico.net/casinoqmc/ . The way QMC works, CASINO
reads a 'trial wave function' generated by an external code using e.g. a
Hartree-Fock or a DFT calculation, and then it proceeds to 'improve the
answer' (details irrelevant). I'm therefore responsible for maintaining
interfaces between CASINO and other people's software - a list of the
fifteen codes we supposedly support is here:

http://vallico.net/casinoqmc/interfaces

For the purposes of my present question, this list includes GAUSSIAN,
GAMESS, CRYSTAL, and MOLPRO.

I've recently started a formal check of the way these interfaces handle
higher angular momentum Gaussian functions (by which I mean f and g along
with d for completeness). The complexity of the expressions and the
different conventions in use mean that this sort of thing is very easy to
screw up.

Basic checks are simple enough, since (1) CASINO does a numerical check of
its own analytic derivatives (it needs the value of the orbitals, the
gradient, and the Laplacian at random points in configuration space), and
(2) CASINO is capable of running in pure Hartree-Fock mode, and thus
through Monte Carlo numerical integration it should be able to give the
same Hartree-Fock energy (within statistical error bars) as the code that
generated the trial wave function.

To check the different angular momenta individually, I've created a set of
three input files for the methane molecule, with only d functions in the
basis, only f functions, and only g functions (let's call them 'd-ane',
'f-ane', and 'g-ane').

However, before we even get to CASINO, and looking first at f-ane, we've
found that the four codes above give very different answers for the
Hartree-Fock energy. In fact GAUSSIAN and CRYSTAL give -11.3966 au, but
both GAMESS and MOLPRO give -11.2286 au.

(For the record, CASINO agrees with GAUSSIAN and CRYSTAL for the HF energy
when fed with their trial wave functions. It's not been possible to check
with GAMESS and MOLPRO as their current interfaces to CASINO don't yet
support f functions.. though they will shortly.)

Now I don't have the experience or any access to any of these codes apart
> from CRYSTAL (I got some kind colleagues to run the calculations for me),
so it's difficult for me to see why this difference exists, and my
colleagues aren't sure either. There was some suggestion that it might be
to do with the spherical/Cartesian basis set conversion? So I was
wondering, are there any GAMESS, GAUSSIAN, or MOLPRO gurus out there who
can shed any light on this problem? It seems strange that such well-known
codes would give such different answers for such a simple system.

The input files for the four codes are here:

http://www.tcm.phy.cam.ac.uk/~mdt26/g/crystal.txt
http://www.tcm.phy.cam.ac.uk/~mdt26/g/gamess.txt
http://www.tcm.phy.cam.ac.uk/~mdt26/g/gaussian.txt
http://www.tcm.phy.cam.ac.uk/~mdt26/g/molpro1.txt
http://www.tcm.phy.cam.ac.uk/~mdt26/g/molpro2.txt

Any assistance will be gratefully appreciated.

Thanks,
Mike Towler

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CCL:G: GAUSSIAN/GAMESS/MOLPRO/CRYSTAL: different energies - f function basis