From owner-chemistry@ccl.net Tue Aug 27 08:49:00 2013
From: "Toon Verstraelen Toon.Verstraelen]^[UGent.be" <owner-chemistry[-]server.ccl.net>
To: CCL
Subject: CCL:G: spherical harmonics in terms of cartesians in G09
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X-Original-From: Toon Verstraelen <Toon.Verstraelen-*-UGent.be>
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Date: Tue, 27 Aug 2013 07:26:19 -0400
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Sent to CCL by: Toon Verstraelen [Toon.Verstraelen!^!UGent.be]
On 08/02/2013 10:26 PM, Salter-Duke, Brian James  
brian.james.duke(_)gmail.com wrote:
>
> Sent to CCL by: "Salter-Duke, Brian James " [brian.james.duke,+,gmail.com]
> Can anyone point me to a source that clearly and simply lists the
> spherical harmonic normalised primitive basis functions used in
> Gaussian09 in terms of the normalised primitive cartesians, preferably
> with the normalisation factors? The former are labeled in order:-
>
> D 0  D+1  D-1  D+2  D-2
> F 0  F+1  F-1  F+2  F-2  F+3 F-3
> G 0  G+1  G-1  G+2  G-2  G+3 G-3 G+4 G-4
>
> and so on for H and I. I want to know the exact expressions for these in
> terms of the cartersians:-
>
> XX YY ZZ XY XZ YZ
> XXX YYY ZZZ XYY XXZ XZZ YZZ YYZ XYZ etc.
>
> There are lots of papers that address how this is done in general, such
> as the paper by Schlegel and Frisch (IJQC, 54, 83-87, 1995), but I
> want a simple list. I have found it very hard to find such a list. Is
> there one in the Gaussian documentation or the Gaussian code?
>
> I did find this in the documentation for Horton:-
>
> http://theochem.github.io/horton/tut_gaussian_basis.html#introduction
>
> Can anyone tell me whether these are in the same order as Gaussian and
> whether the cartesians are normalised?
>
> That Horton list is the kind of thing I am looking for, but I need to be
> clear about the order and the normalisation.
>
> Any help would be appreciated.
>
> Regards from a cool winter down under, even though they tell me
> Melbourne had its hottest ever July this year.
>
> Brian.
>

Hi Brian,

We have implemented a routine to read Gaussian 03/09 FCHK files into 
Horton. From that routine you can deduce all the conventions used in 
Gaussian, as compared to the page you mentioned. For G09/03, only the 
reordering matters. Normalization and sign conventions are the same as 
in Horton. The permutations depends on the shell type and can be found here:

https://github.com/theochem/horton/blob/master/horton/io/gaussian.py#L327

Note that I recently fixed some typos in that basis set tutorial. It 
should be fine now. If you encounter anything suspicious, please let me 
know.

By the way, if you would like to implement some post processing of a 
wavefunction from Gaussian, Horton may be useful as a code base to start 
> from. (That is one of the reasons we developed Horton.)

Best Regards,

Toon