From owner-chemistry@ccl.net Wed Sep  7 07:20:33 2005
From: "CCL" <owner-chemistry^server.ccl.net>
To: CCL
Subject: CCL: W:GTO and STO
Message-Id: <-29085-050907063915-6096-W+2w8DanHA1q/kw2MH4VTw^server.ccl.net>
X-Original-From: Laurence Cuffe <Laurence.Cuffe^ucd.ie>
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Date: Wed, 07 Sep 2005 11:24:40 +0100
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Sent to CCL by: Laurence Cuffe [Laurence.Cuffe^ucd.ie]


----- Original Message -----
> From: CCL <owner-chemistry^ccl.net>
Date: Tuesday, September 6, 2005 6:31 pm
Subject: CCL: W:GTO and STO

> 
> Sent to CCL by: Serguei Patchkovskii [ps:+:ned.sims.nrc.ca]
> > Sent to CCL by: Laurence Cuffe [Laurence.Cuffe]*[ucd.ie]
>> The short answer is that calculating the overlap between two
>> Gaussiantype -Orbitals can be done in closed form. That is given two
>> GTO's A and B you can write an relatively simple algebraic expression
>> for the size of the overlap between them.  This is not possible with
>> Slater type orbitals.
>This statement, of course, is false. Closed-form expressions for
>overlap integrals in terms of exponential integral-type functions
>are very well known. For example:…(cut)
>Dr. Serguei Patchkovskii
A fair point Dr Patchkovskii. In hindsight I should, perhaps, have put
more emphasis on “relatively simple”  As Ahmed. Bouferguene wrote:
The "flip side of the coin" is, multi-center integrals (which is the heart
of ab initio calculations) over STOs is much much more difficult than with
GTOs. I think I’d trust his judgment in this area, as its one where he’s
published a number of papers e.g.
Ahmed Bouferguene 2005 J. Phys. A: Math. Gen. 38 2899-2916 “Addition
theorem of Slater type orbitals: a numerical evaluation of
Barnett–Coulson/Löwdin functions”
Historically evaluating GTO’s was faster, and while there are now claims
that highly optimised STO codes can beat GTO codes, I remain to be
convinced that highly optimised STO codes can beat highly optimised GTO
codes.
In the wider sense original question was about the popularity of
Gaussian type orbital codes over STO based ones. Here I think the reason
is also historical, and is based on the early popularity of the gaussian
program as a collaborative venture among a number of theoretical chemists.  
The use of GTO’s was, I think, first suggested by S.F. Boys, in Proc.
Roy. Soc. A200, 542 (1950)

ADF (using STO’s) has been around for a long time, and I know that the
Zeigler group has made many substantial contributions to it.  It has not
(yet) overtaken Gaussian in popularity, but maybe if( or when) it does
we’ll be wondering what the advantages of GTO’s are. I’m not holding my
breath.
All the best
Dr Laurence Cuffe