From owner-chemistry@ccl.net Fri Aug 10 17:33:00 2018
From: "Thomas Manz thomasamanz . gmail.com" <owner-chemistry!A!server.ccl.net>
To: CCL
Subject: CCL: overlap integral of two simple exponential decay functions (different centers) in three-dimensional space
Message-Id: <-53429-180810172951-6482-9Z4XJz+NHVX6rQuq/JIHiw!A!server.ccl.net>
X-Original-From: Thomas Manz <thomasamanz/a\gmail.com>
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Date: Fri, 10 Aug 2018 15:29:45 -0600
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Sent to CCL by: Thomas Manz [thomasamanz(0)gmail.com]
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Dear colleagues,

I am trying to find an analytic formula and journal reference for the
overlap integral of two simple exponential decay functions (different
centers) in three-dimensional space. For example, consider the overlap
integral of 1s Slater-type basis functions placed on each atom of a
diatomic molecule.

I have looked into the literature at a couple of sources. Frustratingly, I
could not get some of the reported analytic formulas to work (i.e., some of
the claimed analytic formulas in literature give wrong answers). Other
formulas are horrendously complex involving all sorts of angular momentum
and quantum number operators, almost too complicated to comprehend.

I am trying to get an analytic overlap formula for the plain Slater s-type
orbitals that are simple exponential decay functions. Does anybody know
whether a working analytic formula is available for this?

F.Y.I: I am aware of the formula given in Eq. 16 of Vandenbrande et al. J.
Chem. Theory Comput. 13 (2017) 161-179. It is wrong and clearly doesn't
match the numerical integration of the same integral (not even close as
evidenced by comparing accurate numerical integration with the claimed
analytic formula of the same integral). I am not trying to pick on this
paper. I have tried other papers also, but many of them are so complicated
that it is difficult to understand what is actually going on.

Sincerely,

Tom Manz

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<div dir=3D"ltr">Dear colleagues,<div><br></div><div>I am trying to find an=
 analytic formula and journal reference for the overlap integral of two sim=
ple exponential decay functions (different centers) in three-dimensional sp=
ace. For example, consider the overlap integral of 1s Slater-type basis fun=
ctions placed on each atom of a diatomic molecule.</div><div><br></div><div=
>I have looked into the literature at a couple of sources. Frustratingly, I=
 could not get some of the reported analytic formulas to work (i.e., some o=
f the claimed analytic formulas in literature give wrong answers). Other fo=
rmulas are horrendously complex involving all sorts of angular momentum and=
 quantum number operators, almost too complicated to comprehend.</div><div>=
<br></div><div>I am trying to get an analytic overlap formula for the plain=
 Slater s-type orbitals that are simple exponential decay functions. Does a=
nybody know whether a working analytic formula is available for this?</div>=
<div><br></div><div>F.Y.I: I am aware of the formula given in Eq. 16 of Van=
denbrande et al. J. Chem. Theory Comput. 13 (2017) 161-179. It is wrong and=
 clearly doesn&#39;t match the numerical integration of the same integral (=
<span style=3D"font-size:small;background-color:rgb(255,255,255);text-decor=
ation-style:initial;text-decoration-color:initial;float:none;display:inline=
">not even close</span>=C2=A0as evidenced by comparing accurate numerical i=
ntegration with the claimed analytic formula of the same integral). I am no=
t trying to pick on this paper. I have tried other papers also, but many of=
 them are so complicated that it is difficult to understand what is actuall=
y going on.</div><div><br></div><div>Sincerely,</div><div><br></div><div>To=
m Manz</div><div><br></div><div><br></div></div>

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