From owner-chemistry@ccl.net Sat Aug 11 11:31:00 2018 From: "Tymofii Nikolaienko tim_mail,ukr.net" To: CCL Subject: CCL: overlap integral of two simple exponential decay functions (different centers) in three-dimensional space Message-Id: <-53430-180811043227-8302-Q4QgoUrT9k5ZjJcsK5/7kA!A!server.ccl.net> X-Original-From: Tymofii Nikolaienko Content-Language: uk Content-Type: multipart/alternative; boundary="------------EB8CD5782094E29643488B13" Date: Sat, 11 Aug 2018 11:31:18 +0300 MIME-Version: 1.0 Sent to CCL by: Tymofii Nikolaienko [tim_mail-,-ukr.net] This is a multi-part message in MIME format. --------------EB8CD5782094E29643488B13 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Dear Tom, could the overlap integral expression $$ S = e^{ - \rho } \left( {1 + \rho + \frac{{\rho ^2 }}{3}} \right) $$ used in the Heitler-London model for the Hydrogen molecule be of any help here ? Best regards, Tymofii 11.08.2018 0:29, Thomas Manz thomasamanz . gmail.com пише: > 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 > > --------------EB8CD5782094E29643488B13 Content-Type: text/html; charset=utf-8 Content-Transfer-Encoding: 8bit

Dear Tom,

could the overlap integral expression

$$
S = e^{ - \rho } \left( {1 + \rho + \frac{{\rho ^2 }}{3}} \right)
$$

used in the Heitler-London model for the Hydrogen molecule be of any help here ?

Best regards,
Tymofii

11.08.2018 0:29, Thomas Manz thomasamanz . gmail.com пише:

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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