From owner-chemistry@ccl.net Fri Dec  5 12:28:01 2008
From: "Nand Ng andyng111],[hotmail.com" <owner-chemistry(~)server.ccl.net>
To: CCL
Subject: CCL: Molecular integrals using gaussian functions (using boys algorithm
Message-Id: <-38255-081205122612-12279-RtUHdgPHJRAIkBfWgbV7TA(~)server.ccl.net>
X-Original-From: "Nand  Ng" <andyng111[A]hotmail.com>
Date: Fri, 5 Dec 2008 12:26:09 -0500


Sent to CCL by: "Nand  Ng" [andyng111!^!hotmail.com]
Thank you very much for your help. It seems for higher angular momentum, Boys algorithm is not enough. We have to calculate it through some lower angular momentum integrals, am I right? We cannot simply get d-orbitals integrals by D^2 <s|s>. We can only do it for p-orbitals?

Sent to CCL by: Gustavo Mercier [gamercier[A]yahoo.com]
 Hi!
 Take your last equation, multiply by your s function and integrate to get an
 overlap integral.
 <s|D^2(s)> = <s|d_x^2> -(1/2a)<s|s>
 D = d/dXa and D^2=d2/dXa2 (second derivative w.r.t. nuclear coordinates).
 Because the derivatives are w.r.t. nuclear coordinates and the integrals are
 over electronic coordinates, you can
 pull the derivative out of the integra....
 <s|D^2(s)> = D^2(<s|s>)
 You have an analytic form for <s|s>, so you can compute D^2(<s|s>)
 term and rewriting the first equation above:
 <s|d_x^2> = D^2(<s|s>) + (1/2a)<s|s>
 In the end you have a series of recursions to solve your integrals.
 Hope this helps!
 --
 Gustavo A. Mercier, Jr. MD,PhD
 Boston Medical Center
 Radiology - Nuclear Medicine and Molecular Imaging, Chief
 gamercier{}yahoo.com (preferred e-mail address)
 Gustavo.Mercier{}bmc.org
 gumercie{}bu.edu
 cell: 469-396-6750
 work: 617-638-6610; 617-414-6457