CCL: Molecular integrals using gaussian functions (using boys algorithm

["Nand Ng" <andyng111[A]hotmail.com>]

 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