Subject: anharmonic oscillator wavefunctions

From: Wai-To Chan <[email-masked]>
Date: Mon, 12 Nov 2001 07:54:45 -0500 (EST)

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I have a colleague who is interested in computing Franck-Condon factors, 
for which he needs anharmonic oscillator wavefunctions.  I think that I can 
provide him with some good potentials (he is interested in first row 
diatomics) from something like ccsd(t) scans with one of the aug-cc basis 
sets.  My plan was to fit the resulting potential to a Morse function, then 
get the anharmonic wavefunctions by diagonalizing the anharmonic (Morse) 
Hamiltonian on a basis of harmonic oscillator functions.  I am not certain 
that this fit will be good enough, particularly in the repulsive regime.  I 
have poked about in the literature some, but have not yet found the 
definitive "best" way to do this.

 Potential functions slightly more complex than the
Morse function should give reasonably good fit for diatomics. 
You may refer to John Murrell's text: 
 "Molecular potential functions" Wiley, 1984, 
for something like an extended Morse function. 

   In a paper I coauthored from 3 years ago we reported a fitting
procedure for triatomics which entails the use of the Aguado-Paniagua
potential function for diatomics. The functional form includes from
4 to 10 linear parameters and 2 exponential parameters. I fitted
the function to a set of ab initio energy points for the OH radical and 
the O2 anion over a range of about 2 angstroms and extrapolated it to 
the dissociation limits. The accuracy of the fitting
procedure is far from the best for triatomics but the
errors of the fits I obtained for the diatomics are essentially negligible.
The work was reported in

Chemical physics letters, vol 292, (1998), pg 57-62
W.-T. Chan and I. P. Hamilton

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I suspect there are some ccl users who know about getting good quality 
vibrational wavefunctions from ab initio potentials, and there may be some 
existing code out there to help solve this problem.  I'd appreciate any 
suggestions, pointers to papers that I have overlooked, or codes.  I'll 
post a summary on this topic soon.

Steve Williams
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>..

  The program LEVEL by Bob Le Roy at the University of Waterloo 
may suit your purpose. The program was written to solve the 
(nuclear) Schrodinger equation for a given diatomic potential and 
can calculate Frank-Condon factor as well. 
Prof Le Roy's homepage is at 

http://sciborg.uwaterloo.ca/~leroy/

  Click 'Computer Programs' from there and you will find the 
description of LEVEL and other related programs. 

Wai-To Chan