# FC factors and 1D spectrum

In reply the inquiry about synthesizing spectra from one-
dimensional potentials, I have FORTRAN programs that do just that. Thus,
by starting with arbitrary analytical or numerical one-dimensional potentials,
e.g., Morse, 6-12, 6-exp, double minimum, etc. for the lower and upper states,
one obtains a set of eigenvalues and eigenvectors for each state. This approach
uses a finite-element method to represent the one-dimensional Hamiltonian, which
is then diagonalized. Then the ground state is Boltzmann populated and the
Franck-Condon matrix is numerically calculated from the eigenvectors.
A 'stick' spectrum is than computed using the
Condon approximation. My program allows the sticks to be broadened with either
a Gaussian or Lorentzian lineshape. As an example of this method, see J.A.C.S.,
108, 3907 (1986) for the calculation of the pyramidal-to-planar transition in
trimethylamine. Naturally, in the finite element calculation, one has to
specify a reduced mass appropriate for the vibration being considered.
This is a very simple, yet satisfying utility that can provide valuable
insight. Recently I used this method to clculate the vibrational spectra of
van der Waals molecules (submitted for publication).
If anyone would like to have the code for these programs, I can send
same, preferably via ftp (in which case I would need to know the
login and guest password information). Alternatively, I could send the
code if provided with a floppy disk. The programs run well on VMS, AIX, or
even a PC (although the dimension must be reduced).
Arthur M. Halpern
Department of Chemistry
Indiana State University
Terre Haute, IN 47809
(812)237-2182 (voice)
(812)237-4382 (fax)
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