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Manuscript Title: Exact analytical expressions and numerical analysis of two-center Franck-Condon factors and matrix elements over displaced harmonic oscillator wave functions.
Authors: I.I. Guseinov, B.A. Mamedov, A.S. Ekenoglu
Program title: FRANCK (Franck-Condon factors and matrix elements programs)
Catalogue identifier: ADXX_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 175(2006)226
Programming language: Mathematica 5.0.
Computer: Any computer on which Mathimatica is installed. Developed on a Pentium M 1.4 GHz.
Operating system: Any system running Mathimatica.
RAM: 512 MB
Keywords: Franck-Condon factors, harmonic oscillator wave functions, overlap integrals, binomial coefficients, Hermite polynomials.
PACS: 33.70.Ca, 31-15.-p, 02.60.-x, 32.30.-r.
Classification: 16.3.

Nature of problem:
The programs calculate the Franck-Condon factors and matrix elements over displaced harmonic oscillator wave functions with arbitrary quantum numbers (n, n1), frequencies (a, a1) and displacement (d) for the various functions of power (xl), exponential (exp(-2cx)) and Gaussian (exp(-cx2)).

Solution method:
The Franck-Condon factors and matrix elements are evaluated using binomial coefficients and basic integrals.

Restrictions:
The results obtained by the present programs show great numerical stability for arbitrary quantum numbers (n, n1), frequencies (a, a1) and displacement (d).

Running time:
As an example, for the value of Franck-Condon Overlap Integral Inn′(d;α,α')=0.004405001887372332 with n=3, n1=2, a=4, a1=3,d=2, the compilation time on a Pentium M 1.4 GHz computer is 0.18 s. Execution time depends on the values of integral parameters n, n′,d,α,α'.