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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_0Distribution 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 (x), exponential
(exp(-2^{l}cx)) and Gaussian (exp(-cx)).^{2} | ||

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 I(_{nn′}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'. |

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