Programs in Physics & Physical Chemistry
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|Manuscript Title: MORSMATEL: a rapid and efficient code to calculate vibration- rotational matrix elements for r-dependent operators of two Morse oscillators.|
|Authors: A. Lopez-Pineiro, M.L. Sanchez, B. Moreno|
|Program title: MORSMATEL|
|Catalogue identifier: ACHM_v1_0|
Distribution format: gz
|Journal reference: Comput. Phys. Commun. 70(1992)355|
|Programming language: Fortran.|
|Computer: UNISYS 5000/55.|
|Operating system: UNIX.|
|RAM: 1500K words|
|Keywords: Molecular physics, Morse oscillator, Matrix element, Franck-condon factor, Vibrational, Rotational.|
Nature of problem:
In many fields of molecular physics, such as vibration-rotational spectroscopy of polyatomic systems, Franck-Condon factor calculations or transition probabilities, we need to evaluate integrals between Morse wavefunctions of certain r-dependent operators. It is necessary to have a rapid and efficient procedure to calculate integrals of these types in both orthogonal and nonorthogonal cases with wavefunctions belonging to the same or different Morse oscillators. Analytic, asymptotic and numerical methods have been used to evaluate the matrix elements with wavefunctions of this type, although for some operators it was possible to use easily programmed recurrence relations which, however, in some cases produced important round-off errors.
The program MORSMATEL has been developed to calculate vibration- rotational matrix elements involving nonorthogonal Morse wavefunctions. Based on the hypervirial theorem and a second quantization formalism, a set of recurrence relations for matrix elements and Franck-Condon factors of Morse potentials are obtained. MORSMATEL calculates recursively matrix elements of the operators q**k = (r-re)**k, x**s = exp[-as(r-re)], d**l,dr**l, or any combination thereof, corresponding to vibration-rotational states belonging to two distinctly separate Morse- Pekeris oscillators of arbitrary De. The results are valid for any value of the power of the operator and of the quantum numbers v and J of each oscillator.
For the CO molecule, on our system, we have calculated the matrix elements <(r-re)**k>vv' (k=0-4) with v=0-80 in 4 minutes (in contrast to 13 hours for just the diagonal matrix elements.
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