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Manuscript Title: FCFRKR: a procedure to evaluate Franck-Condon type integrals for diatomic molecules.
Authors: H.H. Telle, U. Telle
Program title: FCFRKR
Catalogue identifier: AAOR_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 28(1982)1
Programming language: Fortran.
Computer: SEL 32/75.
Operating system: RTM 7.1.
RAM: 64K words
Word size: 32
Peripherals: disc.
Keywords: Molecular physics, Vibration, Diatomic, Potential curves, Rkr-method, Schrodinger equation, Franck-condon factor, Einstein a-value, R-centroid, Distortion constant, Dipole matrix element.
Classification: 16.3.

Revision history:
Type Tit le Reference
adaptation 0001 FCFRKR*ADAPT1 See below
adaptation 0002 FCFRKR*LEVEL2CDC See below

Nature of problem:
This program package is concerned with the construction of RKR potentials and the solution of the Schrodinger equation for the nuclear motion ofdiatomic molecules (vibrational-rotational wave functions). The calculation of overlap integrals, Franck-Condon factors, dipole matrix elements and Einstein A-factors can be selected by setting the appropriate logical path switch in the program. In addition, options for the calculation of r-centroids and the determination of distortion constants (Dv and Hv) are provided.

Solution method:
The f and g integrals for the evaluation of the RKR potential are obtained by numerical integration. The vibrational wave functions and energy eigenvalues are evaluated from the solution of the radial Schrodinger equation for the nuclear motion of the diatomic molecule. The differential equation of second-order is transformed into a system of first-order differential equations. This allows the application of the rapidly converging correction procedure for the eigenvalues (Newton procedure) and the use of high precision integration procedures with automatic step-size control. Overlap functions are calculated from tabulated eigenfunctions and operator functions (e.g. dipole moment function) applying a Simpson's integration scheme.

Restrictions:
Matrices for the evaluation of Franck-Condon type integrals are bounded to a field of maximum dimension of (70,70) in order to limit the required storage area but at the same time allowing flexibility for a vast number of applications. Changes to smaller maximum dimensions or a different dimension set (a,b) fitting in the reserved storage area can be easily performed. At present no options for the calculation of quasi-bound and free states are included in the procedure for the solution of the Schrodinger equation. The line-strength factors for the calculation of the Einstein A-factors are restricted to singlet-singlet doublet-doublet transitions; changes in the relevant parts of rotational line strength formulae can be achieved without difficulties to apply the procedure to transitions of higher multiplicity.

Running time:
The running time depends strongly on the requested accuracies for the evaluation of the RKR-potential and the energy eigenvalues as well as on the number of raster points in the vibrational-rotational wave function. On the average turning points for vibrational levels in the RKR- potential were computed in 0.01 (low ) to 0.09 (high ) seconds; the integration accuracy was 10**-15. One iteration cycle for a wave function of 1000 raster points required ~~30 s (integration accuracy 10**-8). The calculation of an overlap integral between two such wave functions is usually less than 0.3 s (including time to read the wave functions from the external file).

ADAPTATION SUMMARY
Manuscript Title: Comments on the program FCFRKR.
Authors: H.H. Telle, U. Telle
Program title: 0001 FCFRKR*ADAPT1
Catalogue identifier: AAOR_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 36(1985)109
Programming language: Fortran.
Classification: 16.3.

Nature of problem:
Recent experiences with the program package FCFRKR for the evaluation of wave functions and Franck-Condon type integrals for diatomic molecules are discussed. Some minor modifications for the convenience of the user are described (formats of printing, information in error messages).

ADAPTATION SUMMARY
Manuscript Title: Comments on the program FCFRKR.
Authors: H.H. Telle, U. Telle
Program title: 0002 FCFRKR*LEVEL2CDC
Catalogue identifier: AAOR_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 36(1985)109
Programming language: Fortran.
Classification: 16.3.

Nature of problem:
This adaptation allows one to run the program FCFRKR on CDC computers for which their memory organization makes special storage allocation necessary. The appropriate assignments utilize the LEVEL2, name statement.