Programs in Physics & Physical Chemistry
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|Manuscript Title: Two-center Coulomb functions.|
|Authors: M. Hiyama, H. Nakamura|
|Program title: TCOULOM|
|Catalogue identifier: ADFY_v1_0|
Distribution format: gz
|Journal reference: Comput. Phys. Commun. 103(1997)209|
|Programming language: Fortran.|
|Computer: HP 735.|
|Operating system: UNIX.|
|Keywords: General purpose, Schrodinger equation in, Spheroidal coordinates, Two-center, Coulomb function, Numerical solution.|
Nature of problem:
Subroutine TCOULOM is a FORTRAN77 subroutine to calculate the regular two-center Coulomb functions for the positive energy, epsilon. This program requires six constants. R: internuclear distance, Z1 and Z2: two positive charges, m and q: quantum numbers, epsilon: energy of an outgoing electron. Atomic units are employed.
There are three main subroutines in this program. The first one is to estimate the separation constants. The chain equation is solved there (see ref. ). The other two are to obtain wavefunctions of the angular part, Ximq(eta;kappa,R), and of the radial part, Pimq(xi;kappa,R). The spheroidal angular variable eta ranges between -1 and 1, and the radial variable xi from 1 to infinity. Ximq(eta;kappa,R) is obtained by solving the Schrodinger equation numerically, where we put eta=tanh q. The integral range of q is (-infinity,infinity), but in practice the range between -4.5 and 4.5 was found to be enough. The Numerov method  is used to solve the differential equation. The boundary conditions are provided by power series expansions at both ends. Pimq(xi;kappa,R) is obtained by solving the corresponding Schrodinger equation with use of both forward and backward Numerov procedure (see ref. ).
This program may be used to evaluate the two-center Coulomb functions for the positive energy epsilon. The two positive charges are assumed to satisfy the relation Z2 >= Z1. The wavefunction for the case of Z2 = Z1 also can be calculated using this program. m and q are positive integers. They correspond to magnetic and azimuthal quantum numbers. This program produces only regular solutions both for the angular and radial parts.
|||L.I. Ponomarev and L.N. Somov, J. Comp. Phys. 20(1976)183.|
|||H. Takagi and H. Nakamura, Report of The Institute for Plasma Physics, Nagoya University, IIPJ-AM-16 (1980).|
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