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Manuscript Title: Computation of Fourier transform of a general two-centre STO charge distribution.
Authors: B.R. Junker
Program title: FRTRF
Catalogue identifier: AANO_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 23(1981)377
Programming language: Fortran.
Computer: IBM 360.
Operating system: MVT.
RAM: 57K words
Word size: 32
Keywords: Molecular physics, Integral, Bethe theory, Coherent x-ray, Scattering, Fourier transform, Bessel functions.
Classification: 16.10.

Nature of problem:
The computation of the charge transfer amplitude at energies greater than a few keV's requires the computation of two-centre integrals of the form of Fourier transforms. Similar integrals arise in the Bethe theory of the scattering of charged unstructured particles by molecules and in the computation of the coherent and incoherent intensities of X- rays scattered by molecules. This program provides a means of computing these integrals for an arbitrary Slater Type Orbital (STO) basis.

Solution method:
The technique is a generalization to STO's with arbitrary quantum numbers of McCaroll's method for s-orbitals.

The restrictions on the program are determined only by the dimensions of the arrays. As written, the maximum quantum numbers allowed are n=5, l=5, m=5, and the maximum number of quadrature points is fifty. These restrictions can be relaxed by increasing the appropriate dimension declarations.

Running time:
A number of test runs were performed to determine the variation of run time with respect to the various parameters. In all runs the complete set of integrals was computed at an internuclear separation of 1.0 au with an impact parameter of 0.5 au and at an internuclear separation of 1.5 au. Two different basis sets were used - one contained 1s, 2s, 2po and 2p+-1 STO's on each center while the other contained 3do, 3d+-1, 3d+-2, 3fo, 3f+-1, 3f+-2 and 3f+-3 in addition to the orbitals of the first set. In both cases, the nonlinear parameters were chosen to correspond to a hydrogen atom for center A and a hydrogenlike helium ion for ceneter B. The first basis set resulted in the computation of 150 integrals while the second required 1734 integrals. In the first set of runs CONV was set to 2 X 10**-6 and VEL to 2.5 au. The first basis set required 32 ms/integral when the first 26 points of a 64 Gauss-Laguerre quadrature set was used, 40 ms/integral for the first 50 of 96 points, and 56 ms/integral for 50 of 128. The second basis set required 99 ms/ integral for 50 of 96 and 111 ms/integral for 50 of 128. When VEL was set to 0.25 au, the first basis set required 36 ms/integral for 50 of 96, while the second required 88 ms/integral for 50 of 96 and 94 ms/ integral for 50 of 128. When CONV was set to 2 X 10**-8 and VEL to 2.5 au, the first basis set required 44 ms/integral for 50 of 96 and 56 ms/ integral for 50 of 128, while the second basis set required 121 ms for 50 of 128.