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Manuscript Title: Programs for the evaluation of overlap integrals with B functions.
Authors: H.H.H. Homeier, E.J. Weniger, E.O. Steinborn
Program title: S_INT
Catalogue identifier: ACJU_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 72(1992)269
Programming language: Fortran.
Computer: COMPAREX 8/85.
Operating system: IBM VM/SP CMS Release 5.
RAM: 563K words
Word size: 32
Keywords: Molecular, Integral, Overlap integrals, Expontential-type Orbitals, B functions, Fourier transform method, Numerical quadrature, Mobius-type quadrature.
Classification: 16.10.

Subprograms used:
Cat Id Title Reference
AARL_v1_0 YLM-COUPLING CPC 25(1982)149

Nature of problem:
Overlap integrals and matrix elements of the kinetic energy operator have to be computed in ab initio and semi-empirical quantum chemical calculations using any basis set. A basis set of B functions offers the advantage that these functions - being expotential-type orbitals (ETO's) - can represent the nuclear cusp and the correct large-distance behaviour of the wavefunctions. Consequently smaller basis sets are required than for Gaussian-type orbitals. As compared to other types of ETO's, B functions have a more simple Fourier transform resulting in a large number of compact representations for multicenter integrals using this basis set.

Solution method:
For two-center overlap integrals of B functions with largely differing scaling parameters the Jacobi polynomial representation is used. For smaller differences of these parameters a one-dimensional integral representation is used in combination with Mobius-type quadrature. This is the method recommended in H.H.H. Homeier and E.O. Steinborn, On the Evaluation of Overlap Integrals with Expotential-type Basis Functions, Int. J. Quantum Chem., in press. If the two scaling parameters are identical, or in the one-center case, simple analytical representations of the overlap integrals by finite sums are used. The matrix elements of the kinetic energy operator are computed as differences of two overlap integrals.

The current programs allow the computation of overlap integrals within the following range of indices of the B functions: 0 <\= n1 <\= 12, 0 <\= n2 <\= 12, 0 <\= l1 <\= 5, 0 <\= l2 <\= 5.

Unusual features:
a) In one test deck (program STEST2) the IBM VS FORTRAN Version 2 subroutine CPUTIME is used to determine the running time required.
b) The Gauss-Legendre quadrature rules used by several subroutines are computed using the subroutine D01BCF of the NAG library. For users not having access to this library a dummy subroutine also named D01BCF is provided which allows to simulate a call of the NAG routine but only to compute weights and abscissae of a Gauss-Legendre rule over the interval (-1,1) with 30 points.
c) An initialization subroutine SINI is provided which has to be called before the first overlap integral is computed. Besides computing several COMMON blocks SINI sets several switch variables which can be changed afterwards in order to adapt the programs to specific needs of the user.

Running time:
In the second test deck, the average CPU time per call of subroutine S (i.e., per overlap integral with normalized B functions) was 234 micro- seconds, when geometry related quantities were computed outside routine S, but 273 microseconds in the opposite case.