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Manuscript Title: Programs for the evaluation of nuclear attraction integrals with B functions.
Authors: H.H.H. Homeier, E.O. Steinborn
Program title: D_INT
Catalogue identifier: ACNV_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 77(1993)135
Programming language: Fortran.
Computer: COMPAREX 8/85.
Operating system: IBM VM/SP CMS RELEASE 5.
RAM: 960K words
Word size: 32
Keywords: Molecular physics, Nuclear attraction Integrals, Expotential Type orbitals, Slater-type orbitals, B functions, Fourier transform method, Numerical quadrature, Mobius-type quadrature.
Classification: 16.10.

Subprograms used:
Cat Id Title Reference
ACJU_v1_0 S_INT CPC 72(1992)269

Nature of problem:
Nuclear attraction integrals have to be computed in ab initio quantum chemical LCAO and one-centre calculations. It is advantageous to use a basis set of B functions [2] because these functions are exponential- type orbitals (ETO's) and, hence, allow to describe correctly the nuclear cusps and the large-distance behaviour of the wavefunctions. This entails that relatively small ETO basis sets are required as compared to Gaussian basis sets. Also, for molecular integrals with B functions relatively numerous compact representations exist as compared to other ETO's. This holds because B functions have a very simple Fourier transform [3,4].

Solution method:
For three-centre nuclear attraction integrals of B functions with different expotential parameters a two-dimensional integral representat- ion is evaluated using the LAM method [5] which is based on a combination of Mobius-type quadrature [6] and a special variant of Gauss-Laguerre quadrature. For three-centre nuclear attraction integrals of B functions with equal exponential parameters a more simple two-dimensional integral representation [7] can be used. For two-centre nuclear attraction integrals over a two-centre density of B functions a representation by a finite one-dimensional sum of overlap integrals of B functions is applied; the latter integrals are computed using the programs described in Ref.[1]. The evaluation of two-centre nuclear attraction integrals over one-centre densities of B functions is based on a representation as a finite sum of incomplete Gamma functions. This representation can also be regarded as a finite sum of two-centre nuclear attraction integrals of Slater-type orbitals. In the one-centre case, the nuclear attraction integrals of B functions are calculated using very simple polynomial expressions.

Restrictions:
The current programs allow the computation of nuclear attraction integrals within the following range of indices of the B functions: 0 < n1 < 12, 0 < n2 < 12, 0 < l1 < =5, 0 < l2 < =5. Results for three-centre integrals with max(R1C, R2C) >> R21 may be inaccurate due to oscillations in the Fourier integral representation.

Unusual features:
a) In the test deck the IBM VS FORTRAN Version 2 subroutine CPUTIME [8] is used to determine the running time required.
b) An initialization subroutine DINI is provided which has to be called before the first nuclear attraction integral is computed.

Running time:
In the test deck, the average CPU time per call of subroutine D (i.e., per nuclear attraction integral with normalized B functions) was 137 milliseconds.

References:
[1] H.H.H. Homeier, E.J. Weniger, and E.O. Steinborn, Comput. Phys. Commun. 72(1992)269.
[2] E. Filter and E.O. Steinborn, Phys. Rev. A18(1978)1.
[3] E.J. Weniger and E.O. Steinborn, J. Chem. Phys. 78(1983)6121.
[4] A.W. Niukkanen, Int. J. Quantum Chem. 25(1984)941.
[5] H.H.H. Homeier and E.O. Steinborn, Int. J. Quantum Chem. 39(1991)625
[6] H.H.H. Homeier and E.O. Steinborn, J. Comput. Phys. 87(1990)61.
[7] H.H.H. Homeier, Integraltransformationsmethoden und Quadraturverfahren fur Molekulintegrale mit B-Funktionen (PhD thesis, Universitat Regensburg, 1990; S. Roderer Verlag, Regensburg 1990).
[8] IBM VS FORTRAN Version 2, Language and Library Reference, Release 3 (International Business Machines Corporation, San Jose, 1988).