Programs in Physics & Physical Chemistry
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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.|
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  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].
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  which is based on a combination of Mobius-type quadrature  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  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.. 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.
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.
a) In the test deck the IBM VS FORTRAN Version 2 subroutine CPUTIME  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.
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.
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|||H.H.H. Homeier, Integraltransformationsmethoden und Quadraturverfahren fur Molekulintegrale mit B-Funktionen (PhD thesis, Universitat Regensburg, 1990; S. Roderer Verlag, Regensburg 1990).|
|||IBM VS FORTRAN Version 2, Language and Library Reference, Release 3 (International Business Machines Corporation, San Jose, 1988).|
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