Computer Physics Communications Program LibraryPrograms in Physics & Physical Chemistry |

[Licence| Download | New Version Template] acnv_v1_0.gz(106 Kbytes) | ||
---|---|---|

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_0Distribution 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). |

Disclaimer | ScienceDirect | CPC Journal | CPC | QUB |