Numerical integration for polyatomic systems

Abstract A numerical integration package is presented for three-dimensional integrals occurring in electronic structure calculations, applicable to all polyatomic systems with periodicity in 0 (molecules), 1 (chains), 2 (slabs), or 3 dimensions (crystals). The scheme is cellular in nature, based on Gaussian product formulas and it makes use of the geometrical symmetry. Convergence of accuracy with the number of points is rapid and use of the program has been made easy.

[1]  D. A. Dunavant.  Economical symmetrical quadrature rules for complete polynomials over a square domain , 1985 .

[2]  A. D. McLaren,et al.  Optimal numerical integration on a sphere , 1963 .

[3]  Symmetric numerical integral formulas for regular polygons , 1990 .

[4]  A. Stroud.  Approximate calculation of multiple integrals , 1973 .

[5]  A. Becke.  A multicenter numerical integration scheme for polyatomic molecules , 1988 .

[6]  Interpolatorische Kubaturformeln und reelle Ideale , 1980 .

[7]  D. Ellis,et al.  Discrete variational method for the energy-band problem with general crystal potentials , 1970 .

[8]  C. Haselgrove,et al.  A method for numerical integration , 1961 .

[9]  Painter,et al.  Pseudospherical integration scheme for electronic-structure calculations. , 1989, Physical review. B, Condensed matter.

[10]  H. M. Möller,et al.  Kubaturformeln mit minimaler Knotenzahl , 1976 .

[11]  A. Stroud,et al.  Approximate Calculation of Integrals , 1962 .

[12]  Giovanni Monegato,et al.  Quadrature Rules for Regions Having Regular Hexagonal Symmetry , 1977 .

[13]  Evert Jan Baerends,et al.  Self-consistent molecular Hartree—Fock—Slater calculations I. The computational procedure , 1973 .

[14]  James N. Lyness,et al.  Moderate degree symmetric quadrature rules for the triangle j inst maths , 1975 .

[15]  G. te Velde,et al.  Three‐dimensional numerical integration for electronic structure calculations , 1988 .

[16]  D. A. Dunavant.  High degree efficient symmetrical Gaussian quadrature rules for the triangle , 1985 .

[17]  V. I. Lebedev,et al.  Spherical quadrature formulas exact to orders 25–29 , 1977 .