Highly accurate numerical results for three‐center nuclear attraction and two‐electron Coulomb and exchange integrals over Slater‐type functions

The present work focuses on the recent progress in nonlinear transformation methods for improving the convergence of highly oscillatory integrals and in their applications for an efficient and rapid numerical evaluation of molecular electronic integrals over Slater-type functions (STFs). The nonlinear D transformation, which is probably the most effective general approach for increasing the rate of convergence of semi-infinite oscillatory integrals, is presented. Molecular integrals over STFs are expressed as finite linear combinations of integrals over B functions. The basis set of B functions is suitable to apply the Fourier transform method, which led to analytic expressions, involving highly oscillatory functions, for molecular integrals. Efficient algorithms based on the D transformation are now developed for a numerical evaluation of molecular integrals over STFs. Numerical results that we obtained with linear and nonlinear molecules, and which are in agreement with those obtained using existing codes (Alchemy, STOP, and ADGGSTNGINT), show that the algorithms described in this work are relevant. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

[1]  P. Hoggan,et al.  Three-centre two-electron Coulomb and hybrid integrals evaluated using nonlinear D- and barD-transformations , 1999 .

[2]  Herbert H. H. Homeier,et al.  Some Properties of the Coupling Coefficients of Real Spherical Harmonics and Their Relation to Gaunt Coefficients , 1996 .

[3]  P. Wynn,et al.  On a Device for Computing the e m (S n ) Transformation , 1956 .

[4]  Hassan Safouhi,et al.  Efficient evaluation of Coulomb integrals: the nonlinear D- and -transformations , 1998 .

[5]  H. Safouhi,et al.  Regular Article: Efficient and Rapid Evaluation of Three-Center Two Electron Coulomb and Hybrid Integrals Using Nonlinear Transformations , 1999 .

[6]  Avram Sidi.  Computation of infinite integrals involving Bessel functions of arbitrary order by the D¯ -transformation , 1997 .

[7]  J. A. Gaunt.  The Triplets of Helium , 1929 .

[8]  Guillermo Ramírez,et al.  Calculation of many-centre two-electron molecular integrals with STO , 1997 .

[9]  E. J. Weniger,et al.  The Fourier transforms of some exponential‐type basis functions and their relevance to multicenter problems , 1983 .

[10]  H. P. Trivedi,et al.  Fourier transform of a two-center product of exponential-type orbitals. Application to one- and two-electron multicenter integrals , 1983 .

[11]  E. Filter,et al.  Translations of fields represented by spherical-harmonic expansions for molecular calculations , 1975 .

[12]  J. C. Slater.  Atomic Shielding Constants , 1930 .

[13]  H. L. Cox,et al.  On the Calculation of Multicenter Two‐Electron Repulsion Integrals Involving Slater Functions , 1964 .

[14]  Hassan Safouhi,et al.  Efficient evaluation of integrals for density functional theory: NonlinearD transformations to evaluate three-center nuclear attraction integrals overB functions , 1998 .

[15]  Avram Sidi,et al.  Extrapolation Methods for Oscillatory Infinite Integrals , 1980 .

[16]  John C. Slater,et al.  Analytic Atomic Wave Functions , 1932 .

[17]  E. Steinborn,et al.  Extremely compact formulas for molecular two-center one-electron integrals and Coulomb integrals over Slater-type atomic orbitals , 1978 .

[18]  G. Shortley,et al.  The Theory of Atomic Spectra , 1935 .

[19]  Avram Sidi,et al.  The numerical evaluation of very oscillatory infinite integrals by extrapolation , 1982 .

[20]  Yu-lin Xu,et al.  Fast evaluation of Gaunt coefficients: recursive approach , 1997 .

[21]  Hassan Safouhi,et al.  Non‐linear transformations for rapid and efficient evaluation of multicenter bielectronic integrals over B functions , 1999 .

[22]  Grotendorst,et al.  Numerical evaluation of molecular one- and two-electron multicenter integrals with exponential-type orbitals via the Fourier-transform method. , 1988, Physical review. A, General physics.

[23]  D. Rinaldi,et al.  Integrals over B functions basis sets. I. Three‐center molecular integrals, a numerical study , 1994 .

[24]  David Feller,et al.  Basis Set Selection for Molecular Calculations , 1986 .

[25]  Ahmed Bouferguene,et al.  Convergence analysis of the addition theorem of Slater orbitals and its application to three-center nuclear attraction integrals , 1998 .

[26]  Clemens C. J. Roothaan,et al.  New Developments in Molecular Orbital Theory , 1951 .

[27]  D. Rinaldi,et al.  A new single‐center method to compute molecular integrals of quantum chemistry in slater‐type orbital basis of functions , 1994 .

[28]  E. J. Weniger,et al.  Addition theorems for B functions and other exponentially declining functions , 1989 .