Nonlinear transformation methods for accelerating the convergence of Coulomb integrals over exponential type functions

作     者：Safouhi, Hassan Bouferguene, Ahmed 

作者机构：Univ Alberta Edmonton AB T6C 4G9 Canada 

出 版 物：《THEORETICAL CHEMISTRY ACCOUNTS》 

年 卷 期：2007年第117卷第2期

页      面：213-222页

核心收录：

学科分类：081704[工学-应用化学] 07[理学] 070304[理学-物理化学(含∶化学物理)] 08[工学] 0817[工学-化学工程与技术] 0703[理学-化学] 

主　　题：nonlinear transformations extrapolation methods numerical integration molecular integrals Slater type functions B functions 

摘      要：It is well known that in any ab initio molecular orbital (MO) calculation, the major task involves the computation of molecular integrals, among which the computation of Coulomb integrals are the most frequently encountered. As the molecular system gets larger, computation of these integrals becomes one of the most laborious and time consuming steps in molecular systems calculation. Improvement of the computational methods of molecular integrals would be indispensable to a further development in computational studies of large molecular systems. The atomic orbital basis functions chosen in the present work are Slater type functions. These functions can be expressed as finite linear combinations of B functions which are suitable to apply the Fourier transform method. The difficulties of the numerical evaluation of the analytic expressions of the integrals of interest arise mainly from the presence of highly oscillatory semi-infinite integrals. In this work, we present a generalized algorithm based on the nonlinear (D) over bar transformation of Sidi, for a precise and fast numerical evaluation of molecular integrals over Slater type functions and over B functions. Numerical results obtained for the three-center two-electron Coulomb and hybrid integrals over B functions and over Slater type functions. Comparisons with numerical results obtained using alternatives approaches and an existing code are listed.