Multi‐electron integrals

This review presents techniques for the computation of multi‐electron integrals over Cartesian and solid‐harmonic Gaussian‐type orbitals as used in standard electronic‐structure investigations. The review goes through the basics for one‐ and two‐electron integrals, discuss details of various two‐electron integral evaluation schemes, approximative methods, techniques to compute multi‐electron integrals for explicitly correlated methods, and property integrals. © 2011 John Wiley & Sons, Ltd.

[1]  P. Taylor,et al.  Accurate quantum‐chemical calculations: The use of Gaussian‐type geminal functions in the treatment of electron correlation , 1996 .

[2]  Martin Head-Gordon,et al.  A method for two-electron Gaussian integral and integral derivative evaluation using recurrence relations , 1988 .

[3]  Seiichiro Ten-no,et al.  Initiation of explicitly correlated Slater-type geminal theory , 2004 .

[4]  Michel Dupuis,et al.  Numerical integration using rys polynomials , 1976 .

[5]  Benny G. Johnson,et al.  THE CONTINUOUS FAST MULTIPOLE METHOD , 1994 .

[6]  Trygve Helgaker,et al.  A unified scheme for the calculation of differentiated and undifferentiated molecular integrals over solid-harmonic Gaussians. , 2007, Physical chemistry chemical physics : PCCP.

[7]  N. Handy,et al.  The determination of energies and wavefunctions with full electronic correlation , 1969, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[8]  Roland Lindh,et al.  The reduced multiplication scheme of the Rys quadrature and new recurrence relations for auxiliary function based two‐electron integral evaluation , 1991 .

[9]  P. Knowles,et al.  Poisson equation in the Kohn-Sham Coulomb problem. , 2001, Physical review letters.

[10]  S. F. Boys Electronic wave functions - I. A general method of calculation for the stationary states of any molecular system , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[11]  T. Helgaker,et al.  Variational and robust density fitting of four-center two-electron integrals in local metrics. , 2008, The Journal of chemical physics.

[12]  A. Köster Hermite Gaussian auxiliary functions for the variational fitting of the Coulomb potential in density functional methods , 2003 .

[13]  M. Ratner Molecular electronic-structure theory , 2000 .

[14]  Michel Dupuis,et al.  Computation of electron repulsion integrals using the rys quadrature method , 1983 .

[15]  T. Helgaker,et al.  Accurate quantum-chemical calculations using Gaussian-type geminal and Gaussian-type orbital basis sets: applications to atoms and diatomics. , 2007, Physical chemistry chemical physics : PCCP.

[16]  Christian Ochsenfeld,et al.  Multipole-based integral estimates for the rigorous description of distance dependence in two-electron integrals. , 2005, The Journal of chemical physics.

[17]  Shigeru Obara,et al.  Efficient recursive computation of molecular integrals over Cartesian Gaussian functions , 1986 .

[18]  B. I. Dunlap,et al.  Robust variational fitting: Gáspár's variational exchange can accurately be treated analytically , 2000 .

[19]  T. Helgaker,et al.  An electronic Hamiltonian for origin independent calculations of magnetic properties , 1991 .

[20]  E. Davidson,et al.  One- and two-electron integrals over cartesian gaussian functions , 1978 .

[21]  W. Kutzelnigg,et al.  Møller-plesset calculations taking care of the correlation CUSP , 1987 .

[22]  J. Pople,et al.  Self‐Consistent Molecular‐Orbital Methods. I. Use of Gaussian Expansions of Slater‐Type Atomic Orbitals , 1969 .

[23]  J. G. Zabolitzky,et al.  A new functional for variational calculation of atomic and molecular second-order correlation energies , 1982 .

[24]  Frederick R. Manby,et al.  R12 methods in explicitly correlated molecular electronic structure theory , 2006 .

[25]  S. Ten-no,et al.  Intramolecular charge-transfer excitation energies from range-separated hybrid functionals using the Yukawa potential , 2009 .

[26]  F. London,et al.  Théorie quantique des courants interatomiques dans les combinaisons aromatiques , 1937 .

[27]  R. Ditchfield,et al.  Molecular Orbital Theory of Magnetic Shielding and Magnetic Susceptibility , 1972 .

[28]  S. Ten-no,et al.  Range-separation by the Yukawa potential in long-range corrected density functional theory with Gaussian-type basis functions , 2008 .

[29]  J. Noga,et al.  Alternative formulation of the matrix elements in MP2‐R12 theory , 2005 .

[30]  N. Handy,et al.  A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP) , 2004 .

[31]  R. Ahlrichs Efficient evaluation of three-center two-electron integrals over Gaussian functions , 2004 .

[32]  Werner Kutzelnigg,et al.  r12-Dependent terms in the wave function as closed sums of partial wave amplitudes for large l , 1985 .

[33]  Roland Lindh,et al.  Density fitting with auxiliary basis sets from Cholesky decompositions , 2009 .

[34]  Petr Čársky,et al.  Incomplete GammaFm(x) Functions for Real Negative and Complex Arguments , 1998 .

[35]  Paweł Sałek,et al.  Linear-scaling formation of Kohn-Sham Hamiltonian: application to the calculation of excitation energies and polarizabilities of large molecular systems. , 2004, The Journal of chemical physics.

[36]  Michel Dupuis,et al.  Evaluation of molecular integrals over Gaussian basis functions , 1976 .

[37]  Trygve Helgaker,et al.  Molecular Electronic-Structure Theory: Helgaker/Molecular Electronic-Structure Theory , 2000 .

[38]  Marco Häser,et al.  Improvements on the direct SCF method , 1989 .

[39]  Trygve Helgaker,et al.  Quantitative quantum chemistry , 2008 .

[40]  N. H. Beebe,et al.  Simplifications in the generation and transformation of two‐electron integrals in molecular calculations , 1977 .

[41]  Martin Head-Gordon,et al.  Auxiliary basis expansions for large-scale electronic structure calculations. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[42]  Leslie Greengard,et al.  A fast algorithm for particle simulations , 1987 .

[43]  Sebastian Höfener,et al.  Slater-type geminals in explicitly-correlated perturbation theory: application to n-alkanols and analysis of errors and basis-set requirements. , 2008, Physical chemistry chemical physics : PCCP.