Resolutions of the Coulomb Operator: VII. Evaluation of Long-Range Coulomb and Exchange Matrices.

Use of the resolution of Ewald operator method for computing long-range Coulomb and exchange interactions is presented. We show that the accuracy of this method can be controlled by a single parameter in a manner similar to that used by conventional algorithms that compute two-electron integrals. Significant performance advantages over conventional algorithms are observed, particularly for high quality basis sets and globular systems. The approach is directly applicable to hybrid density functional theory.

[1]  Peter M W Gill,et al.  Resolutions of the Coulomb Operator: IV. The Spherical Bessel Quasi-Resolution. , 2011, Journal of chemical theory and computation.

[2]  Michael J Frisch,et al.  Efficient evaluation of short-range Hartree-Fock exchange in large molecules and periodic systems. , 2006, The Journal of chemical physics.

[3]  Taweetham Limpanuparb,et al.  Applications of Resolutions of the Coulomb Operator in Quantum Chemistry , 2012 .

[4]  Ross D. Adamson,et al.  Efficient calculation of short‐range Coulomb energies , 1999 .

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

[6]  M. Head‐Gordon,et al.  Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections. , 2008, Physical chemistry chemical physics : PCCP.

[7]  V. Rokhlin.  Rapid solution of integral equations of classical potential theory , 1985 .

[8]  G. Scuseria,et al.  Importance of short-range versus long-range Hartree-Fock exchange for the performance of hybrid density functionals. , 2006, The Journal of chemical physics.

[9]  A DFT investigation of methanolysis and hydrolysis of triacetin , 2010, 1212.5655.

[10]  P. Gill,et al.  A remarkable identity involving Bessel functions , 2011, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[11]  Martin Head-Gordon,et al.  A Resolution-Of-The-Identity Implementation of the Local Triatomics-In-Molecules Model for Second-Order Møller-Plesset Perturbation Theory with Application to Alanine Tetrapeptide Conformational Energies. , 2005, Journal of chemical theory and computation.

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

[13]  Peter M W Gill,et al.  Resolutions of the Coulomb operator. , 2007, The Journal of chemical physics.

[14]  L. Greengard.  The Rapid Evaluation of Potential Fields in Particle Systems , 1988 .

[15]  Anna I. Krylov,et al.  Q‐Chem: an engine for innovation , 2013 .

[16]  G. Scuseria,et al.  Hybrid functionals based on a screened Coulomb potential , 2003 .

[17]  Takao Tsuneda,et al.  Long-range corrected density functional study on weakly bound systems: balanced descriptions of various types of molecular interactions. , 2007, The Journal of chemical physics.

[18]  Edward N Brothers,et al.  Accurate solid-state band gaps via screened hybrid electronic structure calculations. , 2008, The Journal of chemical physics.

[19]  Ross D. Adamson,et al.  Coulomb-attenuated exchange energy density functionals , 1996 .

[20]  Peter M W Gill,et al.  Resolutions of the Coulomb Operator: V. The Long-Range Ewald Operator. , 2011, Journal of chemical theory and computation.

[21]  Henrik Koch,et al.  Method specific Cholesky decomposition: coulomb and exchange energies. , 2008, The Journal of chemical physics.

[22]  Artur F Izmaylov,et al.  Influence of the exchange screening parameter on the performance of screened hybrid functionals. , 2006, The Journal of chemical physics.

[23]  Andrew W. Appel,et al.  An Efficient Program for Many-Body Simulation , 1983 .

[24]  Benny G. Johnson,et al.  Linear scaling density functional calculations via the continuous fast multipole method , 1996 .

[25]  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.

[26]  Jack J. Dongarra,et al.  A set of level 3 basic linear algebra subprograms , 1990, TOMS.

[27]  Peter M W Gill,et al.  Resolutions of the Coulomb operator. VI. Computation of auxiliary integrals. , 2011, The Journal of chemical physics.

[28]  Peter M W Gill,et al.  Resolutions of the Coulomb operator. Part III. Reduced-rank Schrödinger equations. , 2009, Physical chemistry chemical physics : PCCP.