Stochastic Formulation of the Resolution of Identity: Application to Second Order Møller-Plesset Perturbation Theory.

A stochastic orbital approach to the resolution of identity (RI) approximation for 4-index electron repulsion integrals (ERIs) is presented. The stochastic RI-ERIs are then applied to second order Møller-Plesset perturbation theory (MP2) utilizing a multiple stochastic orbital approach. The introduction of multiple stochastic orbitals results in an O(NAO3) scaling for both the stochastic RI-ERIs and stochastic RI-MP2, NAO being the number of basis functions. For a range of water clusters we demonstrate that this method exhibits a small prefactor and observed scalings of O(Ne2.4) for total energies and O(Ne3.1) for forces (Ne being the number of correlated electrons), outperforming MP2 for clusters with as few as 21 water molecules.

[1]  D. Reichman,et al.  Chemical Transformations Approaching Chemical Accuracy via Correlated Sampling in Auxiliary-Field Quantum Monte Carlo. , 2017, Journal of chemical theory and computation.

[2]  R. Baer,et al.  Equilibrium configurations of large nanostructures using the embedded saturated-fragments stochastic density functional theory. , 2017, The Journal of chemical physics.

[3]  R. Baer,et al.  Stochastic GW Calculations for Molecules. , 2016, Journal of chemical theory and computation.

[4]  R. Baer,et al.  Stochastic self-consistent Green's function second-order perturbation theory (sGF2) , 2016, 1603.04141.

[5]  Ali Alavi,et al.  Combining the Complete Active Space Self-Consistent Field Method and the Full Configuration Interaction Quantum Monte Carlo within a Super-CI Framework, with Application to Challenging Metal-Porphyrins. , 2016, Journal of chemical theory and computation.

[6]  A. Thom,et al.  Developments in stochastic coupled cluster theory: The initiator approximation and application to the uniform electron gas. , 2015, The Journal of chemical physics.

[7]  R. Baer,et al.  Stochastic Optimally Tuned Range-Separated Hybrid Density Functional Theory. , 2015, The journal of physical chemistry. A.

[8]  R. Baer,et al.  Spontaneous Charge Carrier Localization in Extended One-Dimensional Systems. , 2015, Physical review letters.

[9]  R. Baer,et al.  Time-dependent Stochastic Bethe-Salpeter Approach , 2015, 1502.02784.

[10]  R. Baer,et al.  Sublinear scaling for time-dependent stochastic density functional theory. , 2014, The Journal of chemical physics.

[11]  Eran Rabani,et al.  Communication: Embedded fragment stochastic density functional theory. , 2014, The Journal of chemical physics.

[12]  R. Baer,et al.  Breaking the theoretical scaling limit for predicting quasiparticle energies: the stochastic GW approach. , 2014, Physical review letters.

[13]  S. Hirata,et al.  Stochastic, real-space, imaginary-time evaluation of third-order Feynman-Goldstone diagrams. , 2014, The Journal of chemical physics.

[14]  R. Baer,et al.  A Guided Stochastic Energy-Domain Formulation of the Second Order Møller-Plesset Perturbation Theory. , 2013, The journal of physical chemistry letters.

[15]  So Hirata,et al.  Stochastic evaluation of second-order Dyson self-energies. , 2013, The Journal of chemical physics.

[16]  R. Baer,et al.  Self-averaging stochastic Kohn-Sham density-functional theory. , 2013, Physical review letters.

[17]  R. Baer,et al.  Expeditious Stochastic Calculation of Random-Phase Approximation Energies for Thousands of Electrons in Three Dimensions. , 2012, The journal of physical chemistry letters.

[18]  Robert M Parrish,et al.  Communication: Tensor hypercontraction. III. Least-squares tensor hypercontraction for the determination of correlated wavefunctions. , 2012, The Journal of chemical physics.

[19]  Robert M Parrish,et al.  Tensor hypercontraction. II. Least-squares renormalization. , 2012, The Journal of chemical physics.

[20]  S. Hirata,et al.  Stochastic evaluation of second-order many-body perturbation energies. , 2012, The Journal of chemical physics.

[21]  R. Baer,et al.  Expeditious Stochastic Approach for MP2 Energies in Large Electronic Systems. , 2012, Journal of chemical theory and computation.

[22]  Robert M Parrish,et al.  Tensor hypercontraction density fitting. I. Quartic scaling second- and third-order Møller-Plesset perturbation theory. , 2012, The Journal of chemical physics.

[23]  Alex J W Thom,et al.  Stochastic coupled cluster theory. , 2010, Physical review letters.

[24]  Tjerk P. Straatsma,et al.  NWChem: A comprehensive and scalable open-source solution for large scale molecular simulations , 2010, Comput. Phys. Commun..

[25]  Ali Alavi,et al.  Approaching chemical accuracy using full configuration-interaction quantum Monte Carlo: a study of ionization potentials. , 2010, The Journal of chemical physics.

[26]  Ali Alavi,et al.  Fermion Monte Carlo without fixed nodes: a game of life, death, and annihilation in Slater determinant space. , 2009, The Journal of chemical physics.

[27]  Shigeru Nagase,et al.  Projector Monte Carlo method based on configuration state functions. Test applications to the H4 system and dissociation of LiH , 2008 .

[28]  Ali Alavi,et al.  Stochastic perturbation theory: a low-scaling approach to correlated electronic energies. , 2007, Physical review letters.

[29]  Christof Hättig,et al.  Optimization of auxiliary basis sets for RI-MP2 and RI-CC2 calculations: Core–valence and quintuple-ζ basis sets for H to Ar and QZVPP basis sets for Li to Kr , 2005 .

[30]  F. Weigend,et al.  Efficient use of the correlation consistent basis sets in resolution of the identity MP2 calculations , 2002 .

[31]  D. Neuhauser,et al.  Shifted-contour auxiliary-field Monte Carlo: circumventing the sign difficulty for electronic-structure calculations , 1997 .

[32]  Zhang,et al.  Constrained path quantum Monte Carlo method for fermion ground states. , 1995, Physical review letters.

[33]  J. Almlöf,et al.  Integral approximations for LCAO-SCF calculations , 1993 .

[34]  Martin W. Feyereisen,et al.  Use of approximate integrals in ab initio theory. An application in MP2 energy calculations , 1993 .

[35]  T. H. Dunning.  Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen , 1989 .

[36]  Brett I. Dunlap,et al.  Fitting the Coulomb potential variationally in Xα molecular calculations , 1983 .

[37]  John R. Sabin,et al.  On some approximations in applications of Xα theory , 1979 .

[38]  J. L. Whitten,et al.  Coulombic potential energy integrals and approximations , 1973 .

[39]  Jan Almlöf,et al.  Laplace transform techniques in Mo/ller–Plesset perturbation theory , 1992 .