Hybrid stochastic-deterministic calculation of the second-order perturbative contribution of multireference perturbation theory.

A hybrid stochastic-deterministic approach for computing the second-order perturbative contribution E(2) within multireference perturbation theory (MRPT) is presented. The idea at the heart of our hybrid scheme-based on a reformulation of E(2) as a sum of elementary contributions associated with each determinant of the MR wave function-is to split E(2) into a stochastic and a deterministic part. During the simulation, the stochastic part is gradually reduced by dynamically increasing the deterministic part until one reaches the desired accuracy. In sharp contrast with a purely stochastic Monte Carlo scheme where the error decreases indefinitely as t-1/2 (where t is the computational time), the statistical error in our hybrid algorithm displays a polynomial decay ∼t-n with n = 3-4 in the examples considered here. If desired, the calculation can be carried on until the stochastic part entirely vanishes. In that case, the exact result is obtained with no error bar and no noticeable computational overhead compared to the fully deterministic calculation. The method is illustrated on the F2 and Cr2 molecules. Even for the largest case corresponding to the Cr2 molecule treated with the cc-pVQZ basis set, very accurate results are obtained for E(2) for an active space of (28e, 176o) and a MR wave function including up to 2×107 determinants.

[1]  Yann Garniron,et al.  A Jeziorski-Monkhorst fully uncontracted multi-reference perturbative treatment. I. Principles, second-order versions, and tests on ground state potential energy curves. , 2017, The Journal of chemical physics.

[2]  Ali Alavi,et al.  Stochastic multi-reference perturbation theory with application to the linearized coupled cluster method. , 2016, The Journal of chemical physics.

[3]  Ali Alavi,et al.  Semistochastic Heat-Bath Configuration Interaction Method: Selected Configuration Interaction with Semistochastic Perturbation Theory. , 2016, Journal of chemical theory and computation.

[4]  A. Scemama,et al.  Using CIPSI nodes in diffusion Monte Carlo , 2016, 1607.06742.

[5]  Edward F. Valeev,et al.  Communication: stochastic evaluation of explicitly correlated second-order many-body perturbation energy. , 2014, The Journal of chemical physics.

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

[7]  Ali Alavi,et al.  Taming the First-Row Diatomics: A Full Configuration Interaction Quantum Monte Carlo Study. , 2012, Journal of chemical theory and computation.

[8]  C J Umrigar,et al.  Semistochastic projector Monte Carlo method. , 2012, Physical review letters.

[9]  Garnet Kin-Lic Chan,et al.  Spin-adapted density matrix renormalization group algorithms for quantum chemistry. , 2012, The Journal of chemical physics.

[10]  Christof Hättig,et al.  Explicitly correlated electrons in molecules. , 2012, Chemical reviews.

[11]  H. Lischka,et al.  Multiconfiguration self-consistent field and multireference configuration interaction methods and applications. , 2012, Chemical reviews.

[12]  Dmitry I. Lyakh,et al.  Multireference nature of chemistry: the coupled-cluster view. , 2012, Chemical reviews.

[13]  B. Jeziorski.  Multireference coupled-cluster Ansatz , 2010 .

[14]  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.

[15]  Isaiah Shavitt,et al.  New implementation of the graphical unitary group approach for multireference direct configuration interaction calculations , 2009 .

[16]  M. Nooijen,et al.  State specific equation of motion coupled cluster method in general active space. , 2009, The Journal of chemical physics.

[17]  R. Fink.  The multi-reference retaining the excitation degree perturbation theory: A size-consistent, unitary invariant, and rapidly convergent wavefunction based ab initio approach , 2009 .

[18]  Josef Paldus,et al.  A Critical Assessment of Coupled Cluster Method in Quantum Chemistry , 2007 .

[19]  R. Fink.  Two new unitary-invariant and size-consistent perturbation theoretical approaches to the electron correlation energy , 2006 .

[20]  Kirk A Peterson,et al.  Systematically convergent basis sets for transition metals. I. All-electron correlation consistent basis sets for the 3d elements Sc-Zn. , 2005, The Journal of chemical physics.

[21]  R. Cimiraglia,et al.  n-electron valence state perturbation theory: A spinless formulation and an efficient implementation of the strongly contracted and of the partially contracted variants , 2002 .

[22]  Celestino Angeli,et al.  Introduction of n-electron valence states for multireference perturbation theory , 2001 .

[23]  Mark S. Gordon,et al.  General atomic and molecular electronic structure system , 1993, J. Comput. Chem..

[24]  White,et al.  Density-matrix algorithms for quantum renormalization groups. , 1993, Physical review. B, Condensed matter.

[25]  White,et al.  Density matrix formulation for quantum renormalization groups. , 1992, Physical review letters.

[26]  Björn O. Roos,et al.  Second-order perturbation theory with a complete active space self-consistent field reference function , 1992 .

[27]  Kerstin Andersson,et al.  Second-order perturbation theory with a CASSCF reference function , 1990 .

[28]  Paul Hudak,et al.  Conception, evolution, and application of functional programming languages , 1989, CSUR.

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

[30]  Stefano Evangelisti,et al.  Convergence of an improved CIPSI algorithm , 1983 .

[31]  B. Roos,et al.  The complete active space SCF (CASSCF) method in a Newton–Raphson formulation with application to the HNO molecule , 1981 .

[32]  B. Roos,et al.  A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach , 1980 .

[33]  J. P. Malrieu,et al.  Iterative perturbation calculations of ground and excited state energies from multiconfigurational zeroth‐order wavefunctions , 1973 .

[34]  R. Nesbet.  Configuration interaction in orbital theories , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[35]  P. S. Epstein,et al.  The Stark effect from the point of view of Schroedinger's quantum theory , 1926 .

[36]  Thomas Müller,et al.  High-level multireference methods in the quantum-chemistry program system COLUMBUS: Analytic MR-CISD and MR-AQCC gradients and MR-AQCC-LRT for excited states, GUGA spin–orbit CI and parallel CI density , 2001 .

[37]  B. Roos,et al.  A Comparison of the Super-CI and the Newton-Raphson Scheme in the Complete Active Space SCF Method , 1980 .