Communication: An efficient and accurate perturbative correction to initiator full configuration interaction quantum Monte Carlo.

We present a perturbative correction within initiator full configuration interaction quantum Monte Carlo (i-FCIQMC). In the existing i-FCIQMC algorithm, a significant number of spawned walkers are discarded due to the initiator criteria. Here we show that these discarded walkers have a form that allows the calculation of a second-order Epstein-Nesbet correction, which may be accumulated in a trivial and inexpensive manner, yet substantially improves i-FCIQMC results. The correction is applied to the Hubbard model and the uniform electron gas and molecular systems.

[1]  S. Ten-no.  Multi-state effective Hamiltonian and size-consistency corrections in stochastic configuration interactions. , 2017, The Journal of chemical physics.

[2]  Y. Smeyers,et al.  Half‐Projected and Projected Hartree‐Fock Calculations for Singlet Ground States. i. four‐Electron Atomic Systems , 1973 .

[3]  Ali Alavi,et al.  An excited-state approach within full configuration interaction quantum Monte Carlo. , 2015, The Journal of chemical physics.

[4]  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.

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

[6]  Charles J. C. Scott,et al.  Stochastic coupled cluster theory: Efficient sampling of the coupled cluster expansion. , 2017, The Journal of chemical physics.

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

[8]  Sandeep Sharma,et al.  PySCF: the Python‐based simulations of chemistry framework , 2018 .

[9]  Walter Thiel,et al.  Benchmarks for electronically excited states: CASPT2, CC2, CCSD, and CC3. , 2008, The Journal of chemical physics.

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

[11]  Sandeep Sharma,et al.  Excited states using semistochastic heat-bath configuration interaction. , 2017, The Journal of chemical physics.

[12]  Adam A Holmes,et al.  Cheap and Near Exact CASSCF with Large Active Spaces. , 2017, Journal of chemical theory and computation.

[13]  A. Scemama,et al.  Accurate nonrelativistic ground-state energies of 3d transition metal atoms. , 2014, The Journal of chemical physics.

[14]  N. S. Blunt,et al.  Accurate Exchange-Correlation Energies for the Warm Dense Electron Gas. , 2016, Physical review letters.

[15]  P. Bunker,et al.  A precise solution of the rotation bending Schrödinger equation for a triatomic molecule with application to the water molecule , 1979 .

[16]  C J Umrigar,et al.  Efficient Heat-Bath Sampling in Fock Space. , 2015, Journal of chemical theory and computation.

[17]  George H. Booth,et al.  Density matrices in full configuration interaction quantum Monte Carlo: Excited states, transition dipole moments, and parallel distribution. , 2017, The Journal of chemical physics.

[18]  Paul M Zimmerman,et al.  Excited States of Methylene, Polyenes, and Ozone from Heat-Bath Configuration Interaction. , 2018, The journal of physical chemistry. A.

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

[20]  Yann Garniron,et al.  Deterministic Construction of Nodal Surfaces within Quantum Monte Carlo: The Case of FeS. , 2017, Journal of chemical theory and computation.

[21]  M. H. Kalos,et al.  Bilinear quantum Monte Carlo: Expectations and energy differences , 1992 .

[22]  Ali Alavi,et al.  Communications: Survival of the fittest: accelerating convergence in full configuration-interaction quantum Monte Carlo. , 2010, The Journal of chemical physics.

[23]  Ali Alavi,et al.  Convergence of many-body wave-function expansions using a plane-wave basis: From homogeneous electron gas to solid state systems , 2012, 1202.4990.

[24]  Yann Garniron,et al.  Hybrid stochastic-deterministic calculation of the second-order perturbative contribution of multireference perturbation theory. , 2017, The Journal of chemical physics.

[25]  Ali Alavi,et al.  Towards an exact description of electronic wavefunctions in real solids , 2012, Nature.

[26]  Verena A. Neufeld,et al.  A study of the dense uniform electron gas with high orders of coupled cluster. , 2017, The Journal of chemical physics.

[27]  Garnet Kin-Lic Chan,et al.  The ab-initio density matrix renormalization group in practice. , 2015, The Journal of chemical physics.

[28]  Robert J. Buenker,et al.  Individualized configuration selection in CI calculations with subsequent energy extrapolation , 1974 .

[29]  N. Blunt,et al.  Interaction picture density matrix quantum Monte Carlo. , 2015, The Journal of chemical physics.

[30]  S. Ten-no,et al.  A study of potential energy curves from the model space quantum Monte Carlo method. , 2015, The Journal of chemical physics.

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

[32]  Ali Alavi,et al.  Unbiased reduced density matrices and electronic properties from full configuration interaction quantum Monte Carlo. , 2014, The Journal of chemical physics.

[33]  Michel Caffarel,et al.  Using perturbatively selected configuration interaction in quantum Monte Carlo calculations , 2013 .

[34]  Matthew B Hastings,et al.  Measuring Renyi entanglement entropy in quantum Monte Carlo simulations. , 2010, Physical review letters.

[35]  Seiichiro Ten-no,et al.  Stochastic determination of effective Hamiltonian for the full configuration interaction solution of quasi-degenerate electronic states. , 2013, The Journal of chemical physics.

[36]  Ali Alavi,et al.  Semi-stochastic full configuration interaction quantum Monte Carlo: Developments and application. , 2015, The Journal of chemical physics.

[37]  Jeffrey B Schriber,et al.  Communication: An adaptive configuration interaction approach for strongly correlated electrons with tunable accuracy. , 2016, The Journal of chemical physics.

[38]  Wenjian Liu,et al.  iCI: Iterative CI toward full CI. , 2016, Journal of chemical theory and computation.

[39]  Ali Alavi,et al.  Accurate Ab initio calculation of ionization potentials of the first-row transition metals with the configuration-interaction quantum Monte Carlo technique. , 2015, Physical review letters.

[40]  N. S. Blunt,et al.  The sign problem and population dynamics in the full configuration interaction quantum Monte Carlo method. , 2011, The Journal of chemical physics.

[41]  Ali Alavi,et al.  Full Configuration Interaction Excitations of Ethene and Butadiene: Resolution of an Ancient Question. , 2012, Journal of chemical theory and computation.

[42]  Ali Alavi,et al.  A study of electron affinities using the initiator approach to full configuration interaction quantum Monte Carlo. , 2011, The Journal of chemical physics.

[43]  Sandeep Sharma.  A general non-Abelian density matrix renormalization group algorithm with application to the C2 dimer. , 2015, The Journal of chemical physics.

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

[45]  C J Umrigar,et al.  Heat-Bath Configuration Interaction: An Efficient Selected Configuration Interaction Algorithm Inspired by Heat-Bath Sampling. , 2016, Journal of chemical theory and computation.

[46]  N. S. Blunt,et al.  Density-matrix quantum Monte Carlo method , 2013, 1303.5007.

[47]  Martin Head-Gordon,et al.  A deterministic alternative to the full configuration interaction quantum Monte Carlo method. , 2016, The Journal of chemical physics.