Stochastic multi-reference perturbation theory with application to linearized coupled cluster method

Abstract

In this article we report a stochastic evaluation of the recently proposed LCC multireference perturbation theory [Sharma S., and Alavi A., J. Chem. Phys. 143, 102815, (2015)]. In this method both the zeroth order and first order wavefunctions are sampled stochastically by propagating simultaneously two populations of signed walkers. The sampling of the zeroth order wavefunction follows a set of stochastic processes identical to the one used in the FCIQMC method. To sample the first order wavefunction, the usual FCIQMC algorithm is augmented with a source term that spawns walkers in the sampled first order wavefunction from the zeroth order wavefunction. The second order energy is also computed stochastically but requires no additional overhead outside of the added cost of sampling the first order wavefunction. This fully stochastic method opens up the possibility of simultaneously treating large active spaces to account for static correlation and recovering the dynamical correlation using perturbation theory. This method is used to study a few benchmark systems including the carbon dimer and aromatic molecules. We have computed the singlet-triplet gaps of benzene and m-xylylene. For m-xylylene, which has proved difficult for standard CASSCF+PT, we find the singlet-triplet gap to be in good agreement with the experimental values.

22 pages, 4 figures

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• Direct comparison of many-body methods for realistic electronic Hamiltonians
• Unbiasing the initiator approximation in Full Configuration Interaction Quantum Monte Carlo
• Efficient and Stochastic Multireference Perturbation Theory for Large Active Spaces within a Full Configuration Interaction Quantum Monte Carlo Framework
• A Jeziorski-Monkhorst fully uncontracted Multi-Reference perturbative treatment I: principles, second-order versions and tests on ground state potential energy curves
• Multi-state effective Hamiltonian and size-consistency corrections in stochastic configuration interactions
• Symmetry projected Jastrow mean field wavefunction in variational Monte Carlo
• Improved Stochastic Multireference Perturbation Theory for Correlated Systems with Large Active Spaces
• A combined on-the-fly/interpolation procedure for evaluating energy values needed in molecular simulations
• Stochastic evaluation of four-component relativistic second-order many-body perturbation energies: A potentially quadratic-scaling correlation method