Efficient and Stochastic Multireference Perturbation Theory for Large Active Spaces within a Full Configuration Interaction Quantum Monte Carlo Framework

Abstract

Full Configuration Interaction Quantum Monte Carlo (FCIQMC) has been effectively applied to very large configuration interaction (CI) problems, and was recently adapted for use as an active space solver and combined with orbital optimisation. In this work, we detail an approach within FCIQMC to allow for efficient sampling of fully internally-contracted multireference perturbation theories within the same stochastic framework. Schemes are described to allow for the close control over the resolution of stochastic sampling of the effective higher-body intermediates within the active space. It is found that while CASPT2 seems less amenable to a stochastic reformulation, NEVPT2 is far more stable, requiring a similar number of walkers to converge the NEVPT2 expectation values as to converge the underlying CI problem. We demonstrate the application of the stochastic approach to the computation of NEVPT2 within a (24,24) active space in a biologically relevant system, and show that small numbers of walkers are sufficient for a faithful sampling of the NEVPT2 energy to chemical accuracy, despite the active space already exceeding the limits of practicality for traditional approaches. This raises prospects of an efficient stochastic solver for multireference chemical problems requiring large active spaces, with an accurate treatment of external orbitals.

18 pages, 8 figures

References in corpus (15)

• BAGEL: Brilliantly Advanced General Electronic-structure Library
• Semistochastic Projector Monte Carlo Method
• Excited states using semistochastic heat-bath configuration interaction
• Unbiased Reduced Density Matrices and Electronic Properties from Full Configuration Interaction Quantum Monte Carlo
• An excited-state approach within full configuration interaction quantum Monte Carlo
• The sign problem and population dynamics in the full configuration interaction quantum Monte Carlo method
• Semi-stochastic full configuration interaction quantum Monte Carlo: developments and application
• DMRG-CASPT2 study of the longitudinal static second hyperpolarizability of all-trans polyenes
• A time-dependent formulation of multi-reference perturbation theory
• Krylov-projected quantum Monte Carlo
• Density matrices in full configuration interaction quantum Monte Carlo: Excited states, transition dipole moments and parallel distribution
• Coordinate descent full configuration interaction
• Stochastic multi-reference perturbation theory with application to linearized coupled cluster method
• An efficient and accurate perturbative correction to initiator full configuration interaction quantum Monte Carlo
• Non-linear biases, stochastically-sampled effective Hamiltonians and spectral functions in quantum Monte Carlo methods

Cited by in corpus (10)

• NECI: N-Electron Configuration Interaction with emphasis on state-of-the-art stochastic methods
• Reduced Density Matrix Sampling: Self-consistent Embedding and Multiscale Electronic Structure on Current Generation Quantum Computers
• Efficient multireference perturbation theory without high-order reduced density matrices
• Towards near-exact solutions of molecular electronic structure: Full coupled-cluster reduction with a second-order perturbative correction
• Multiconfigurational quantum chemistry: The CASPT2 method
• Evaluating a quantum-classical quantum Monte Carlo algorithm with Matchgate shadows
• Improved Stochastic Multireference Perturbation Theory for Correlated Systems with Large Active Spaces
• FragPT2: Multi-Fragment Wavefunction Embedding with Perturbative Interactions
• Equation of state of atomic solid hydrogen by stochastic many-body wave function methods
• Full configuration interaction quantum Monte Carlo for coupled electron--boson systems and infinite spaces