Stochastic evaluation of four-component relativistic second-order many-body perturbation energies: A potentially quadratic-scaling correlation method

Abstract

A second-order many-body perturbation correction to the relativistic Dirac-Hartree-Fock energy is evaluated stochastically by integrating 13-dimensional products of four-component spinors and Coulomb potentials. The integration in the real space of electron coordinates is carried out by the Monte Carlo (MC) method with the Metropolis sampling, whereas the MC integration in the imaginary-time domain is performed by the inverse-CDF (cumulative distribution function) method. The computational cost to reach a given relative statistical error for spatially compact but heavy molecules is observed to be no worse than cubic and possibly quadratic with the number of electrons or basis functions. This is a vast improvement over the quintic scaling of the conventional, deterministic second-order many-body perturbation method. The algorithm is also easily and efficiently parallelized with demonstrated 92% strong scalability going from 64 to 4096 processors for a fixed job size.

References in corpus (9)

• Applications of quantum Monte Carlo methods in condensed systems
• Perspective: Essentials of Relativistic Quantum Chemistry
• Stochastic multi-reference perturbation theory with application to linearized coupled cluster method
• Multi-state effective Hamiltonian and size-consistency corrections in stochastic configuration interactions
• Multireference Stochastic Coupled Cluster
• Large Scale Parallelization in Stochastic Coupled Cluster
• Stochastic many-body perturbation theory for electron correlation energies
• Grid-based diffusion Monte Carlo for fermions without the fixed-node approximation
• Evaluating two-electron-repulsion integrals over arbitrary orbitals using Zero Variance Monte Carlo: Application to Full Configuration Interaction calculations with Slater-type orbitals