Stochastic many-body perturbation theory for electron correlation energies

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Electronic Structure Theory

Background:

• Accurate calculation of electron correlation is crucial for electronic structure methods.
• Conventional methods like Møller-Plesset (MP) series face steep computational scaling (O(N^n+3)).
• Existing stochastic approaches have limitations in calculating high-order correlation energies.

Purpose of the Study:

• To develop a more efficient stochastic approach for evaluating high-order electron correlation energies.
• To reformulate ab initio many-body perturbation theory (MBPT) for Monte Carlo applications.
• To overcome the factorial scaling problem in high-order perturbation theory.

Main Methods:

• Reformulation of Goldstone's time-dependent formulation of ab initio MBPT.
• Development of a Monte Carlo scheme based on the reformulated MBPT.
• Implementation of a quantum Monte Carlo algorithm for electron correlation energy calculations.

Main Results:

• The proposed Monte Carlo scheme achieves a significantly improved computational scaling of O(nN^2 + n^2N + f(n)).
• Proof-of-concept calculations demonstrate successful extension to higher-order electron correlation energies.
• The factorial scaling problem inherent in traditional methods is overcome.

Conclusions:

• The developed quantum Monte Carlo algorithm provides a numerically viable method for calculating electron correlation energies.
• Goldstone's time-dependent formulation is now practically applicable beyond theoretical use.
• This work advances the efficiency and accessibility of high-order electronic structure calculations.