Stochastic many-body perturbation theory for anharmonic molecular vibrations

Area of Science:

• Quantum chemistry
• Computational physics
• Spectroscopy

Background:

• Vibrational perturbation theory requires high-order force constants, which are computationally intensive.
• Existing quantum Monte Carlo (QMC) methods can suffer from fixed-node errors.

Purpose of the Study:

• Develop a novel QMC method for anharmonic vibrational energies and transition frequencies.
• Improve computational efficiency and accuracy in vibrational spectroscopy calculations.

Main Methods:

• Combines diagrammatic vibrational many-body perturbation theory (MBPT) with Monte Carlo (MC) integration.
• Expresses infinite sums of anharmonic corrections as integrals computed via the Metropolis algorithm.
• Avoids explicit calculation and storage of high-order force constants.

Main Results:

• The new method accurately reproduces deterministic energy and frequency values (within cm⁻¹).
• Calculates transition frequencies, overtones, and relative intensities (pole strengths) stochastically.
• Captures a greater proportion of anharmonic effects compared to traditional methods.

Conclusions:

• The developed QMC method offers a scalable and memory-efficient approach for vibrational spectroscopy.
• It overcomes limitations of traditional perturbation theory and avoids fixed-node errors in QMC.
• Enables direct, stochastic computation of anharmonic vibrational properties with high fidelity.