# Direct evaluation of the force constant matrix in quantum Monte Carlo

## TL;DR

This paper introduces a formalism for directly evaluating force constant matrices in Quantum Monte Carlo, enabling highly accurate molecular relaxation and vibrational frequency calculations that outperform many existing methods.

## Contribution

It presents a novel approach to compute force constants directly within Quantum Monte Carlo, improving the accuracy of molecular geometries and vibrational frequencies.

## Key findings

- Bond lengths within 0.007 Å of experimental values.
- Vibrational frequencies within 0.1% for H2 and HCl.
- Vibrational frequencies within 1.1% for CO2 and CH4.

## Abstract

We develop a formalism to directly evaluate the matrix of force constants within a Quantum Monte Carlo calculation. We utilize the matrix of force constants to accurately relax the positions of atoms in molecules and determine their vibrational modes, using a combination of Variational and Diffusion Monte Carlo. The computed bond lengths differ by less than 0.007{\AA} from the experimental results for all four tested molecules. For hydrogen and hydrogen chloride, we obtain fundamental vibrational frequencies within 0.1% of experimental results and ~10 times more accurate than leading computational methods. For carbon dioxide and methane, the vibrational frequency obtained is on average within 1.1% of the experimental result, which is at least 3 times closer than results using Restricted Hartree-Fock and Density Functional Theory with a Perdew-Burke-Ernzerhof (PBE) functional and comparable or better than Density Functional Theory with a semi-empirical functional.