Optimized structure and vibrational properties by error affected potential energy surfaces

TL;DR

This paper presents a new method to accurately determine molecular structures and vibrational properties from error-prone quantum Monte Carlo data, reducing uncertainties and enabling affordable high-level calculations.

Contribution

It introduces a multidimensional fitting approach that effectively accounts for stochastic errors in quantum Monte Carlo calculations of molecular properties.

Findings

Using forces instead of energies reduces statistical uncertainty by an order of magnitude.

The method achieves small stochastic uncertainties (<0.07% geometries, <0.7% vibrational properties).

Preliminary results on water demonstrate feasibility and efficiency.

Abstract

The precise theoretical determination of the geometrical parameters of molecules at the minima of their potential energy surface and of the corresponding vibrational properties are of fundamental importance for the interpretation of vibrational spectroscopy experiments. Quantum Monte Carlo techniques are correlated electronic structure methods promising for large molecules, which are intrinsically affected by stochastic errors on both energy and force calculations, making the mentioned calculations more challenging with respect to other more traditional quantum chemistry tools. To circumvent this drawback in the present work we formulate the general problem of evaluating the molecular equilibrium structures, the harmonic frequencies and the anharmonic coefficients of an error affected potential energy surface. The proposed approach, based on a multidimensional fitting procedure, is illustrated together with a critical evaluation of systematic and statistical errors. We observe that the use of forces instead of energies in the fitting procedure reduces the the statistical uncertainty of the vibrational parameters by one order of magnitude. Preliminary results based on Variational Monte Carlo calculations on the water molecule demonstrate the possibility to evaluate geometrical parameters, harmonic and anharmonic coefficients at this level of theory with an affordable computational cost and a small stochastic uncertainty (<0.07% for geometries and <0.7% for vibrational properties).