Optimized structure and vibrational properties by error affected potential energy surfaces

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).

Reprinted (adapted) with permission from J. Chem. Theory Comput., 2012, 8 (11), pp 4204--4215, DOI:10.1021/ct300576n. Copyright (2012) American Chemical Society

References in corpus (8)

• Weak binding between two aromatic rings: feeling the van der Waals attraction by quantum Monte Carlo methods
• Applications of quantum Monte Carlo methods in condensed systems
• Stable liquid Hydrogen at high pressure by a novel ab-initio molecular dynamics
• Accurate, efficient and simple forces with Quantum Monte Carlo methods
• Heavy-tailed random error in quantum Monte Carlo
• Diamond -> beta-tin phase transition in Si within diffusion quantum Monte Carlo
• The Fermion Monte Carlo revisited
• Alternative sampling for variational quantum Monte Carlo

Cited by in corpus (8)

• Ab-initio molecular dynamics simulation of liquid water by Quantum Monte Carlo
• TurboRVB: a many-body toolkit for {\it ab initio} electronic simulations by quantum Monte Carlo
• Static and dynamical correlation in diradical molecules by Quantum Monte Carlo using the Jastrow Antisymmetrized Geminal Power ansatz
• Molecular properties by Quantum Monte Carlo: an investigation on the role of the wave function ansatz and the basis set in the water molecule
• Atomic forces by quantum Monte Carlo: application to phonon dispersion calculation
• Properties of Reactive Oxygen Species by Quantum Monte Carlo
• Computation of forces and stresses in solids: Towards accurate structural optimization with auxiliary-field quantum Monte Carlo
• A structural optimization algorithm with stochastic forces and stresses