Direct evaluation of the force constant matrix in quantum Monte Carlo

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 0.007Å 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.

Variational and diffusion quantum Monte Carlo calculations with the CASINO code

“…Including protons in QMC calculations will require (i) bespoke backflow functions to ensure that the cusps in DFTgenerated electron orbitals occur at the electron-proton coalescence points, even when the protons have moved; (ii) a bespoke Jastrow factor of Gaussian form in either the proton positions (Einstein approximation) or the phonon normal coordinates (from a DFT quasiharmonic phonon calculation with the nonhydrogen nuclei having infinite mass); and (iii) modifications to the DMC Green's function near electron-proton coalescence points similar to those currently used between electrons and fixed nuclei. 68 A novel extension for hydrogenbearing compounds would be to include the electrons and protons in the QMC calculations, evaluate the matrix of force constants for the remaining nuclei using QMC, 241 and then evaluate their zero-point energy within the quasiharmonic approximation. We would then have a fully quantum treatment of the protons and a quasiharmonic treatment of the remaining nuclei.…”

“…These affect other expectation values too, such as elements of the matrix of force constants. 241 Here we focus on VMC forces for simplicity, but the methodology applies to DMC forces as well.…”

Finite-Size Error Cancellation in Diffusion Monte Carlo Calculations of Surface Chemistry

“…One approach involves calculating the energies of structures obtained by intentionally displacing the diffusing species (adsorbate) along a uniform grid of interpolated points between the initial and final positions. , Alternatively, one can rely on DFT-based NEB calculations or semi-empirical methods like SRP-DFT , (intended to reproduce experimental barrier heights) to provide structures corresponding to a reactive trajectory, which are then studied using QMC methods. Recently, it has also become possible to use QMC-level approaches to obtain forces, optimized geometries, and minimum energy pathways; − ref is particularly relevant in the context of reactions involving CO on the Pt(111) surface. However, this is accompanied by the increased computational cost of QMC methods.…”

Absence of diagonal force constants in cubic Coulomb crystals

“…Two decades later, Wigner predicted, in his seminal paper, that the electron jellium in metals can form a bodycentered cubic crystal at sufficiently low densities 21,22 . The subsequent numerical and experimental confirmation of Wigner crystals sparked interest in the condensed matter community, and a plethora of papers on the general theory [23][24][25][26][27][28][29] and stability [30][31][32][33] of these systems followed, including detailed quantum Monte Carlo simulations [34][35][36][37][38][39][40][41] . From the plasma physics perspective on the other hand, interest in strongly coupled plasmas, i.e.…”