Atomic forces by quantum Monte Carlo: application to phonon dispersion calculation

Abstract

We report the first successful application of the {\it ab initio} quantum Monte Carlo (QMC) framework to a phonon dispersion calculation. A full phonon dispersion of diamond is successfully calculated at the variational Monte Carlo (VMC) level, based on the frozen-phonon technique. The VMC-phonon dispersion is in good agreement with the experimental results, giving renormalized harmonic optical frequencies very close to the experimental values, by significantly improving upon density functional theory (DFT) in the generalized gradient approximation. Key to success for the QMC approach is the statistical error reduction in atomic force evaluation. We show that this can be achieved by using well conditioned atomic basis sets, by explicitly removing the basis-set redundancy, which reduces the statistical error of forces by up to two orders of magnitude. This leads to affordable and accurate QMC-phonons calculations, up to $10^4$ times more efficient than previous attempts, and paves the way to new applications, particularly in correlated materials, where phonons have been poorly reproduced so far.

10 pages

References in corpus (7)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Jastrow correlation factor for atoms, molecules, and solids
• Impact of the electron-electron correlation on phonon dispersions: failure of LDA and GGA functionals in graphene and graphite
• Weak binding between two aromatic rings: feeling the van der Waals attraction by quantum Monte Carlo methods
• Stable liquid Hydrogen at high pressure by a novel ab-initio molecular dynamics
• Photoemission kinks and phonons in cuprates
• Vibrational spectrum and electron-phonon coupling of doped solid picene from first principles