Efficient Quantum Monte Carlo Energies for Molecular Dynamics Simulations

A method is presented to treat electrons within the many-body quantum Monte Carlo (QMC) approach “on-the-fly” throughout a molecular dynamics (MD) simulation. Our approach leverages the large (10–100) ratio of the QMC electron to MD ion motion to couple the stochastic, imaginary-time electronic and real-time ionic trajectories. This continuous evolution of the QMC electrons results in highly accurate total energies for the full dynamical trajectory at a fraction of the cost of conventional, discrete sampling. We show that this can be achieved efficiently for both ground and excited states with only a modest overhead to an ab initio MD method. The accuracy of this dynamical QMC approach is demonstrated for a variety of systems, phases, and properties, including optical gaps of hot silicon quantum dots, dissociation energy of a single water molecule, and heat of vaporization of liquid water.

Figure 1

DMC total ground state energies vs time for 5  fs time intervals of an AIMD simulation of ${\mathrm{S}\mathrm{i}\mathrm{H}}_4$, ${\mathrm{S}\mathrm{i}}_5{\mathrm{H}}_{12}$, and ${\mathrm{S}\mathrm{i}}_{14}{\mathrm{H}}_{20}$ at 1000 K. The circles (lines) correspond to discretely sampled (continuous) DMC calculations. The error bars of the discretely sampled data are smaller than the symbol size.

Figure 2

DMC HOMO-LUMO gap (eV, top panel) and difference between DMC and LDA gaps (eV, lower panel) vs time for a 100 fs time interval of an AIMD simulation of ${\mathrm{S}\mathrm{i}}_5{\mathrm{H}}_{12}$ at 1000 K. For the DMC gaps, the circles (lines) correspond to discretely sampled (continuous) DMC calculations.

Figure 3

DMC energies for the dissociation of a single ${\mathrm{H}}_2\mathrm{O}$ molecule as a function of the change in O-H distance ($\Delta R$) with respect to the equilibrium value. The circles correspond to discretely sampled DMC energies with error bars approximately of the size of the symbols. The solid line corresponds to CDMC energies.