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.
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