Algorithms for quantum molecular dynamics: from matrix product states to path integrals

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Date

2021-01-13

Authors

Iouchtchenko, Dmitri

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University of Waterloo

Abstract

This thesis describes several novel approaches in quantum molecular dynamics for obtaining properties of molecular systems in different regimes. We investigate ground state properties of chains of linear rotors with dipole–dipole interactions via the density matrix renormalization group (DMRG), by deriving the appropriate form of the interaction operator and implementing it in ITensor. This provides us with further evidence of a quantum phase transition in this system. We also improve the sampling of Gaussian mixture distributions for finite temperature path integral Monte Carlo (PIMC) of vibronic Hamiltonians. To do this, we replace random sampling by quasi-random sampling, and improve sampling distributions by optimizing their parameters. Finally, we introduce estimators and integrators for constrained free energy simulations in path integral molecular dynamics (PIMD). This method is applied to the study of a water dimer, for which we obtain a quantum potential of mean force.

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quantum molecular dynamics, linear rotor, density matrix renormalization group, Gaussian mixture distribution, path integral Monte Carlo, quasi-random, parameter optimization, path integral molecular dynamics, holonomic constraint, free energy, potential of mean force, water dimer

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