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42340-AC6
Forward-Backward Semiclassical Simulation of H+ Translocation in Proton Wires
In the past year our efforts have focused on extending the validity of our calculations to longer times. This is essential for capturing quantum mechanical effects associated with tunneling and possibly coherence in the dynamics of proton translocation along water chains. To this end, we have made a crucial modification to our forward-backward semiclassical dynamics (FBSD) methodology, allowing a special particle to be treated by a fully quantum mechanical procedure, and explored the possibility of performing accurate path integral calculations in complex time. The work along these directions is described below.
1. Quantum-classical FBSD
FBSD is a phase-free semiclassical methodology suitable for describing the dynamics of quantum particles in condensed phase or biological environments. Protons interacting weakly via high-frequency springs with their environment may exhibit dynamics characterized by quantum interference, an effect that cannot be accounted for in simple FBSD calculations. Such quantum coherence effects may be relevant in proton translocation. To address the inability of FBSD to capture quantum coherence, we have formulated a quantum-classical version , where the FBSD integrand is partitioned into solute and solvent parts, each of which is treated at a different level. Adopting the ideas of quantum-classical approximations, the dynamics of the proton is calculated by full quantum mechanics in potential field of the water molecules which are treated via classical trajectories. At the same time, the classical trajectories for the water environment are integrated in the mean field of the proton. Just as in earlier FBSD calculations, the thermal density matrix is fully quantized. Our preliminary results using this scheme on a tunneling model are encouraging.
2. Path integral calculations in complex time
As an alternative approach to quantum-classical FBSD, we are exploring the possibility of treating the dynamics via quantum mechanics in complex (rather than real) time. Such calculations appear feasible via the use of accurate propagators that are valid over large time steps, such that two or three path integral "beads" are adequate for the protons and a single bead is needed for heavier atoms. The practical difficulty encountered is the well-known sign problem, but we hope the use of a small number of beads for a system with 10-20 quantized protons will make the situation controllable. In combination with information-guided noise reduction (IGNoR), a procedure developed by the PI for reducing the statistical error in the Monte Carlo sampling of oscillatory functions, we hope that this approach will lead to an accurate picture of proton translocation.
