Quantum-Classical Path Integral Methodology

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Nancy Makri of the University of Illinois Urbana-Champaign is supported by an award from the Chemical Theory, Models and Computational Methods program in the Chemistry division and the Computational and Data-Enabled Science and Engineering Program (CDS&E) to develop theoretical and computational methods to describe electron and proton transfer processes in molecular systems. Electron and proton transfer play a vital role in many chemical and biological reactions. These small particles are subject to the laws of quantum mechanics, and thus standard simulations based on classical mechanics cannot correctly predict their behavior. Unfortunately, the exact solution of the quantum mechanical equations of motion for processes in liquid or biological environments requires enormous computing power that does not exist. Makri is developing accurate algorithms for simulating these processes; treating the electron or proton at the full quantum mechanical level, while capturing the dynamics of the rest of the system via inexpensive classical trajectories. These algorithms are being implemented in computer code which will be freely available to the research community. The central theme of this work is the further development and application of the quantum-classical path integral (QCPI) methodology. The spatially localized, trajectory-like nature of quantum paths makes the path integral framework ideal for quantum-classical dynamics. The proposed methodology exploits the memory-free nature of system-independent solvent trajectories to account for all "classical decoherence" effects on the dynamics of the quantum system. Inclusion of the residual, less prominent "quantum decoherence" is accomplished by evaluating the full path integral, which is amenable to large time steps and iterative decompositions. Application to electron and proton transfer in solution and in biological molecules will shed light on important mechanisms with unprecedented accuracy. The PI's core computer code, QCPI, is being interfaced with the powerful molecular dynamics packages, NAMD and LAMMPS. The goal is to produce a computer package, QCPI-MD, suitable for the simulation of proton, charge and energy transfer processes with unprecedented accuracy.