Schematic representation of a forward-backward trajectory for the double-slit experiment: quantum interference is reproduced by the superposition of forward and backward trajectories that cross the obstacle through different slits.

William Miller, University of California, Berkeley

Research Objectives
This project continues the methodology development of the semiclassical initial value representations and their practical application to complex molecular systems: reactions in solutions, protein complexes, DNAs, and on surfaces. The main effort of this project is to include quantum effects (tunnelings, interferences, etc.) into classical molecular dynamics simulations, and to address complex problems that are beyond any other existing quantum dynamical methods. Specific studies are grouped in three main areas: (1) methodological developments to extend the capability of the current semiclassical initial value representation (SC-IVR) algorithms, (2) SC-IVR to study the reaction dynamics in complex systems, and (3) ab initio potential surface and quantum and molecular mechanics (QM/MM) development

Computational Approach
Implementation of the SC-IVR is based on classical molecular dynamics (MD) simulation but invoking the quantum superposition principle in gathering the dynamical information. Monte Carlo phase space average is usually carried out over a large number of degrees of freedom. Importance sampling techniques as well as various filtering methods are used to evaluate the high-dimensional integrals efficiently. Quantum effects are finally obtained from the phase information uniquely defined in semiclassics (but missing in traditional classical MD simulations). We plan to adopt the QM/MM method in our SC-IVR algorithms to evaluate the potential surface "on the fly" during dynamical simulations. This enhances our capability to study bond-breaking/forming processes in biological systems.

Accomplishments
(1) Application of the forward-backward initial value representation (FB-IVR) to the study of quantum coherence effects and their quenching in complex systems. (2) The development of the generalized forward-backward initial value representation (GFB-IVR) to study complex systems. (3) Application of the SC-IVR and the Meyer-Miller mapping technique to describing tunneling effects for chemical reactions. (4) Application of the SC-IVR to the study of nonadiabatic dynamics for multiple electronic state problems. (5) The development of a new powerful filtering method, the generalized Filinov transformation technique, to practically solve the sign problem in an SC-IVR calculation. (6) Application of the generalized Filinov transformation method to evaluating thermal rate constants for proton transfer reactions in the condensed phase.

Significance
SC-IVR is the only practical tool for accurately obtaining quantum dynamical effects for complex systems, which is a major improvement over the traditional classical molecular dynamics methods and goes beyond current rigorous quantum mechanical method (only capable of treating few-body problems). The accuracy and efficiency of SC-IVR have been demonstrated in many publications from our group and others. With our methodological developments, we are treating much more complex systems than previously reported in the literature, including applications that break the 100-degrees-of-freedom boundary for the first time in SC-IVR calculations.

Publications
H. Wang, M. Thoss, K. L. Sorge, R. Gelabert, X. Gimenez, and W. H. Miller, "Semiclassical description of quantum coherence effects and their quenching: A forward-backward initial value representation study," J. Chem. Phys. 114, 2562 (2001).

M. Thoss, H. Wang, and W. H. Miller, "Generalized forward-backward initial value representation for the calculation of correlation functions in complex systems," J. Chem. Phys. 114, 9220 (2001).

W. H. Miller, "The semiclassical initial value representation: A potentially practical way of adding quantum effects to classical molecular dynamics simulations," J. Phys. Chem. A 105, 2942 (2001).