Methods for Simulating Nonadiabatic Dynamics with Trajectories

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Craig C. Martens of the University of California, Irvine is supported by an award from the Chemical Theory, Models and Computational Methods program in the Division of Chemistry to develop computational methods to simulate quantum processes in molecular systems. Ordinary Newtonian or classical mechanics is used to understand the motion of everyday objects such as golf balls or airplanes. Very light particles such as electrons, however, must be described using quantum mechanics. The motion of atoms and electrons that accompany chemical reactions falls in the frontier separating classical and quantum mechanical descriptions of matter. Martens and his research group explore this frontier by incorporating quantum effects into the conceptually intuitive and computationally efficient framework of classical mechanics. They focus on nonadiabatic dynamics of molecules, where quantum electronic transitions accompany the nearly classical vibrations and chemical rearrangements of the constituent atoms. Martens' goal is to gain an understanding of the nature of quantum mechanics at a fundamental level while at the same time developing methods that are more efficient and accurate than existing approaches. Their research activities are paralleled by an outreach program that includes mentoring undergraduate and high school students to write educational computer games that add quantum effects to familiar but inherently classical gameplay to illustrate quantum mechanics in a manner that is accessible to nonscientists, and even to children. Martens and his group are developing a new stochastic surface hopping approach that captures quantum nonlocality and coherence fully and accurately in a classical trajectory context. Unlike current methodology, the novel approach describes quantum properties of the system such as the populations, coherence, and the partitioning of energy collectively through interrelationships between the trajectories of the ensemble taken as a whole. Martens and coworkers aim to achieve a quantitatively accurate trajectory-based method for simulating molecular dynamics with electronic transitions within this framework, both as a fundamental achievement and as a benchmark for the introduction of further approximations. Ultimately, they seek accurate but economical and efficient methodologies based on well-understood and tested compromises rather than ad hoc simplifications. They are constructing an independent trajectory approach incorporating rigorously derived quantum generalized forces that avoid ad hoc features of standard methodology with the goal of broader applicability while being roughly equal in cost. The Martens group is pursuing extensions to multidimensional systems, where energy partitioning and geometric phase effects provide challenging tests of the new approach. In addition, Martens is implementing an outreach program that bridges the gap between performing arts and science, with the goals of enhancing the image and accessibility of science as a career. He is also mentoring undergraduate and high school students in the development of video games that illustrate the fundamentals of quantum mechanics to youth and nonscientists.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.