Phase Space Approaches to Electronic Structure

Abstract

The Born-Oppenheimer approximation is the cornerstone of chemistry. For a system of light electrons and heavy nuclei, the BO framework allows the chemist and physicist to separate one large matrix diagonalization into two smaller matrix diagonalizations. In so doing, chemists gain (i) the notion of molecular orbitals and electronic state that are defined relative to a stationary set of coordinates for the nuclei, and (ii) the concept of a potential energy surface that governs how nuclei move and thus forms the basis for all of classical mechaincs. Unfortunately, it is known that the Born-Oppenheimer approximation breaks down quite often, quite famously and obviously in the context of photochemistry and/or electron transfer. Slightly less well known is the fact that a classical BO theory does not conserve momentum (linear or angular) even when there is no obvious breakdown. In this talk, I will discuss this failure of the BO approximation, offer up a phase space framework as an improvement to restore conservation, and then suggest a new paradigm for understanding how nuclear entanglement with electronic degrees of freedom may well lead to chiral induced spin selectivity (an exciting phenomenon discovered in recent years). I will also highlight the many computational and applied math problems that will need to be overcome for a practical and meaningful implementation in practice.

Joseph Subotnik - Bio

Joe Subotnik is a Professor of Chemistry at Princeton University. He graduated from Harvard (BA, physics and math) in 2000 and from Berkeley (PhD, biophysics) in 2007. He was an NSF postdoctoral fellow in Israel from 2007-2010, and was previously a Professor of Chemistry at the University of Pennsylvania (2010-2024). His research focuses on developing tools to describe energy conversion, the manner by which electrons, photons and nuclei exchange energy and angular momentum, especially in the condensed phase, merging fundamental chemical physics with practical computational methods. He has made fundamental contributions to the semiclassical surface hopping algorithm, the theory of electronic friction at metal surfaces, and the theory of vibrational circular dichroism.