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International Symposium on Molecular Spectroscopy (ISMS)

SURFACE CROSSING AND ENERGY FLOW IN MANY-DIMENSIONAL QUANTUM SYSTEMS

Chenghao Zhang, Peter Guy Wolynes

Published Jun 21, 2023• 0 citations
Publisher

Abstract

Vibrational energy flow in molecules, like the dynamics of other many dimensional finite systems, involves quantum transport across a dense network of near resonant states. For molecules in their electronic ground state, the network is ordinarily provided by anharmonic vibrational Fermi resonances. Surface crossing between different electronic states provides another route to chaotic motion and energy redistribution. We show that nonadiabatic coupling between electronic energy surfaces facilitates vibrational energy flow, and conversely, anharmonic vibrational couplings facilitate nonadiabatic electronic state mixing. A generalization of the Logan-Wolynes theory of quantum energy flow in many-dimensional Fermi resonance systems to the two-surface case gives a phase diagram describing the boundary between localized quantum dynamics and global energy flow. We explore these predictions and test them using a model inspired by the problem of electronic excitation energy transfer in the photosynthetic reaction center. Using an explicit numerical solution of the time dependent Schrödinger equation for this ten-dimensional model, we find quite good agreement with the expectations from the approximate analytical theory.

DOI
10.15278/isms.2023.6682

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Vibrational energy flow in molecules, like the dynamics of other many dimensional finite systems, involves quantum transport across a dense network of near resonant states. For molecules in their electronic ground state, the network is ordinarily provided by anharmonic vibrational Fermi resonances. Surface crossing between different electronic states provides another route to chaotic motion and energy redistribution. We show that nonadiabatic coupling between electronic energy surfaces facilitates vibrational energy flow, and conversely, anharmonic vibrational couplings facilitate nonadiabatic electronic state mixing. A generalization of the Logan-Wolynes theory of quantum energy flow in many-dimensional Fermi resonance systems to the two-surface case gives a phase diagram describing the boundary between localized quantum dynamics and global energy flow. We explore these predictions and test them using a model inspired by the problem of electronic excitation energy transfer in the photosynthetic reaction center. Using an explicit numerical solution of the time dependent Schrödinger equation for this ten-dimensional model, we find quite good agreement with the expectations from the approximate analytical theory.
Criteria for ergodicity and rates of energy flow in a quantum mechanical system of NNN coupled anharmonic oscillators where NNN is large are determined at energies near the ground state of the system. High-order resonances are important for the transition at large NNN. The role of numerous virtual transitions, ``vibrational superexchange,'' in global transport is examined both for typical parts of the state space and special states often interrogated experimentally.
Abstract A new model of vibrational energy transfer in molecular systems taking into account anharmonic (third order) interactions of localized vibrations with a chain of harmonic oscillators is developed. The role of the energy spectrum of the chain and of the magnitude of the non-linear coupling is discussed in detail by an exact numerical solution of the quantum dynamical problem based on the tensor-train (matrix product state) representation of the vibrational wave function. Results show that the type of wave packet motion is determined by the eigen-spectrum of the chain and by its excitation time. It is found that when the excitation of the chain takes place on a much shorter timescale than the energy transfer along the chain the vibrational wave packet moves in a ballistic way independently of the length of the chain. On the other hand when the excitation of the chain takes place on the timescale of the energy transfer along the chain the overall motion becomes superballistic. These findings shed new light on recent observations of ballistic energy transfer along polymethylene chains.
The coupled Schrödinger equations that describe nonadiabatic dynamics are recast using the Bohm formulation of quantum mechanics. The resulting coupled Bohm equations are solved numerically for two scattering models, giving results that are essentially identical to wave-packet solution of the original coupled Schrödinger equations. The classical limit of the set of coupled Bohm equations is then described, producing a mixed quantum-classical theory incorporating classical-like motion on each potential energy surface accompanied by quantum transitions between the quantum states. Numerical tests of the mixed quantum-classical method are in excellent agreement with the accurate full-quantum results for the model problems. The method is contrasted with the related surface-hopping approach. It is shown that computing the dynamics of a distribution of classical particles is more consistent and more accurate than computing the motion of independent point particles as with surface hopping.
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A theory for the effect of a strong intra-atomic Coulomb repulsion U on the nonadiabatic transfer of charge between a metallic surface and a moving atomic species is presented. Using slave bosons and a nonequilibrium Green's-function technique, we solve the equations appropriate for the U=\ensuremath{\infty} problem in the case when either the atom-surface hopping matrix element is small, or the number of degenerate atomic states is large. We generalize the earlier treatment of Langreth and Nordlander (LN) to include off-diagonal self-energies and present a general numerical scheme for the exact solution of the Dyson equations. We verify that our scheme gives the correct answer in several limiting cases where an exact solution is known, and give quantitative predictions of when deviations from these limits become important. These limits include (1) the simple master equation limit for low velocities and weak coupling, (2) the generalized master equation of LN for larger velocities and atom-surface coupling, (3) the approach to thermal equilibrium when the time dependence is removed, and (4) the maintenance of local thermal equilibrium when the energy parameters vary sufficiently slowly. From a calculation of the instantaneous (nonequilibrium) spectral function of the level on the scattering atom, we are able to study the rate of formation of the Kondo and mixed valent resonances near the Fermi level. We find a slow formation rate for such resonances relative to that of the broader parts of the spectral density centered near the bare atom level positions.