We present a universal expression for the electronic friction as felt by a set of classical nuclear degrees of freedom (DoF's) coupled to a manifold of quantum electronic DoF's; no assumptions are made regarding the nature of the electronic Hamiltonian and electron-electron repulsions are allowed. Our derivation is based on a quantum-classical Liouville equation (QCLE) for the coupled electronic-nuclear motion, followed by an adiabatic approximation whereby electronic transitions are assumed to equilibrate faster than nuclear movement. The resulting form of friction is completely general, but does reduce to previously published expressions for the quadratic Hamiltonian (i.e. Hamiltonians without electronic correlation). At equilibrium, the second fluctuation-dissipation theorem is satisfied and the frictional matrix is symmetric. To demonstrate the importance of electron-electron correlation, we study electronic friction within the Anderson-Holstein model, where a proper treatment of electron-electron interactions shows signatures of a Kondo resonance and a mean-field treatment is completely inadequate.Introduction.-The Born-Oppenheimer (BO) approximation is probably the most important framework underlying modern physics and chemistry. According to the BO approximation, for a system of nuclei and electrons, we split up the total Hamiltonian into the nuclear kinetic energy (T nuc ) and the electronic HamiltonianĤ:

We present a preliminary extension of the fewest switches surface hopping (FSSH) algorithm to the case of complex Hamiltonians as appropriate for modeling the dynamics of photoexcited molecules in magnetic fields. We make ansätze for the direction of momentum rescaling and we account for Berry's phase effects through "magnetic" forces as applicable in the adiabatic limit. Because Berry's phase is a nonlocal, topological characteristic of a set of entangled potential energy surfaces, we find that Tully's local FSSH algorithm can only partially capture the correct physics.

The symmetrical quasi-classical approach to electronically nonadiabatic dynamics applied to ultrafast exciton migration processes in semiconducting polymers

We isolate and dissect exactly how and why Tully’s fewest switches surface hopping (FSSH) algorithm fails when two wave packets come together at a crossing and “recohere”. Using two different one-dimensional avoided crossing models and an initial wave function, which is a superposition of wave packets on different adiabats, we show that the key failures pertain to asymptotic nuclear momenta rather than electronic populations. Moreover, these FSSH failures stem from the fundamental assumption of independent trajectories with time-local hopping. As such, there is no possible means to correct FSSH without either (i) introducing time-nonlocal dynamics (i.e., allowing trajectories to move forward and backward in time) or (ii) requiring that trajectories interact.

Within the context of a simple avoided crossing, we investigate the effect of a complex-valued diabatic coupling in determining spin-dependent rate constants and scattering states. We find that, if the molecular geometry is not linear and the Berry force is not zero, one can find significant spin polarization of the products. This study emphasizes that, when analyzing nonadiabatic reactions with spin orbit coupling (and a complex-valued Hamiltonian), one must consider how Berry force affects nuclear motionat least in the context of gas phase reactions. Work is currently ongoing as far as extrapolating these conclusions to the condensed phase, where interesting spin selection has been observed in recent years.