Physics Seminar: Prof. Artur Izmaylov

Dynamical consideration that goes beyond the common Born−Oppenheimer approximation (BOA) becomes

necessary when energy differences between electronic potential energy surfaces become small or vanish. One

of the typical scenarios of the BOA breakdown in molecules beyond diatomics is a conical intersection (CI) of

electronic potential energy surfaces. CIs provide an efficient mechanism for radiationless electronic transitions:

acting as “funnels” for the nuclear wave function, they enable rapid conversion of the excessive electronic

energy into the nuclear motion. In addition, CIs introduce nontrivial topological or Berry phases for both

electronic and nuclear wave functions. These phases manifest themselves in change of the wave function signs

if one considers an evolution of the system around the CI. This sign change is independent of the shape of the

encircling contour and thus has a topological character. How these extra phases affect nonadiabatic dynamics is

the main question that is addressed in this lecture. I start by considering the simplest model providing the CI

topology: two-dimensional two-state linear vibronic coupling model. Selecting this model instead of a real

molecule has the advantage that various dynamical regimes can be easily modeled in the model by varying

parameters, whereas any fixed molecule provides the system specific behavior that may not be very

illustrative. After demonstrating when topological phase effects are important and how they modify the

dynamics for two sets of initial conditions (starting from the ground and excited electronic states), I give

examples of molecular systems where the described topological phase effects are crucial for adequate

description of nonadiabatic dynamics. Understanding an extent of changes introduced by the topological phase

in chemical dynamics poses a problem of capturing its effects by approximate methods of simulating

nonadiabatic dynamics that can go beyond simple models. I assess the performance of both fully quantum (wave

packet dynamics) and quantum-classical (surface-hopping, Ehrenfest, and quantum-classical Liouville

equation) approaches in various cases where topological phase effects are important. It has been identified that

the key to success in approximate methods is a method organization that prevents the quantum nuclear kinetic

energy operator to act directly on adiabatic electronic wave functions.