On Nonadiabatic Dynamical Simulations near Conical Intersections via Surface Hopping Methods

Many chemical processes involve nuclear dynamics on multiple potential energy surfaces. These often involve conical intersections, which cause nonadiabatic couplings and diagonal Born-Oppenheimer corrections to diverge and thus a complete breakdown of the Born-Oppenheimer approximation. Furthermore, conical intersections make electronic and nuclear wavefunctions double-valued, requiring proper consideration of the boundary conditions of molecular wavefunctions. In this work we rationalize why the fewest switches surface hopping method, despite not involving nuclear wavefunctions nor any consideration for diagonal Born-Oppenheimer corrections, can approximate the exact quantum dynamics of conical intersection-induced interstate crossings. In addition, we identify regimes when it is beneficial to include diagonal Born-Oppenheimer corrections in surface hopping dynamics through the phase-space formalism. Lastly, we consider the use of neural networks within the surface hopping framework, to approximate the nonadiabatic dynamics of fewest switches surface hopping by emulating its hopping criterion. We show that a properly trained “neural network-induced surface hopping” algorithm can approximately simulate populations dynamics without the need to propagate electronic wavefunctions.Ph.D