Natural Orbital Branching Scheme for Time-Dependent Density Functional Theory Nonadiabatic Simulations.

Real time-time-dependent density functional theory (rt-TDDFT) has now been used to study a wide range of problems, from optical excitation to charge transfer, to ion collision, and to ultrafast phase transition. However, conventional rt-TDDFT Ehrenfest dynamics for nuclear movement lacks a few critical features to describe many problems: the detail balance between state transitions, decoherence for the wave function evolution, and stochastic branching of the nuclear trajectory. There are many-body formalisms to describe such nonadiabatic molecular dynamics, especially the ones based on mixed quantum/classical simulations, like the surface hopping and wave function collapsing schemes. However, there are still challenges to implement such many-body formalisms to the rt-TDDFT simulations, especially for large systems where the excited state electronic structure configuration space is large. Here we introduce two new algorithms for nonadiabatic rt-TDDFT simulations: the first is a Boltzmann factor algorithm which introduces decoherence and detailed balance in the carrier dynamics but uses mean field theory for nuclear trajectory. The second is a natural orbital branching (NOB) formalism, which uses a time-dependent density matrix for electron evolution and a natural orbital set to collapse the wave function upon. It provides the features of decoherence, detailed balance, and trajectory branching. We have tested these methods for a molecule radiolysis decay problem. We found that these methods can be used to study such radiolysis problems in which the molecule is broken into many fragments following complex electronic structure transition paths. The computational time of NOB is similar to that of the original plain rt-TDDFT simulations.