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

Abstract

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, 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 transition, 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 algorithm 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 use time dependent density matrix for electron evolution, and natural orbital to collapse the wave function upon. It provides decoherence, detailed balance and trajectory branching properties. We have tested these methods for a molecule radiolysis decay problem. We found these methods can be used to study such radiolysis problem in which the molecule is broken into many fragments following complex electronic structure transition paths. The computational time of NOB is similar to the original plain rt-TDDFT simulations File list (2) download file view on ChemRxiv manuscript_NOB.pdf (1.61 MiB) download file view on ChemRxiv Supplementary_Material.pdf (151.04 KiB) A natural orbital branching scheme for time dependent density functional theory nonadiabatic simulations

The critical role of hot carrier cooling in optically excited structural transitions

“…As a matter of fact, the Ehrenfest dynamics tend to overheat the electronic subsystem. In this work, to include the hot carrier cooling effect, we have improved our rt-TDDFT algorithm by including a Boltzmann factor, 30 which can restore the detailed balance between various electronic state transitions and hence treat the carrier cooling properly.…”

“…[1][2][3][11][12][13][14][15] This transfer of the energy also heats the lattice subsystem. To explore the hot carrier cooling effect, we carry out the rt-TDDFT simulation again but by adding a particular Boltzmann factor in the algorithm 30 . Figure 2B shows the dynamic evolution of excited electrons and holes following photoexcitation.…”

“…To verify the effect of the increase in the atomic kinetic energy of Ir dimers unambiguously, we re-do our simulation in the NVT ensemble during carrier cooling. In contrast to the above-adopted NVE ensemble, which considers the energy transfer from hot carrier cooling to the kinetic energy in the transition degree of freedom, 30 in the NVT the lattice kinetic energy is kept constant for a given initial temperature to mimic a situation for heat dissipates quickly. Figure S2 shows that in this case, the increase in the occupation of the Ir-Ir dimers' antibonding states strengthens the atomic driving forces following hot carrier cooling.…”

“…To depict hot carrier cooling, we utilize the Boltzmann formula in rt-TDDFT. 30 Boltzmann formula will depend on adiabatic state ( ) in eq. 1.…”

“…For a more detailed description of the Boltzmann factor formalism, we refer to it in Ref. 30. In the NVT ensemble with carrier cooling, the total kinetic energy of all the atoms is kept the same by a simple rescaling.…”