A 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, 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

A 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, 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

Uniquely $K_r$-Saturated Graphs

A graph $G$ is uniquely $K_r$-saturated if it contains no clique with $r$ vertices and if for all edges $e$ in the complement, $G+e$ has a unique clique with $r$ vertices. Previously, few examples of uniquely $K_r$-saturated graphs were known, and little was known about their properties. We search for these graphs by adapting orbital branching, a technique originally developed for symmetric integer linear programs. We find several new uniquely $K_r$-saturated graphs with $4 \leq r \leq 7$, as well as two new infinite families based on Cayley graphs for $\mathbb{Z}_n$ with a small number of generators.