Fragment-based Time-dependent Density-functional Theory

TL;DR

This paper establishes a theoretical foundation for fragment-based time-dependent density functional theory (TDDFT), introducing a unique partition potential that enables accurate time-dependent electronic property calculations through a novel fragmentation approach.

Contribution

It proves the existence and uniqueness of a time-dependent partition potential in fragment-TDDFT, providing a new framework for computing electronic dynamics.

Findings

Proves the uniqueness of the time-dependent partition potential.

Derives an exact relationship between the partition potential and total density.

Demonstrates the approach on a simple binary fragmentation model.

Abstract

Using the Runge-Gross theorem that establishes the foundation of Time-dependent Density Functional Theory (TDDFT) we prove that for a given electronic Hamiltonian, choice of initial state, and choice of fragmentation, there is a unique single-particle potential (dubbed time-dependent partition potential) which, when added to each of the pre-selected fragment potentials, forces the fragment densities to evolve in such a way that their sum equals the exact molecular density at all times. This uniqueness theorem suggests new ways of computing time-dependent properties of electronic systems via fragment-TDDFT calculations. We derive a formally exact relationship between the partition potential and the total density, and illustrate our approach on a simple model system for binary fragmentation in a laser field.