Hamiltonian formulation and symplectic split-operator schemes for time-dependent density-functional-theory equations of electron dynamics in molecules

TL;DR

This paper presents a Hamiltonian framework for TDDFT, developing symplectic split-operator schemes for efficient electron dynamics simulation, demonstrated on a carbon chain with promising accuracy and computational efficiency.

Contribution

It introduces a geometric Hamiltonian formalism for TDDFT and develops symplectic split-operator methods tailored for certain DFT functionals, enhancing simulation accuracy and efficiency.

Findings

An optimized 4th order scheme balances complexity and accuracy.

Numerical simulations show effective modeling of electron dynamics.

Discussion on basis set effects and challenges for symplectic schemes.

Abstract

We revisit Kohn-Sham time-dependent density-functional theory (TDDFT) equations and show that they derive from a canonical Hamiltonian formalism. We use this geometric description of the TDDFT dynamics to define families of symplectic split-operator schemes that accurately and efficiently simulate the time propagation for certain classes of DFT functionals. We illustrate these with numerical simulations of the far-from-equilibrium electronic dynamics of a one-dimensional carbon chain. In these examples, we find that an optimized 4th order scheme provides a good compromise between the numerical complexity of each time step and the accuracy of the scheme. We also discuss how the Hamiltonian structure changes when using a basis set to discretize TDDFT and the challenges this raises for using symplectic split-operator propagation schemes.