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Article Dans Une Revue Communications in Nonlinear Science and Numerical Simulation Année : 2023

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

Mette Gaarde
Kenneth Schafer

Résumé

We revisit Kohn-Sham time-dependent density-functional theory (TDDFT) equations, in the adiabatic approximation, 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.

Dates et versions

hal-03972581 , version 1 (03-02-2023)

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Citer

François Mauger, Cristel Chandre, Mette Gaarde, Kenneth Lopata, Kenneth Schafer. Hamiltonian formulation and symplectic split-operator schemes for time-dependent density-functional-theory equations of electron dynamics in molecules. Communications in Nonlinear Science and Numerical Simulation, 2023, 129, pp.107685. ⟨10.1016/j.cnsns.2023.107685⟩. ⟨hal-03972581⟩
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