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

communications in nonlinear science and numerical simulation/communications in nonlinear science and numerical simulation

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