Adrián Gómez Pueyo, Miguel A. L. Marques, Angel Rubio, and Alberto Castro, J. Chem. Thelr. Comp. 14, 3040 (2018)

We examine various integration schemes for the time-dependent Kohn−Sham equations. Contrary to the time-dependent Schrödinger’s equation, this set of equations is nonlinear, due to the dependence of the Hamiltonian on the electronic density. We discuss some of their exact properties, and in particular their symplectic structure. Four different families of propagators are considered, specifically the linear multistep, Runge−Kutta, exponential Runge−Kutta, and the commutator-free Magnus schemes. These have been chosen because they have been largely ignored in the past for time-dependent electronic structure calculations. The performance is analyzed in terms of cost-versus-accuracy. The clear winner, in terms of robustness, simplicity, and efficiency is a simplified version of a fourth- order commutator-free Magnus integrator. However, in some specific cases, other propagators, such as some implicit versions of the multistep methods, may be useful.

Adrián Gómez Pueyo and Alberto Castro, Eur. Phsy. J B 91, 105 (2018)

We investigate, numerically, the possibility of associating to each approximation to the exchange-and-correlation functional in density-functional theory (DFT), an optimal electron-electron interaction potential for which it performs best. The fundamental theorems of density-functional theory (DFT) make no assumption about the precise form of the electron–electron interaction: to each possible electron–electron interaction corresponds an exchange-and-correlation functional. This fact suggests the opposite question: given some functional of the density, is there any electron–electron interaction for which it is the exact exchange-and-correlation functional? And, if not, what is the interaction for which the functional produces the best results? Within the context of lattice DFT, we study these questions by working on the one-dimensional Hubbard chain. The idea of associating an optimal interaction potential to each approximation to the exchange and correlation functionals suggests, finally, a procedure to optimise parameterised families of functionals: find that one whose associated interaction most closely resembles the real one.