title: Numerical density-to-potential inversions in time-dependent density functional theory.
abstract: We treat the density-to-potential inverse problem of time-dependent density functional theory as an optimization problem with a partial differential equation constraint. The unknown potential is recovered from a target density by applying a multilevel optimization method controlled by error estimates. We employ a classical optimization routine using gradients efficiently computed by the discrete adjoint method. The inverted potential has both a real and imaginary part to reduce reflections at the boundaries and other numerical artifacts. We demonstrate this method on model one-dimensional systems. The method can be straightforwardly extended to a variety of numerical solvers of the time-dependent Kohn-Sham equations and to systems in higher dimensions.
authors.affiliation: Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA. awasser@purdue.edu.
authors.forename: Daniel S
authors.initials: DS
authors.lastname: Jensen
authors.affiliation: Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA. awasser@purdue.edu and Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, USA.
authors.forename: Adam
authors.initials: A
authors.lastname: Wasserman