# Investigation of optimal control problems governed by a time-dependent Kohn-Sham model

arXiv: https://arxiv.org/abs/1701.02679 · HTML: https://mlsanity.com/paper/1701.02679/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jan 2017.

## Built on by (most cited first, 1 of 1)

- [Dynamic Learning of Correlation Potentials for a Time-Dependent Kohn-Sham System](https://mlsanity.com/paper/2112.07067/) (2021)

## Abstract (arXiv)

Many application models in quantum physics and chemistry require to control multi-electron systems to achieve a desired target configuration. This challenging task appears possible in the framework of time-dependent density functional theory (TDDFT) that allows to describe these systems while avoiding the high dimensionality resulting from the multi-particle Schr"odinger equation. For this purpose, the theory and numerical solution of optimal control problems governed by a Kohn-Sham TDDFT model are investigated, considering different objectives and a bilinear control mechanism. Existence of optimal control solutions and their characterization as solutions to Kohn-Sham TDDFT optimality systems are discussed. To validate this control framework, a time-splitting discretization of the optimality systems and a nonlinear conjugate gradient scheme are implemented. Results of numerical experiments demonstrate the computational capability of the proposed control approach.