New optimal control problems in density functional theory motivated by photovoltaics
Abstract
We present and study novel optimal control problems motivated by the search for photovoltaic materials with high power-conversion efficiency. The material must perform the first step: convert light (photons) into electronic excitations. We formulate various desirable properties of the excitations as mathematical control goals at the Kohn-Sham-DFT level of theory, with the control being given by the nuclear charge distribution. We prove that nuclear distributions exist which give rise to optimal HOMO-LUMO excitations, and present illustrative numerical simulations for 1D finite nanocrystals. We observe pronounced goal-dependent features such as large electron-hole separation, and a hierarchy of length scales: internal HOMO and LUMO wavelengths atomic spacings (irregular) fluctuations of the doping profiles system size.
Cite
@article{arxiv.1808.04200,
title = {New optimal control problems in density functional theory motivated by photovoltaics},
author = {Gero Friesecke and Michael Kniely},
journal= {arXiv preprint arXiv:1808.04200},
year = {2018}
}