New optimal control problems in density functional theory motivated by photovoltaics^∗

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 we present illustrative numerical simulations for one-dimensional 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.