New optimal control problems in density functional theory motivated by photovoltaics

TL;DR

This paper formulates novel optimal control problems in density functional theory to design photovoltaic materials with high efficiency, demonstrating existence of optimal nuclear charge distributions and illustrating key properties through numerical simulations.

Contribution

It introduces new control problems in DFT for photovoltaic material design, proving the existence of optimal nuclear distributions and providing numerical insights.

Findings

Existence of nuclear distributions leading to optimal excitations.

Observation of goal-dependent features like electron-hole separation.

Identification of a hierarchy of length scales in the system.

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.