Freeze-and-Release Direct Optimization Method for Variational Calculations of Excited Electronic States.

Variational optimization of orbitals in time-independent density functional calculations of excited electronic states presents a significant challenge, as excited states typically correspond to saddle points on the electronic energy landscape. The optimization can be particularly difficult if the excitation involves significant rearrangement of the electron density, as for charge-transfer excitations. A simple strategy for variational orbital optimization of excited states is presented. The approach involves minimizing the energy while freezing the orbitals directly involved in the excitation, followed by a fully unconstrained saddle-point optimization. Both steps of this freeze-and-release strategy are carried out using direct optimization algorithms with the same computational scaling as ground-state calculations. The performance of the method is extensively assessed in calculations of intramolecular and intermolecular charge-transfer excited states of organic molecules and molecular dimers using a generalized gradient approximation functional. It is found that the freeze-and-release direct optimization approach can avoid variational collapse to spurious, charge-delocalized solutions for cases where conventional algorithms based on the maximum overlap method fail. For intermolecular charge transfer, the orbital-optimized calculations are found to provide the correct dependency of the energy on the donor-acceptor separation without requiring long-range exact exchange, something common time-dependent density functional theory approaches fail to achieve.