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Orthogonality constrained density functional theory for electronic excited states.

We report a novel scheme for computing electronic excitation energies within the framework of density functional theory (DFT) based on a time-independent variational formulation of DFT. The excited state density functional is recast as a Kohn-Sham functional, which is further simplified by an adiabatic approximation of the exchange-correlation functional. Under the adiabatic approximation, the minimization of the excited state Kohn-Sham functional is shown to be equivalent to a ground state DFT computation augmented with orthogonality constraints with respect to the ground state Kohn-Sham determinant. An algorithm for the optimization of the energy subject to orthogonality constraints, which does not suffer from variational collapse, is described and implemented. A benchmark test set containing 28 organic molecules (Schreiber, M. J. Chem. Phys. 2008, 128, 134110) was used to assess the quality of the excitation energies obtained. Two novel approaches to spin-adapt the resulting excitation energies are discussed and found to provide results with error metrics similar to those of time-dependent DFT. Similarities and differences with respect to other time-independent DFT approaches are highlighted and some of the advantages of our scheme-including the ability to correctly describe charge-transfer excitations-are critically assessed.