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.