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Elucidation of the mechanism for optical spin initialization of point defectsin solids in the context of quantum applications requires an accuratedescription of the excited electronic states involved. While variationaldensity functional calculations have been successful in describing the groundstate of a great variety of systems, doubts have been expressed in theliterature regarding the ability of such calculations to describe electronicexcitations of point defects. A direct orbital optimization method is used hereto perform time-independent, variational density functional calculations of aprototypical defect, the negatively charged nitrogen-vacancy center in diamond.The calculations include up to 511 atoms subject to periodic boundaryconditions and the excited state calculations require similar computationaleffort as ground state calculations. Contrary to some previous reports, the useof local and semilocal density functionals gives the correct ordering of thelow-lying triplet and singlet states, namely ${}^{3}A_2 < {}^{1}E < {}^{1}A_1 <{}^{3}E$. Furthermore, the more advanced meta generalized gradientapproximation functionals give results that are in remarkably good agreementwith high-level, many-body calculations as well as available experimentalestimates, even for the excited singlet state which is often referred to ashaving multireference character. The lowering of the energy in the tripletexcited state as the atom coordinates are optimized in accordance withanalytical forces is also close to the experimental estimate and the resultingzero-phonon line triplet excitation energy is underestimated by only 0.15 eV.The approach used here is found to be a promising tool for studying electronicexcitations of point defects in, for example, systems relevant for quantumtechnologies.

Electronic excitations of the charged nitrogen-vacancy center in diamond obtained using time-independent variational density functional calculations