Cheap and reliable optimization of excited state orbitals with the Square Gradient Minimization (SGM) approach.*

Orbital optimized (OO) excited state methods eliminate many of the shortcomings of linear-response theories like TDDFT or EOM-CCSD for excited states with charge transfer, double or core excitation character. However, use of OO methods has been hindered by the risk of “variational collapse” from excited state solutions (typically saddle points of energy) to the ground state. We present an orbital optimization scheme based on square gradient minimization (SGM) that reliably converges to excited state solutions. The computational cost of SGM is only 2-3 times the cost of ground state orbital optimization (per iteration). We subsequently demonstrate that OO-DFT with SGM can predict energies of doubly excited states to significantly greater accuracy than expensive coupled cluster approaches (that often have > 1 eV error). Similarly, we demonstrate that OO-DFT approaches predict core excitation energies to < 0.5 eV RMS error for both closed and open-shell systems. In contrast, TDDFT typically has > 10 eV error and EOM-CCSD often fails qualitatively for open-shell cases. OO-DFT with SGM thus permits reliable simulation of both static and transient X-ray absorption spectra, which can be employed to interpret experimental studies of chemical dynamics.