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We present a general approach to converge excited state solutions to anyquantum chemistry orbital optimization process, without the risk of variationalcollapse. The resulting Square Gradient Minimization (SGM) approach onlyrequires analytic energy/Lagrangian orbital gradients and merely costs 3 timesas much as ground state orbital optimization (per iteration), when implementedvia a finite difference approach. SGM is applied to both single determinant$\Delta$SCF and spin-purified Restricted Open-Shell Kohn-Sham (ROKS) approachesto study the accuracy of orbital optimized DFT excited states. It is found thatSGM can converge challenging states where the Maximum Overlap Method (MOM) oranalogues either collapse to the ground state or fail to converge. We alsoreport that $\Delta$SCF/ROKS predict highly accurate excitation energies fordoubly excited states (which are inaccessible via TDDFT). Singly excited statesobtained via ROKS are also found to be quite accurate, especially for Rydbergstates that frustrate (semi)local TDDFT. Our results suggest that orbitaloptimized excited state DFT methods can be used to push past the limitations ofTDDFT to doubly excited, charge-transfer or Rydberg states, making them auseful tool for the practical quantum chemist's toolbox for studying excitedstates in large systems.

journal of chemical theory and computation

Excited state orbital optimization via minimizing the square of the  gradient: General approach and application to singly and doubly excited  states via density functional theory