The development of variational density functional theory approaches to excited electronic states is impeded by limitations of the commonly used self-consistent field (SCF) procedure. A method based on a direct optimization approach as well as the maximum overlap method is presented, and the performance is compared with previously proposed SCF strategies. Excited-state solutions correspond to saddle points of the energy as a function of the electronic degrees of freedom. The approach presented here makes use of a preconditioner determined with the help of the maximum overlap method to guide the convergence on a target nth-order saddle point. This method is found to be more robust and converge faster than previously proposed SCF approaches for a set of 89 excited states of molecules. A limited-memory formulation of the symmetric rank-one method for updating the inverse Hessian is found to give the best performance. A conical intersection for the carbon monoxide molecule is calculated without resorting to fractional occupation numbers. Calculations on the excited states of the hydrogen atom and a doubly excited state of the dihydrogen molecule using a self-interaction corrected functional are presented. For these systems, the self-interaction correction is found to improve the accuracy of density functional calculations of excited states.

Recent ultrafast experiments have unveiled the time scales of vibrational cooling and decoherence upon photoexcitation of the diplatinum complex [Pt2(P2O5H2)4]4– in solvents. Here, we contribute to the understanding of the structure and dynamics of the lowest lying singlet excited state of the model photocatalyst by performing potential energy surface calculations and Born–Oppenheimer molecular dynamics simulations in the gas phase and in water. Solvent effects were treated using a multiscale quantum mechanics/molecular mechanics approach. Fast sampling was achieved with a modified version of delta self-consistent field implemented in the grid-based projector-augmented wave density functional theory code. The known structural parameters and the PESs of the first singlet and triplet excited states are correctly reproduced. Besides, the simulations deliver clear evidence that pseudorotation of the ligands in the excited state leads to symmetry lowering of the Pt2P8 core. Coherence decay of Pt–Pt stretching vibrations in solution was found to be governed by vibrational cooling, which is in agreement with previous ultrafast experiments. We also show that the flow of excess Pt–Pt vibrational energy is first directed toward vibrational modes involving the ligands, with the solvent favoring intramolecular vibrational energy redistribution. The results are supported by thorough vibrational analysis in terms of generalized normal modes.

A direct optimization method for obtaining excited electronic states using density functionals is presented. It involves selective convergence on saddle points on the energy surface representing the variation of the...

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