A Guided Self-Consistent-Field Method for Excited-State Wave Function Optimization: Applications to Ligand-Field Transitions in Transition-Metal Complexes

A guided self-consistent field (SCF) method is presented in this paper. This method uses the eigenspace update-and-following idea to improve the SCF method for optimizing wave functions that are higher-energy solutions to the Roothaan-Hall equation. In this method, the eigenvectors of the previous SCF step are used to prediagonalize the current Fock/Kohn-Sham matrix, preserving the ordering of orbital occupations. When the subject of interest is an excited state of the same spin symmetry as the ground state, the initial guess of excited wave function is improved with a preconditioning step. The preconditioning step is an SCF iteration applied to the beta spin manifold if the initial guess is generated by orbital permutation in the a spin manifold. This simple preconditioning step gives rise to more-stable SCF convergence using the algorithm presented herein. The guided SCF method is used to optimize ligand-field excited states in tetrahedral transition-metal complexes, and calculate Delta SCF excitation energies. The calculated ligand-field transition energies are compared with those obtained from orbital energy differences, linear response time-dependent density functional theory, and experiments. The excitation energies obtained using the method presented in this work show a significant improvement over orbital energy differences and linear response method.