A combined DFT and restricted open-shell configuration interaction method including spin-orbit coupling: Application to transition metal L-edge X-ray absorption spectroscopy

A novel restricted-open-shell configuration interaction with singles (ROCIS) approach for the calculation of transition metal L-edge X-ray absorption spectra is introduced. In this method, one first calculates the ground state and a number of excited states of the non-relativistic Hamiltonian. By construction, the total spin is a good quantum number in each of these states. For a ground state with total spin S excited states with spin S′ = S, S − 1, and S + 1 are constructed. Using Wigner-Eckart algebra, all magnetic sublevels with MS = S, …, −S for each multiplet of spin S are obtained. The spin-orbit operator is represented by a mean-field approximation to the full Breit-Pauli spin-orbit operator and is diagonalized over this N-particle basis. This is equivalent to a quasi-degenerate treatment of the spin-orbit interaction to all orders. Importantly, the excitation space spans all of the molecular multiplets that arise from the atomic Russell-Saunders terms. Hence, the method represents a rigorous first-principles approach to the complicated low-symmetry molecular multiplet problem met in L-edge X-ray absorption spectroscopy. In order to gain computational efficiency, as well as additional accuracy, the excitation space is restricted to single excitations and the configuration interaction matrix is slightly parameterized in order to account for dynamic correlation effects in an average way. To this end, it is advantageous to employ Kohn-Sham rather than Hartree-Fock orbitals thus defining the density functional theory/ROCIS method. However, the method can also be used in an entirely non-empirical fashion. Only three global empirical parameters are introduced and have been determined here for future application of the method to any system containing any transition metal. The three parameters were carefully calibrated using the L-edge X-ray absorption spectroscopy spectra of a test set of coordination complexes containing first row transition metals. These parameters are universal and transferable. Hence, there are no adjustable parameters that are used to fit experimental X-ray absorption spectra. Thus, the new approach classifies as a predictive first-principles method rather than an analysis tool. A series of calculations on transition metal compounds containing Cu, Ti, Fe, and Ni in various oxidation and spin states is investigated and a detailed comparison to experimental data is reported. In most cases, the approach yields good to excellent agreement with experiment. In addition, the origin of the observed spectral features is discussed in terms of the electronic structure of the investigated compounds.