On the performance of DFT/MRCI Hamiltonians for electronic excitations in transition metal complexes: The role of the damping function.

The combination of density functional theory and multireference configuration interaction (DFT/MRCI) is a well-established semi-empirical method suitable for computing spectral properties of large molecular systems. To this day, three different Hamiltonians and various parameter set combinations exist. These DFT/MRCI variants are well tried and tested when it comes to electronic excitations of organic molecules. For transition metal complexes, systematic benchmarks against experimental data are missing, however. Here we present an assessment of the DFT/MRCI variants and of time-dependent, linear-response density functional theory (TDDFT) for a diverse set of ligand-centered, metal-to-ligand charge transfer, metal-centered, and ligand-to-metal charge transfer (LMCT) excitations on 21 3 and 4 complexes comprising 10 small inorganic and 11 larger metalorganic compounds with closed-shell ground states. In the course of this assessment, we realized that the excitation energies of transition metal complexes can be very sensitive with respect to the details of the damping function that scales off-diagonal matrix elements. This scaling is required in DFT/MRCI to avoid double counting of dynamic electron correlation. These insights lead to a new Hamiltonian, denoted R2018, with improved performance on transition metal compounds, while the results for organic molecules are nearly unaffected by the modified damping function. Two parameter sets were optimized for this Hamiltonian: One set is to be used in conjunction with the standard configuration selection threshold of 1.0 E and a second set is for use with a selection threshold of 0.8 E which leads to shorter wave function expansions. The R2018 Hamiltonian in standard parameterization achieves root-mean-square errors (RMSEs) of merely 0.15 eV for the metalorganic complexes, followed by 0.20 eV for the original DFT/MRCI ansatz, and 0.25 eV for the redesigned DFT/MRCI approach. In comparison, TDDFT gives a much larger RMSE of 0.46 eV for metalorganic complexes. None of the DFT/MRCI variants yields convincing results for small oxides and fluorides which exhibit LMCT transitions. Here, TDDFT performs better. If the oxides and fluorides are excluded from the inorganic test set, satisfactory agreement can be achieved, with RMSE values between 0.26 eV and 0.30 eV for DFT/MRCI and 0.34 eV for TDDFT. The performance of the original and the new DFT/MRCI Hamiltonians deteriorates only slightly, when a tighter selection threshold is chosen, thus enabling the computation of reliable spectral properties even for large metalorganic complexes.