Enhancing the applicability of multicomponent time-dependent density functional theory

The multicomponent extension of time-dependent density functional theory (TDDFT) within the nuclear-electronic orbital (NEO) framework enables the calculation of both electronic and vibrational excitations simultaneously. In this NEO-TDDFT approach, all electrons and select nuclei, typically protons, are treated quantum mechanically on the same level. Herein, the dependence of the proton vibrational excitation energies on the nuclear and electronic basis sets is examined. Protonic basis sets that include f basis functions in conjunction with substantial electronic basis sets for the quantum hydrogen are found to produce accurate proton vibrational excitation energies that are mostly within ∼30 cm^-1 of reference values for the molecules studied. The NEO-TDDFT approach is shown to be effective for open-shell as well as closed-shell systems. Additionally, an approach for computing and visualizing the nuclear transition densities associated with the proton vibrational excitations is implemented. These nuclear transition densities are important for characterizing the proton vibrational excitations and determining the spatial orientations of the corresponding vibrational modes. These capabilities are essential for a variety of applications, including the incorporation of anharmonic effects into molecular vibrational frequency calculations.