Excited-State Vibrational Frequencies: Restricted Virtual Space Time-Dependent Density Functional Theory

Calculating accurate vibrational frequencies for molecules with electronically excited states has an important function in many areas of photochemistry. However, calculations are often limited to smaller molecules due to the rapid growth in the degrees of freedom that must be taken into account to accurately describe larger systems. The applicability of the restricted virtual space (RVS) approximation has been studied within adiabatic linear response time-dependent density functional theory when calculating excited-state nuclear vibrational frequencies. Using the S1 and T1 electronic states of CO, CN–, HOF, H2CS, and C2H4 as representative examples, it is found that vibrational frequency calculations are particularly sensitive to this approximation, with no more than 10–20% of orbitals recommended for safe removal without a priori knowledge when using the 6-311+G­(d,p) and aug-cc-pVTZ basis sets. Higher-frequency vibrations such as those with a high degree of CH bond stretching character are found to be less sensitive to the RVS than the lower-frequency vibrations, and several of the triplet states are also found to be less sensitive to this approximation than their equivalent singlet states. Occupied core orbitals and high-energy virtual orbitals with core character can also be removed without introducing significant error.