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

Abstract

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 S 1 and T 1 electronic states of CO, CN − , HOF, H 2 CS, and C 2 H 4 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.

TD-DFT simulations of K-edge resonant inelastic X-ray scattering within the restricted subspace approximation

“…As the excitation energy is tuned beyond the core-ionization threshold, the scattering cross-section is overtaken by the non-resonant emission process. Furthermore, restricting the virtual space in TD-DFT has been proposed early on as a means for tackling states for adsorbed molecules as well as molecules in solution, [41][42][43] and it has been shown to also be a suitable route to obtaining excited states energies, 29 geometries 44 and vibrational frequencies 45 of large systems. Virtual space restriction has also been successfully used in RIXS simulations at the L-edge of transition metal complexes within the multi-configurational Kohn-Sham ROCIS method.…”

Reduced Two-Electron Interactions in Anharmonic Molecular Vibrational Calculations Involving Localized Normal Coordinates

“…Even greater reductions in the computational complexity may also be possible through the development of colocalization procedures that localize both the normal mode and molecular orbital spaces at the same time to achieve an optimal balance of coordinates. A recent study has suggested that a similar combination of orbital and normal mode localizations could show potential for improving the efficiency of calculating vibrational frequencies for electronically excited states when using the restricted virtual space approximation to time-dependent DFT (RVS-TDDFT) . However, this is considered to be outside the scope of the current investigation.…”

“…A recent study has suggested that a similar combination of orbital and normal mode localizations could show potential for improving the efficiency of calculating vibrational frequencies for electronically excited states when using the restricted virtual space approximation to time-dependent DFT (RVS-TDDFT). 93 However, this is considered to be outside the scope of the current investigation. Similarly, given the potential that two-electron attenuation has to improve efficiency in the calculation of vibrational properties, future investigations may also be warranted into the distance decay behavior of the correlated two-electron terms in attenuated MP2 theory.…”

Static Electron Correlation in Anharmonic Molecular Vibrations: A Hybrid TAO-DFT Study

“…Experimental observations and theoretical models can be linked by accurately matching theoretically predicted and observed properties. The development of theoretical methods to efficiently and accurately predict these properties and the assessment of these methods is therefore an area of ongoing research, − and molecular vibrational simulations have even recently been performed using blockchain computers. , …”