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

Area of Science:

• Computational Chemistry
• Theoretical Chemistry
• Photochemistry

Background:

• Accurate calculation of molecular vibrational frequencies is essential for understanding photochemistry.
• Computational limitations restrict these calculations to smaller molecules due to the high computational cost associated with increasing degrees of freedom.

Purpose of the Study:

• To investigate the applicability of the restricted virtual space (RVS) approximation for calculating excited-state nuclear vibrational frequencies.
• To determine the sensitivity of these calculations to the RVS approximation across various molecular systems and electronic states.

Main Methods:

• Employed adiabatic linear response time-dependent density functional theory (TD-DFT).
• Studied the S₁ and T₁ electronic states of representative molecules: CO, CN^-, HOF, H₂CS, and C₂H₄.
• Utilized 6-311+G(d,p) and aug-cc-pVTZ basis sets.

Main Results:

• Vibrational frequency calculations are highly sensitive to the RVS approximation.
• Recommended removing no more than 10-20% of orbitals for safe application of RVS without prior knowledge.
• Higher-frequency vibrations (e.g., CH bond stretching) and triplet states showed less sensitivity to RVS compared to lower-frequency vibrations and singlet states, respectively.
• Removal of occupied core orbitals and high-energy virtual orbitals with core character did not introduce significant errors.

Conclusions:

• The RVS approximation must be applied cautiously in excited-state vibrational frequency calculations.
• Specific orbital subsets (core and high-energy virtual) can be removed without compromising accuracy.
• Further research may refine RVS application for larger molecular systems in photochemistry.