Herzberg–Teller Effect Predominates in Sum-Frequency Vibrational Spectroscopy of Limonene Chiral Liquids

Abstract

We theoretically study the bulk sum-frequency vibrational spectroscopy of chiral liquids under the influence of the Franck−Condon, Herzberg−Teller, and nonadiabatic effects. With quantum chemistry computations we calculate the chiral spectra for the R-limonene molecule. When we compare the theoretical and experimental spectra, we find that the Herzberg−Teller effect under the Born−Oppenheimer approximation, instead of the nonadiabatic effect, predominates in the chiral spectra.

Doubly Resonant Sum-Frequency Vibrational Spectroscopy of 1,1′-Bi-2-naphthol Chiral Solutions Due to the Nonadiabatic Effect

“…The advantage of CIS is that it can analytically calculate the properties of the excited electronic states including the nonadiabatic couplings, and its disadvantage is that the results it can calculate are inaccurate. In ref , SFVS computed by CIS is many times larger than experiment. Hence, there is an urgent need for an accurate method to study bulk SFVS.…”

“…The anti-Stokes Raman tensor is given by , where | n ,δ⟩ is the vibronic state of the excited electronic state | n ⟩, ω ( n ,δ)( g ,0) and ω ( g ,1)( n ,δ) are the energy differences between the corresponding vibronic states, and Γ ( n ,δ)( g ,0) and Γ ( g ,1)( n ,δ) are the damping constants. M ij is rewritten as the sum of A (HT) and B (nonadiabatic) terms , where |0 g ⟩ = | g ,0⟩ and |1 g ⟩ = | g ,1⟩, |ν s ⟩ and |δ n ⟩ are the vibrational states for the excited electronic states | s ⟩ and | n ⟩, respectively, Q t is the normal coordinate for the t vibrational mode, and μ i gn = ⟨ g |μ i | n ⟩ is the i ( i = x , y , z ) component of the electric dipole transition moment from the ground to excited electronic states. A term can be where ω ng is the electronic energy difference, and ω δ0 and ω δ1 are the vibrational energy differences.…”

“…A term can be where ω ng is the electronic energy difference, and ω δ0 and ω δ1 are the vibrational energy differences. When the vibrational energy differences are much smaller than the energy differences between the light and the electronic states, we expand the denominators in eq into three terms using the Taylor series, and the first two terms are neglected for they do not contribute to antisymmetric nonresonant Raman polarizability and only the third term is taken into consideration . Different from the nonresonant case, the resonant electronic states dominate antisymmetric resonant Raman polarizability and we do not expand the denominators.…”

“…In our previous studies, , we utilized CIS to compute the transition electric fields and the nonadiabatic couplings between the different excited electronic states. Just as we know, the properties calculated by CIS are not accurate.…”

“…They discovered that antisymmetric nonresonant Raman polarizability is much smaller than symmetric one . In 2018 and 2020, we computed antisymmetric nonresonant Raman polarizability and the corresponding SFVS off electronic resonance on limonene chiral liquids due to the Herzberg–Teller (HT) and nonadiabatic effects, which suggested that the nonadiabatic corrections are small and the HT effect predominates in the nonresonant case …”