Origin invariance in vibrational resonance Raman optical activity

Area of Science:

• Spectroscopy
• Theoretical Chemistry
• Quantum Mechanics

Background:

• Resonance Raman Optical Activity (RROA) spectroscopy is a powerful technique for probing molecular chirality.
• Understanding the origin dependence of spectroscopic signals is crucial for accurate interpretation.

Purpose of the Study:

• To theoretically investigate the origin dependence of vibronic polarizabilities and rotational invariants in RROA spectroscopy.
• To analyze the influence of Franck-Condon (FC) and Herzberg-Teller (HT) approximations on origin dependence.
• To numerically validate theoretical predictions using specific chiral molecules.

Main Methods:

• Theoretical derivation of origin-dependent expressions for RROA polarizabilities under resonance conditions.
• Application of FC and HT approximations for electronic transition moments.
• Numerical calculations using velocity representation of electric dipole and quadrupole transition moments for chiral molecules.

Main Results:

• RROA spectra can exhibit origin dependence, unlike far-from-resonance scattering, even for electronic Hamiltonian eigenfunctions.
• At the FC level, RROA is origin invariant for single or degenerate excited states; otherwise, origin effects appear.
• At the HT level, RROA is origin dependent even for a single excited state, though the effect is expected to be small.

Conclusions:

• Theoretical predictions regarding origin dependence in RROA spectroscopy are confirmed by numerical calculations.
• The study quantifies the extent of origin effects and demonstrates methods to mitigate them.
• The findings provide insights into the interpretation of RROA spectra and the role of theoretical approximations.