Velocity formulations for hyper-Rayleigh scattering optical activity spectroscopy: Addressing the origin-dependence...

Area of Science:

• * Theoretical Chemistry
• * Spectroscopy
• * Quantum Mechanics

Background:

• * Hyper-Rayleigh scattering optical activity (HRS-OA) spectroscopy is crucial for molecular characterization.
• * Previous theoretical descriptions relied on the length formulation of molecular hyperpolarizabilities.
• * The length formulation involves pure electric-dipole and mixed electric-dipole/magnetic-dipole or electric-dipole/electric-quadrupole hyperpolarizabilities.

Purpose of the Study:

• * To develop an alternative formulation for the first hyperpolarizabilities in HRS-OA spectroscopy.
• * To introduce a velocity formulation for these hyperpolarizabilities.
• * To ensure the origin-independence of the theoretical framework.

Main Methods:

• * Employed the velocity form of electric-dipole and electric-quadrupole moment operators.
• * Utilized quadratic response functions within the new formulation.
• * Investigated the gauge-origin shifts and their correspondence with the length formulation.

Main Results:

• * Established a one-to-one correspondence for gauge-origin shifts between length and velocity formulations.
• * Demonstrated the origin-independence of the velocity formulation.
• * Showcased the suitability of the velocity formulation for calculations using approximated wave functions.

Conclusions:

• * The velocity formulation provides a robust and origin-independent theoretical framework for HRS-OA.
• * This new approach simplifies the calculation of HRS-OA invariants, especially with approximated wave functions.
• * The findings enhance the theoretical understanding and computational applicability of HRS-OA spectroscopy.