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

Andrea Bonvicini¹, Sonia Coriani², Benoît Champagne¹

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Summary

This study introduces a new velocity formulation for hyper-Rayleigh scattering optical activity (HRS-OA) spectroscopy. This approach ensures origin-independence, making it ideal for calculating HRS-OA invariants with approximated wave functions.

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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.