Hyper-Rayleigh scattering optical activity: Theory, symmetry considerations, and quantum chemistry applications

This work reports on the first computational quantum-chemistry implementation of the hyper-Rayleigh scattering optical activity (HRS-OA), a nonlinear chiroptical phenomenon. First, from the basics of the theory, which is based on quantum electrodynamics, and focusing on the electric dipole, magnetic-dipole, and electric-quadrupole interactions, the equations for the simulation of the differential scattering ratios of HRS-OA are re-derived. Then, for the first time, computations of HRS-OA quantities are presented and analyzed. They have been enacted on a prototypical chiral organic molecule (methyloxirane) at the time-dependent density functional theory level using a broad range of atomic orbital basis sets. In particular, (i) we analyze the basis set convergence, demonstrating that converged results require basis sets with both diffuse and polarization functions, (ii) we discuss the relative amplitudes of the five contributions to the differential scattering ratios, and (iii) we study the effects of origin-dependence and derived the expression of the tensor shifts and we prove the origin-independence of the theory for exact wavefunctions. Our computations show the ability of HRS-OA as a nonlinear chiroptical method, able to distinguish between the enantiomers of the same chiral molecule.

Automated summary

This study presents the first computational quantum-chemistry implementation of hyper-Rayleigh scattering optical activity (HRS-OA), a nonlinear chiroptical phenomenon. The equations for simulating the differential scattering ratios of HRS-OA are derived based on the theory of quantum electrodynamics and the interactions of electric dipole, magnetic dipole, and electric quadrupole. Computation results of HRS-OA quantities for a chiral organic molecule (methyloxirane) using a broad range of atomic orbital basis sets are presented and analyzed, demonstrating the ability of HRS-OA to distinguish between enantiomers of the same chiral molecule.