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Second spectral moment of vibrational hyper‐Raman and hyper‐Rayleigh spectra
Author(s) -
Bancewicz T.,
Kielich S.
Publication year - 1990
Publication title -
journal of raman spectroscopy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.748
H-Index - 110
eISSN - 1097-4555
pISSN - 0377-0486
DOI - 10.1002/jrs.1250210309
Subject(s) - hyperpolarizability , rayleigh scattering , raman spectroscopy , moment (physics) , raman scattering , tensor (intrinsic definition) , second moment of area , molecular physics , rank (graph theory) , spectral line , chemistry , physics , optics , geometry , mathematics , quantum mechanics , molecule , polarizability , combinatorics
Equations for the second spectral moment of vibrational hyper‐Raman and hyper‐Rayleigh spectra are derived. It is shown that owing to the simultaneous dependence of the hyper‐Raman and hyper‐Rayleigh intensities on the irreducible spherical first‐ and third‐rank hyperpolarizability tensors, both the unnormalized and the normalized second moments of both the above types of scattering are geometry dependent. However, for some molecular symmetries and for some molecular vibrations, the irreducible first‐rank hyperpolarizability tensor vanishes; then the normalized second spectral moment of the second‐harmonically scattered rediation is independent of the scattering geometry, as in the linear case.