Two-dimensional (2D) fifth-order Raman spectroscopy is a coherent spectroscopy that can be used as a structural tool, in a manner analogous to 2D nuclear magnetic resonance (NMR) but with much faster time scale. By including the effect of dipole-induced dipole interactions in the molecular polarizability, it is shown that 2D Raman experiments can be used to extract distances between coupled dipoles, and thus elucidate structural information on a molecular level. The amplitude of cross peaks in the 2D Raman spectrum arising from dipole-induced dipole interactions is related to the distance between the two dipoles and the relative orientation of the dipoles. In an isotropic sample with randomly distributed dipole orientations, such as a liquid, the cross peak amplitude scales as In an anisotropic sample such as a solid, where the orientational averaging effects do not nullify the leading order contribution, the amplitude scales as These scaling relationships have analogy to the dipole coupling relationships that are observed in solid state and liquid 2D NMR measurements.
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With this definition of , the polarizability of the A mode should depend on the B mode in general, since , etc. are merely expansion coefficients of the dipole (interacting with other dipoles) in terms of the electric field at the time t; this is not the polarizability for an isolated mode although this point might not been emphasized in the literature. This understanding allows us to expand the polarizability in terms of the nuclear coordinates of A which is affected by the B mode as we discuss below. It should be noted that depends on the electric field at the time before t in general as we see below.
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In the purely isotropic case, is randomly distributed; .
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