Translational diffusion in liquids: Specific features of the spectral densities for isotropic intermolecular interactions

Abstract

In theories of electron spin exchange and diffusion-induced direct proton tunnelling in solution, one has to calculate the spectral densities J(ω) of a purely radial intermolecular coupling resulting from a translational diffusion. By using the exact solutions of the diffusion equation, it is shown that at low frequencies, J(ω) = J(0)− Aω 1 2 , where J(0) and A are independent of the procedure used to incorporate the molecular impenetrability. On the other hand, at high frequencies, J(ω) strongly depends on the boundary conditions, decreasing as ω −2 in the presence of a reflecting wall at the molecular contact.