Solvent-induced red-shifts for the proton stretch vibrational frequency in a hydrogen-bonded complex. 1. A valence bond-based theoretical approach

A theory is presented for the proton stretch vibrational frequency ν_AH for hydrogen (H-) bonded complexes of the acid dissociation type, that is, AH⋯B ⇔ A^-⋯HB⁺(but without complete proton transfer), in both polar and nonpolar solvents, with special attention given to the variation of ν_AH with the solvent's dielectric constant ε. The theory involves a valence bond (VB) model for the complex's electronic structure, quantization of the complex's proton and H-bond motions, and a solvent coordinate accounting for nonequilibrium solvation. A general prediction is that ν_AH decreases with increasing ε largely due to increased solvent stabilization of the ionic VB structure A^-⋯HB⁺ relative to the neutral VB structure AH⋯B. Theoretical ν_AH versus 1/ε slope expressions are derived; these differ for polar and nonpolar solvents and allow analysis of the solvent dependence of ν_AH. The theory predicts that both polar and nonpolar slopes are determined by (i) a structure factor reflecting the complex's size/geometry, (ii) the complex's dipole moment in the ground vibrational state, and (iii) the dipole moment change in the transition, which especially reflects charge transfer and the solution phase proton potential shapes. The experimental proton frequency solvent dependence for several OH⋯O H-bonded complexes is successfully accounted for and analyzed with the theory.