Solvent-Induced
Red-Shifts for the Proton Stretch
Vibrational Frequency in a Hydrogen-Bonded Complex. 1. A Valence Bond-Based
Theoretical Approach
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Abstract
A theory is presented for the proton
stretch vibrational frequency
ν<sub>AH</sub> for hydrogen (H−) bonded complexes of
the acid dissociation type, that is, AH···B ⇔
A<sup>–</sup>···HB<sup>+</sup>(but without complete
proton transfer), in both polar and nonpolar solvents, with special
attention given to the variation of ν<sub>AH</sub> 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<sub>AH</sub> decreases with increasing
ε largely due to increased solvent stabilization of the ionic
VB structure A<sup>–</sup>···HB<sup>+</sup> relative
to the neutral VB structure AH···B. Theoretical ν<sub>AH</sub> versus 1/ε slope expressions are derived; these differ
for polar and nonpolar solvents and allow analysis of the solvent
dependence of ν<sub>AH</sub>. 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