**International Journal of Quantum Chemistry**

# Redshifts and blueshifts of OH vibrations

## Abstract

Ab initio calculations of potential energy, dipole moment, equilibrium OH distance, force constants, and anharmonic frequencies, and correlation between these quantities, are presented for a water molecule and an OH^{−} ion in a uniform electric field of varying field strength. It is explained why a bound H_{2}O molecule in nature always experiences a frequency downshift with respect to the free molecule, and a bound OH^{−1} ion, either a downshift or an upshift. The frequency-field variation is well accounted for by the expression Δν_{OH} α −*E*‖ · (d μ/d*r*_{OH} + 1/2 · ∂μ/∂*r*_{OH}). A frequency maximum occurs at the field strength where ∂μ‖^{tot}/∂*r*_{OH} ∼ 0. Two cases can be discerned: (1) the frequency maximum falls at a positive field strength when dμ/d*r*_{OH} is positive (this is the situation for OH^{−}), and (2) the maximum frequency falls at a negative field when dμ/d*r*_{OH} is negative (this occurs for water). In general, for an OH bond in a bonding situation where the intermolecular interactions are dominated by electrostatic forces, the nonlinearity of the frequency shift with respect to an applied field is governed by how close to the frequency maximum one is, i.e., by both dμ/d*r*_{OH} and ∂μ/∂*r*_{OH}. Correlation curves between the external linear force constant, *k*^{ext}, and *r*_{OH,e} are closely linear over the whole field range studied here, whereas the frequency vs. *r*_{OH,e} and force constants vs. *r*_{OH,e} correlation curves form two approximately linear, parallel branches, corresponding to “before” and “after” the maximum in the frequency vs. field curves. Each branch of the ν vs. *r*_{OH,e} curves has a slope of ∼ − 16,000 cm^{−1}/Å. © 1993 John Wiley & Sons, Inc.