Electric-field effects on the OH vibrational frequency and infrared absorption intensity for water

The variations of the anharmonic OH frequency and the infrared absorption intensity with field strength have been calculated for the uncoupled OH stretching vibration of a water molecule in a static, homogeneous electric field using ab initio methods at the MP4 level with a nearly saturated basis set. The OH frequency is found to be virtually independent of the field components perpendicular to the vibrating OH bond. For the parallel component, the frequency vs field curve is close to quadratic, with a maximum for a slightly negative (directed from H to O) field strength. The external field perturbation, defined as Vext(E∥,rOH)=Vtot(E∥, rOH)−Vfree(rOH), is found to be closely linear in rOH, except when the field strength E∥ is both large and negative. The linear external force constant is almost perfectly accounted for by the sum of two terms, −E∥⋅dμ∥free/drOH and −1/2⋅E∥⋅∂μ∥induced/∂rOH. These derivatives are quite insensitive to the choice of basis-set. The ∂μ∥induced/∂rOH derivative is approximately proportional to E∥, and gives rise to the arclike shape of the frequency vs field curve. The frequency maximum occurs where ∂μ∥tot/∂rOH≊0. It is the sign of dμ∥free/drOH which determines that the frequency maximum occurs at a negative field strength for water (but at a positive field strength for OH−, for example), i.e., that a frequency red-shift (blue-shift for OH−) occurs when the molecule is bound. The linear relationship between the infrared absorption intensity and frequency of the water OH vibration is derived.