To gain insight on the absorption intensities, as well as the direction of the transition moment for the OH stretching vibration in alcohols and acids, we performed detailed analyses for nitric acid, acetic acid, methanol, tert-butyl alcohol, water, and OH radical. We obtained both the potential energy surface and the dipole moment function (DMF) by the B3LYP method and performed quantum mechanical vibrational calculation using the grid variational method based on the local mode model. In this work, we employed the sum rule of the absorption intensities for the one-dimensional (1-D) vibrational Hamiltonian to construct an effective 1-D DMF, which is responsible for the total sum of the overtone intensities. The direction of this effective DMF was found to be tilted away from the OH bond by about 30° for the polyatomic molecules. The nonlinearity of the DMFs in the directions parallel and perpendicular to the OH bond is discussed to rationalize the tilting. Furthermore, we analyzed the effective 1-D DMFs with the vibrational wave function expansion method and derived the effective portion of the 1-D DMF that is responsible for the overtone transition moment.
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