Infrared Spectra of Charge-Transfer Complexes. VI. Theory

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Abstract
The general theory of molecular vibrational transition intensities is discussed with emphasis on electronic reorientation contributions to the intensities. The wavefunctions used by Mulliken to represent the electronic states of donor—acceptor complexes are written to include an explicit dependence on the vibrational coordinates. These functions and the general theory are applied to the intensities of halogen vibrations in donor—acceptor complexes. Specific application to actual complexes requires the estimation of the derivative of the vertical electron affinity of the halogen molecule with respect to its internuclear distance, the electronic transition moment of the charge‐transfer band, the coefficients in the donor—acceptor ground‐state wavefunctions and the difference between the energies of the dative‐ and no‐bond states. Evaluation of each of these parameters is discussed for a number of complexes of halogens and relationships between the wavefunction coefficients and the infrared frequency shifts are described. The calculations indicate that all of the intensity enhancement of the halogen—halogen stretching vibration may be due to electronic reorientation during the vibration. Partly as a result of this conclusion, it is argued that no information about the geometry of the benzene—halogen complexes may be deduced form the infrared spectrum, at least in any simple way. The argument is extended qualitatively to hydrogen‐bonded systems to indicate the probable similarity in explanation for the enhancement of the X—H stretching vibrations. In conclusion, a number of generalizations are presented regarding the spectra of complexes.