Anharmonicity in Polyatomic Molecules. The CH-Stretching Overtone Spectrum of Benzene

Abstract

A long series of CH‐stretching overtones in the infrared and visible spectrum of benzene can be analyzed using a single anharmonicity constant (− 57.5 cm⁻¹). This anharmonicity is associated with an independently vibrating local CH oscillator and the spectrum is interpreted in terms of such a local‐mode representation. A transformation is made to normal modes which leads to five different normal‐mode anharmonicity constants, which are representative of the 13 different CH‐stretching anharmonicity constants that characterize benzene. The CH‐overtone spectrum of benzene is described in terms of its normal‐mode components. A method of assigning relative intensities to these components is developed, and, along with the calculated normal‐mode anharmonicity constants, is used to construct the overtone spectrum as a superposition of Lorentzian bands calculated for each individual component. The maxima of these bands compare favorably with the observed band maxima. By adjusting the local‐mode anharmonicity constant from − 57.5 to − 55.2 cm⁻¹, the agreement can be made perfect so that the latter value appears to be the appropriate local‐mode CH‐stretching anharmonicity constant in benzene. This number is relevant to the theory of radiationless transitions in aromatic hydrocarbons. The effect of introducing anharmonic coupling between local modes is investigated and found to be unimportant.