Mean Amplitudes of Vibration of the Halogen Molecules

During the last years, we have performed systematic calculations on the vibrational properties of simple molecules and ions containing interhalogen bonds. Surprisingly, during our literature searches we found that detailed information on the mean amplitudes of vibration of the halogen molecules themselves ar not available. In the classic work of Cyvin [1] only a brief mention of these values for Cl2, I2, and 79Br81Br, at two selected temperatures, are given. There is no information about F2 [1, 2]. In order to fill this gap and to complement and extend our studies, we have now performed a calculation of the mean amplitudes of vibration of the four halogen molecules. The calculations are relatively simple due to the fact that diatomic species present only onevibrational degree of freedom. The vibrational frequencies were taken from the book of Siebert [3]. They correspond to the gaseous F2, Cl2, and Br2 molecules and to a chloroformic solution of I2. These data, together with the corresponding force constants, calculated using the “two-masses model” [4], are presented in Table 1. According toKimura andKimura [5];mean-square amplitudes of vibration for a normal coordinate with one characteristic vibrational frequency can be calculated with the expression