A Generalization of Badgers Rule

Already in the 30s of this century, diatomic molecules were investigated to correlate vibrational spectroscopic constants with bond lengths. The most successful of these relations was the Badger s rule (82) [49] 

However, Badger s rule is fully confirmed by the adiabatic force constants of polyatomic molecules, which explains its usefulness even for today s research. 

Once internal modes are defined, it is also possible to define the infrared intensity of these modes. For a normal mode, the infrared intensity is calculated with the help of the dipole moment derivatives. The dipole derivatives 3p/5x with regard to Cartesian coordinates can be determined in the course of an ab initio calculation of vibrational frequencies. The corresponding dipole derivatives with regard to normal coordinates are obtained by the transformation 

The matrix of dipole derivatives with regard to normal coordinates contains the derivatives of the dipole moment components with regard to each normal coordinate. The infrared intensity 1 of the normal mode is calculated according to Eq. (84) 

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