Vibrational softening of diatomic molecules

An analysis of a model molecular oscillator is presented: a vibrating diato mic molecule carrying N-0 electrons. The energy derivatives over the number of electron (N) and the deformation (Q), partial derivative (n)/partial de rivativeN(n) and partial derivative (n)/partial derivativeQ(n) have been an alyzed up to second order (n = 2), including the appropriate mixed derivati ves. The effect of coupling between distortion of the electron density indu ced by DeltaN and the vibrational deformation of the molecule has been stud ied. Anharmonicity of the oscillator has been shown to be a possible result of that coupling; new relations between the parameters characterizing the anharmonicity of the oscillator and the energy derivatives at density funct ional theory level have been obtained. Ah initio calculations for a set of diatomic molecules have been performed, yielding values for all the derivat ives discussed and demonstrating the effect of coupling with vibrations.