Question

Why force constant k does not depend on isotopic substitution?

Answer 1

It is shown that more accurate calculations of the hydrogen vibrational frequencies require more precise calculations of corrections of the zero-temperature vibration. Using, as an example, the silane molecule, we interpret the isotope frequency shift of the H(D)-stretch modes in terms of both the bond length change upon isotopic substitution (due to cubic anharmonicity), as well as ofcubic and quartic anharmonic corrections to vibrations. The Si-H bond length is always longer than that of Si-D. The harmonic force constant and anharmonic parameters depend not only on the electronic structure but also, indirectly, on the masses of the atoms involved. The importance of intermode mixing by anharmonic terms is demonstrated.