Rotation Vibration Spectrum of the HCl Molecule

One might expect that quantum mechanical calculations capable of predicting the structure of even the simplest molecules would be quite complex. Indeed, solving the Schrödinger equation for the nuclei and all electrons would be a formidable task. Fortunately, this is not always necessary. Because of their large mass difference, accurate results can be obtained while treating the electron and nuclear motion in separate steps. This is called the Born-Oppenheimer approximation. The rapid changes that occur in the electronic wavefunction as the nuclei slowly move relative to one another gives rise to effective interatomic forces that can then be used in determining the nuclear motion. The forces need not even be well determined ahead of time. Instead, they can be treated as unknowns to be determined by experiments such as this one.