DISCUSSION ON THE ROTATION-VIBRATION HAMILTONIAN OF LINEAR POLYATOMIC MOLECULES

Abstract

A large number of computations have been performed on energy levels and intensities in the rotation-vibration spectrum of linear polyatomic molecules, using a method suggested by H. H. Nielsen and consisting in the following scheme: a) to take the general formulation derived for non-linear polyatomic molecules from the Darling-Dennison Hamiltonian. b) then to particularize to linear molecules by writing the Sayvetz condition $P_{x}=P_{x}$. Other authors however have questioned the validity of this procedure and have insisted on the need to use special methods for linear molecules, based on an Hamiltonian where rotational and vibrational operators do not commute. This point will be discussed and it will be established that Nielsen’s method is perfectly valid while some of the alternative methods which have been used are not correct.