The molecular vibration-rotation Hamiltonian in the Bargmann-Hilbert space

Abstract

The molecular vibration-rotation Hamiltonian of polyatomic molecules is developed in the Bargmann-Hilbert space of entire functions. The vibration-rotation eigenvectors of polyatomic molecules are described as polynomials in complex variables where the number of complex variables is equal to the number of degrees of freedom of the molecule. Simple differential operator representations are found for all rotational and vibrational operators. A special procedure is developed, in the new representation, for describing the direction cosine operators of a rigid symmetric rotor. The new basis of molecular states is shown to be very convenient for calculating energy or intensity perturbations of molecules with axial symmetry. The theoretical methods include a treatment of doubly degenerate modes of vibration.