On the Vector Model of Transformation of the Kinetic Energy Operator of Multiparticle Systems to the Description of Internal Motions

High-resolution spectroscopy of small molecules and radicals is associated with the interpretation of rotational-vibrational spectra, the theory of which is based on the study of the internal motions of a free system of particles and its rotation as a whole. In this paper, in addition to the differential geometry methods, a vector version of the transformation of the kinetic energy operator for a system of many particles is considered, in which the energy operator of the system rotation as a whole is expressed in terms of the square of the total angular momentum relative to the center of mass of the particle system. It is shown that the construction of a solution to the Schrödinger equation for atomic-molecular systems in the form of a multipolar harmonic product and an energy eigenfunction is consistent with the conclusion obtained by methods of differential geometry that the internal motions of multiparticle systems are realized under the condition of zero angular momentum and under the influence of effective centrifugal potentials, and additional gradient contributions corresponding to the rotational states of the total angular momentum that take place in the system of many particles also at zero value of the total angular momentum.