For nonrigid M_kXY_n (k>=1) molecules, a model is constructed that describes the motion of k M nuclei relative to the quasirigid XY_n fragment taking into account 3*k degrees of freedom. The parameters of the potential and kinetic terms of the model Hamiltonian are determined from results of ab initio calculations of the properties of a molecule and its fragments. Solutions of the corresponding Schrödinger equations are obtained by a variational method using the basis sets constructed from products of spherical harmonics and harmonic-oscillator eigenfunctions.  The form of model Hamiltonians for the nonrigid MXY₄ and M₂XY­₄ molecules with quasi-tetrahedral XY₄ fragments are discussed in detail.  Group-theoretical analysis of symmetry of the Hamiltonians is performed. It is shown that the molecular symmetry groups of nonrigid MXY₄ and M₂XY₄ molecules are the G₂₄ and G₄₈ groups, which are isomorphic to the T_d and O_h point groups, respectively.

This non-empirical model for M_kXY_n (k>=1) nonrigid molecules describing the motion of k M nuclei relative to a quasirigid XY_n fragment is used to study the dynamics of nuclei in the LiReO₄ and K₂SO₄ molecules. The parameters of the kinetic and potential parts of the model Hamiltonian and dipole moment functions are determined from results of ab initio calculations of the molecules and their fragments by the Hartree-Fock and CISD + Q configuration interaction methods. The dynamic problem is solved by the variational method. Energy levels, transition frequencies, transition dipole moments, and expectation values of geometrical parameters of the molecules are calculated. It is shown that the lowest energy levels of LiReO₄ and K₂SO₄ molecules can be described within high accuracy in the harmonic approximation using a quasirigid, single-minimum model, whereas for the energy levels located near and above the barriers of intramolecular rearrangements, these approximations are completely unsuitable.

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