Rotational-vibrational relative equilibria and the structure of quantum energy spectrum of the tetrahedral molecule P-4

We find relative equilibria (RE) of the rotating and vibrating tetrahedral Molecule P-4 and study the correspondence of these RE's to the extremal qua ntum states in the vibration-rotation multiplet and to the extrema of the s emi-quantum rotational energy surfaces obtained for a number of excited vib rational states. To compute the energy of RE's we normalize the full rotati on-vibration Hamiltonian H of P-4 in the approximation of nonresonant modes nu (E)(2) and nu (F2)(3) and find the stationary point of the resulting no rmal form (known as reduced effective Hamiltonian H-eff) which is defined o il the reduced phase space CP(2)xCP(1)xS(2). Most of these points are fixed points of the symmetry group action oil CP(2)xCP(1)xS(2). To explain our r esults in more detail we introduce numerical values of the parameters of H, such as the cubic force constants, using an atom-atom harmonic potential W ith One adjustable parameter. This simple model gives correct qualitative d escription of the rotational structure of the lowest excited vibrational st ates nu (2), nu (3) and nu (2) + nu (3) Of P-4.