ROTATIONAL-VIBRATIONAL RELATIVE EQUILIBRIA AND 
THE STRUCTURE OF QUANTUM ENERGY SPECTRUM OF THE TETRAHEDRAL MOLECULE P_4
 
Ch. Van Hecke, D. A. Sadovskií, and B. I. Zhilinskií

Université du Littoral, B.P. 5526, 59379 Dunkerque Cedex, France

V. Boudon

Laboratoire de Physique de l'Université de Bourgogne -- CNRS,
B.P. 47870, 21078 Dijon Cedex, France}

EPJ-D manuscript no D01073, received 30.03.01, final rev 06/22/01

     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
     quantum states in the vibration-rotation multiplet and to the extrema of
     the semi-quantum rotational energy surfaces obtained for a number of
     excited vibrational states.  To compute the energy of RE's we normalize
     the full rotation-vibration Hamiltonian H of P_4 in the approximation
     of nonresonant modes nu_2^E and nu_3^{F_2} and find stationary
     points of the resulting normal form (known as reduced effective
     Hamiltonian Heff) which is defined on the reduced phase space CP2xCP1xS2.
     Most of these points are fixed points of the symmetry group action on
     CP2xCP1xS2. To explain our results in more detail we introduce numerical
     values of parameters of H, such as cubic force constants, using an
     atom-atom harmonic potential with one adjustable parameter. This simple
     model gives correct qualitative description of the rotational structure of
     the lowest excited vibrational states nu_2, nu_3 and nu_2+nu_3
     of P_4.

PACS: 33.15.Mt Rotation, vibration, and vibration-rotation constants
      33.20.Vq Vibration-rotation analysis

Europ. Phys. J. D 17, 13-35 (2001)