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)