https://doi.org/10.1007/s100530170033
Rotational-vibrational relative equilibria and the structure of quantum energy spectrum of the tetrahedral molecule P4
1
Université du Littoral (UMR 8101 du CNRS) ,
B.P. 5526, 59379 Dunkerque Cedex, France
2
Laboratoire de Physique de l'Université de Bourgogne -CNRS,
B.P. 47870, 21078 Dijon Cedex, France
Corresponding author: a zhilin@univ-littoral.fr
Received:
30
March
2001
Revised:
22
June
2001
Published online: 15 October 2001
We find relative equilibria (RE) of the rotating and vibrating tetrahedral
molecule P4 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 P4 in the approximation
of nonresonant modes 
and 
and find the stationary
points of the resulting normal form (known as reduced effective
Hamiltonian 
) which is defined on the reduced phase space 
.
Most of these points are fixed points of the symmetry group action on
. To explain our results in more detail we introduce numerical
values of the parameters of H, such as the 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 
, 
and 
of P4.
PACS: 33.15.Mt – Rotation, vibration, and vibration-rotation constants / 33.20.Vq – Vibration-rotation analysis
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2001
