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 This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
30
March
2001
Revised:
22
June
2001
Published online: 15 October 2001
Abstract
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
