Rotational-vibrational relative equilibria and the structure of quantum energy spectrum of the tetrahedral molecule P 4
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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 ν E 2 and ν F_2 3 and find the stationary points of the resulting normal form (known as reduced effective Hamiltonian H eff ) which is defined on the reduced phase space CP 2 ×CP 1 ×S 2 . Most of these points are fixed points of the symmetry group action on CP 2 ×CP 1 ×S 2 . 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 ν 2 , ν 3 and ν 2 + ν 3 of P4.
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