Rotational energy surface and quasiclassical analysis of the rotational energy level cluster formation in the ground vibrational state of PH3

Rotation–vibration energy cluster formation in XH2D and XHD2 molecules (X=Bi, P, and Sb)

“…[35], Petrov and Kozlovskii introduced a so-called 'quasiclassical' critical value J qc corresponding to the formation of the first classical trajectory around the local maximum on the RES. We do not repeat their analysis in terms of Bohr-Sommerfeld quantization here, but we estimate from the BiHD 2 energy level pattern in Fig.…”

“…XH 3 molecules exhibit sixfold energy clusters [20,22], different from the fourfold clusters found in H 2 X molecules [33]. In the H 2 X case, the energy level pattern is such that at a particular critical J-value J c , the fourfold energy cluster formation sets in [14,17,34], whereas for XH 3 molecules, the clusters form more gradually and no critical J-value can be defined [20,22,35].…”

“…For H 2 X and XH 3 localization axis approximately coincides with one of the equivalent X-H bonds in the molecule [17]. An analysis of the topology of the classical or semi-classical rotational energy surface (RES) [17,20,22,35,[37][38][39][40][41], in particular of the stationary points on the RES, determines these localization axes and predicts the critical angular momentum value J c for H 2 X molecules [14,17,34].…”

Trajectory analysis of the rotational dynamics of molecules

“…The rotational dynamics of the mol ecule will be described only by generalized Euler equa tions (5) with the Hamiltonian H r . It is easy to obtain the Hamiltonian in the explicit form [19,20]: (20) The rotation of the molecule described by the approx imate rotational Hamiltonian given by Eq. (20) can be called the rotation of a "soft body" taking into account that the equilibrium geometry of the molecule is deter mined by the rotation state: q e = q e (J).…”

“…It is easy to obtain the Hamiltonian in the explicit form [19,20]: (20) The rotation of the molecule described by the approx imate rotational Hamiltonian given by Eq. (20) can be called the rotation of a "soft body" taking into account that the equilibrium geometry of the molecule is deter mined by the rotation state: q e = q e (J). Stationary states, where = 0, are of particular interest among solutions describing the rotation of the soft body.…”