Description of vibration-rotation energies of nonrigid triatomic molecules using the generating function method

High-Lying Rotational Levels of Water: An Analysis of the Energy Levels of the Five First Vibrational States

“…Hamiltonian leads to the eigenfunctions and eigenvalues X v (r 1 , r 2 ; t) and v (t), [3] which both depend parametrically on the coordinate t and which are identified by the quantum number v. Since in this paper the vibrational states up to the first triad are dealt with, we need only concern ourselves with three stretching-type states, which will be characterized by a v-value equal to 0, 1, or 2. The first of these states is the ground state; the second and third correspond respectively to one quantum of vibration in the symmetrical ν 1 mode and one in the antisymmetrical ν 3 mode.…”

“…Figure 2 shows the expected behavior of the three eigenvalues given in Eqs. [3] as functions of the Radau coordinate θ. These curves were obtained using the molecular parameters obtained by Partidge and Schwenke (35), available on the Web (36), and solving Eq.…”

“…[3]; |J, k is the usual symmetric-top rotational wavefunction; and G v 2 v (t) is the bending wavefunction. In order to determine the equation satisfied by this wavefunction, we make the same approximation as for Eq.…”

“…The investigation of the rovibrational energy of water is both theoretically and experimentally challenging since, due to the lightness of the hydrogen atoms and the shortness of the OH bonds, water is among the nonlinear triatomic molecules displaying the largest rotational constants. For that reason, when a theoretical energy level calculation is performed, a large vibration-rotation interaction must be accounted for and leads to an arduous rovibrational energy level calculation in which the nonrigidity of the molecule must be dealt with (3). For the same reason, the large rotational spacing makes it very difficult to carry out a thorough experimental investigation of the rotational energy, as only a small number of rotational levels are populated at room temperature.…”

Fourier transform measurements of water vapor line parameters in the 4200–6600cm−1 region

“…For the set of levels of the (1 1 0) and (0 1 1) states common to previous determinations, our values are generally very close to those reported by Toth [22], except for 4 levels of the (0 1 1) 3 8 , and 14 1 14 ) and two levels of the (1 1 0) state (6 6 1 and 6 6 0 ) where a difference amounting up to 1.27 cm À1 was observed for 8 8 The new set of experimental energies of the (0 3 0), (1 1 0), and (0 1 1) states was fitted using a rovibrational Hamiltonian for a triad of interacting states [54]. Similarly to recent works on the second triads of others water isotopic species [19,51] we used the generating function model (G-function) [55,56] for an effective Hamiltonian that takes into account resonance interactions of both anharmonic and Coriolis type. The results of the fit of the energy levels for all three states are shown in Table 6.…”