Vibrational rotational state

The name dissociation energy is given to the work required to break up a diatomic molecule which is in its lowest rotation-vibrational state, and to leave the two particles (either atoms or ions) at rest in a vacuum. This quantity, which will be denoted by D , corresponds to the length of the arrow in Fig. 7 or Fig. 8a, where the length is the vertical distance between the lowest level of the molecule and the horizontal line which... 

The carboxylic acid dimers are quite heavy, with rotational constants typically around 1 GHz, and the microwave absorption experiments are conducted at high temperatures of 200-300 K. The resulting large number of rotation-vibration states populated, coupled with low dimer number densities, on the order of 5 x 1014 mole-cules/cm3, makes complete resolution of the rotational spectrum not feasible. However, virtually all dimers are prolate rotors with only moderate asymmetry. Thus, AJ = 1 transitions (a-type) with the same initial and final quantum numbers, but otherwise of different asymmetric rotor state or different vibrational state, will have the same frequency within about 50 MHz for moderate J values e.g. for J < 5 and for transition frequencies less than 50 GHz. At this level of resolution, isotope shifts are not discernible, and the resulting spectra (Fig. 1) yield one rotational constant, (B + C)/2, with an accuracy of about 0.5 %. 

Generally, constants and quantum numbers with single and double prime refer to the upper and the lower state, respectively. It is m = J -b 1 for the P-branch and m = -J for the P-branch. Wavenumber combinations of pairs of lines with common upper or lower rotation-vibration state can give the corresponding rotational constants of the ground or excited vibrational state ... 

Line intensities are also governed by symmetry properties of the rotation-vibration states, which may show degeneracies arising from different orientations of existing nuclear spins. For each nucleus with spin quantum number /, there are 21+1 possible orientations of the spin with M/ = l,...,+I, as discussed before in connection with the rotational quantum number Mj. Two examples will demonstrate the effects that have to be taken into account. 

In the case of the reverse CT calculations, a different picture was obtained. There are many accessible rotational states of the HF molecule which can be populated at the nominal experimental energies. Therefore, the reverse CT studies had to be done for a variety of rotational states. It was found that all rotational states for HF In the v=3 state yielded backwards scattering, but several of the most probable rotational states for HF with v=2 yielded sideways scattering. It was felt by RPB that these results point up a technical problem with the forward CT calculations having to do with boxing of the HF rotational-vibrational states. In the reverse CT... 

In this connection an extended Hamiltonian has been developed that includes an additional vibrational degree of freedom. This extended model was tested with three molecules. It was possible to fit the splittings in the rotational spectra of the lowest three internal rotation/vibration states with one set of coefficients. There is an indication that for higher states an even more extended Hamiltonian is necessary. 

Data are for the v = 0,J =1 rotational-vibrational state unless otherwise stated. Spin-rotation constant. 

When an electronic transition of a thermally equilibrated molecule is excited by a short pulse of electromagnetic radiation at t = 0, amplitude is removed from rotational-vibrational states of the electronic ground state, g, and amplitude is created in rotational-vibrational states of an electronically excited state, e. At t < 0, the molecular density matrix is entirely diagonal and time-independent,... 

As we demonstrated above, CVPT can be used to compute properties of rotation-vibration states of H2CO. To calculate the rotation-vibration spectrum, we must also be able to calculate the intensity of the transition between the energy eigenstate vT M J ) and vfM7). Here the eigenstates are defined in terms of their total angular momentum... 

J, the projection of the angular momentum onto the space-fixed Z-axis M and the point group symmetry I The label v serves to enumerate the rotation-vibration states whose T, M, and J labels are the same. The contribution to the intensity, due to the F component of the space-fixed dipole moment operator p, is obtained by evaluating (85)... 

Nuclear spin weightings are given by gv. For H2CO states that are symmetric with respect to a rotation by -tt about the symmetry axis, gv = 0.25 for the antisymmetric states gv = 0.75. Here we will be considering the 10 K spectrum for H2CO, where only the ground vibrational state is populated. For this vibrational state, the symmetric and antisymmetric rotation-vibration states are those for which K is even and odd, respectively (91). The effective dipole moment operator p,/.ff is obtained from p,/. via the transformation of Eq. (34). To transform pA, we first reexpress it in terms of the body-fixed dipole moment operators pa, described above, by... 

Most resonant photoacoustic experiments performed up to now used an infrared laser to excite a rotational-vibrational state of the absorbing molecule. Energy exchange processes between vibrational levels (V—V vibration to vibration transfer) and from vibrational states to rotational and translational degrees of freedom (V—R,T transfer) have been extensively studied by several methods. Most data on V—R,T transfer in polyatomic molamles has been obtained by acoustic methods such as ultrasonic dispersion and absorption The information on V—V exchange comes... 

A. Geers, J. Kappert, F. Temps, J.W. Wiebrecht, Preparation of single rotation-vibration states of CH30(C( E)) above the H-CH2O dissociation threshold by stimulated emission pumping. Ben Bunsenges. Phys. Chem. 94, 1219 (1990)... 

The use of the master equation to describe the relaxation of internal energy in molecules is, in fact, nothing more than the writing of a set of kinetic rate equations, one equation for each individual rotation-vibration state of the molecule. The simplest case we can consider is that of an assembly of diatomic molecules highly diluted in a monatomic gas under these conditions, we only need to consider the set of processes... 

For a few molecules which span our general range of interest, e.g. CO2, CHjNC, cyclo-C4H8, C2F6, the densities of (rotation-vibration) states at the thermal thresholds are approximately 10 , 10 , 10 , 10 states per wavenumber respectively. 

Mussa, H.Y. and Tennyson, J., Bound and quasi-bound rotation-vibrational states using massively parallel computers, Comput. Phys. Commun., 128, 434-445, 2000. 

The PR model considers, as a zero approximation, a motion of a diatom perturbed by the interaction with an atom placed at a fixed distance R from the center of mass of a diatom. For a particular case of a planar collision, this motion corresponds either to vibration or to hindered rotation of the diatom. Adiabatically-perturbed rotational-vibrational states of a collision complex are coupled by the relative radial motion. This coupling induces transition between different adiabatic channel states the nature of these transitions is such that near-resonant channels are strongly favored [31-33]. The latter dynamical property allows one to regard the R-mode as a spectator mode and to consider the energy transfer as a pure VR event. 

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