Perturbed rotational state

Quantum effects become important only at veiy low temperatures, i.e. for BIkT 1. The best candidates for observing these effects thus are hydrides. Quantum effects become more pronounced when A and/or B are species with open electronic shells see e.g. the differences between the associations N2 + N2 —> N4 and Q2 + Q2 —> 4 at temperatures below 10 K [10], Before leaving this section, it should be mentioned that alternative approaches such as the ACCS A treatment Irom [18], the perturbed rotational state treatment finm [19] and the semiclassical adiabatic invariance method Irom [20] all represent simplified variants of the here described SACM/CT approach and, like the... 

A large number of approximate theories have been proposed for ion-dipole reactions. Some of these include the average dipole orientation (ADO) approximation and its extension to include conservation of angular momentum (the AADO method ), various transition-state theories involving variational and statistical modifications, the semiclassi-cal perturbed rotational state (PRS) approximation, classical trajectory studies, the adiabatic invariance method, and the statistical adiabatic channel model (SACM). 

It can be seen that the agreement between all three methods is excellent. Furthermore, the adiabatic invariance method of Bates and Morgan [15] also gives good agreement with these theories for this temperature range as does the perturbed rotational state approximation [13]. Our quantum-mechanical results thus verify the trajectory formula of equation (6) and we recommend that it be used in interstellar simulations for reactions that go at the capture rate. However, to be sure that a reaction does go at the capture rate it is important to have experimental data, at least at room temperature. 

Sakimoto K. (1982) Perturbed rotational state method for collisions between an ion and an asymmetric-top rigid rotor. Chem. Phys. 68 155-170. 

Adiabatic energy transfer occurs when relative collision velocities are small. In this case the relative motion may be considered a perturbation on adiabatic states defined at each intermolecular position. Perturbed rotational states have been introduced for T-R transfer at low collision energies and for systems of interest in astrophysics.A rotational-orbital adiabatic basis expansion has also been employed in T-R transfer,as a way of decreasing the size of the bases required in close-coupling calculations. In T-V transfer, adiabatic-diabatic transformations, similar to the one in electronic structure studies, have been implemented for collinear models.Two contributions on T-(R,V) transfer have developed an adiabatical semiclassical perturbation theory and an adiabatic exponential distorted-wave approximation. Finally, an adiabati-cally corrected sudden approximation has been applied to RA-T-Rg transfer in diatom-diatom collisions. 

K. Takayanagi, Low energy ion-polar molecule collisions The perturbed rotational state approach, J. Phys. Soc. Japan 45 ... 

The Time Dependent Processes Seetion uses time-dependent perturbation theory, eombined with the elassieal eleetrie and magnetie fields that arise due to the interaetion of photons with the nuelei and eleetrons of a moleeule, to derive expressions for the rates of transitions among atomie or moleeular eleetronie, vibrational, and rotational states indueed by photon absorption or emission. Sourees of line broadening and time eorrelation funetion treatments of absorption lineshapes are briefly introdueed. Finally, transitions indueed by eollisions rather than by eleetromagnetie fields are briefly treated to provide an introduetion to the subjeet of theoretieal ehemieal dynamies. 

These so-called interaction perturbations Hint are what induces transitions among the various electronic/vibrational/rotational states of a molecule. The one-electron additive nature of Hint plays an important role in determining the kind of transitions that Hint can induce. For example, it causes the most intense electronic transitions to involve excitation of a single electron from one orbital to another (recall the Slater-Condon rules). 

The tools of time-dependent perturbation theory can be applied to transitions among electronic, vibrational, and rotational states of molecules. 

The value o+l <0.4 found for H2 shows that even in the lowest state the molecules are rotating freely, the intermolecular forces producing only small perturbations from uniform rotation. Indeed, the estimated (3vq<135° corresponds to Fo <28 k, which is small compared with the energy difference 164 k of the rotational states j = 0 and j= 1, giving the frequency with which the molecule in either state reverses its orientation. The perturbation treatment shows that with this value of Fo the eigenfunctions and energy levels in all states closely approximate those for the free spatial rotator.9... 

Utilization of both ion and neutral beams for such studies has been reported. Toennies [150] has performed measurements on the inelastic collision cross section for transitions between specified rotational states using a molecular beam apparatus. T1F molecules in the state (J, M) were separated out of a beam traversing an electrostatic four-pole field by virtue of the second-order Stark effect, and were directed into a noble-gas-filled scattering chamber. Molecules which were scattered by less than were then collected in a second four-pole field, and were analyzed for their final rotational state. The beam originated in an effusive oven source and was chopped to obtain a velocity resolution Avjv of about 7 %. The velocity change due to the inelastic encounters was about 0.3 %. Transition probabilities were calculated using time-dependent perturbation theory and the straight-line trajectory approximation. The interaction potential was taken to be purely attractive ... 

In this analysis and in that of the next section, the vibrational motion effects presume a field source that is rotating with the molecule, such as when the electrical perturbation is due to a weakly complexed partner molecule. A freely rotating molecule in a laboratory-fixed field source, however, is different, and then evaluations of electrical properties should account for rotational state dependence as well [114, 115]. 

Fig. 6.13 The energies of the rotational states of dihydrogen as a perturbed planar rotor in a deep attractive field, the 2-DP type. The dashed vertical line shows the transitions expected for [W(CO)3(H2) P(cyclohexyI)3 2] with a tunnel splitting of 0.89 cm (inset).

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