Collision-induced transitions

Infrared Spectroscopy. The infrared spectroscopy of adsorbates has been studied for many years, especially for chemisorbed species (see Section XVIII-2C). In the case of physisorption, where the molecule remains intact, one is interested in how the molecular symmetry is altered on adsorption. Perhaps the conceptually simplest case is that of H2 on NaCl(lOO). Being homo-polar, Ha by itself has no allowed vibrational absorption (except for some weak collision-induced transitions) but when adsorbed, the reduced symmetry allows a vibrational spectrum to be observed. Fig. XVII-16 shows the infrared spectrum at 30 K for various degrees of monolayer coverage [96] (the adsorption is Langmuirian with half-coverage at about 10 atm). The bands labeled sf are for transitions of H2 on a smooth face and are from the 7 = 0 and J = 1 rotational states Q /fR) is assigned as a combination band. The bands labeled... 

Because non-adiabatic collisions induce transitions between rotational levels, these levels do not participate in the relaxation process independently as in (1.11), but are correlated with each other. The degree of correlation is determined by the kernel of Eq. (1.3). A one-parameter model for such a kernel adopted in Eq. (1.6) meets the requirement formulated in (1.2). Mathematically it is suitable to solve integral equation (1.2) in a general way. The form of the kernel in Eq. (1.6) was first proposed by Keilson and Storer to describe the relaxation of the translational velocity [10]. Later it was employed in a number of other problems [24, 25], including the one under discussion [26, 27]. 

Fig. 4.1. The La line of the H atom and its structure in the constant electric field (a) and the rotational structure of the vibrational transition (b). Wavy arrows show collision-induced transitions, thick horizontal arrows indicate the optical transitions that mutually interfere.

Finally, we would like to point out that in the off-resonance region, the response time of the nonlinearity is limited only by the optical pulse width r, as long as (Ea -Tiaj)/h >>2ir(x ). (8) This is no longer true when collisions (or phonons in solids) are present. For optical frequencies close enough to the absorption edge, the collision induced transitions to the excited state will cause the x s response time to be limited by the relaxation time of the excited states. (8)... 

The deviation from first-order kinetics for the uridylic acids is also reflected in quantum yields which vary with concentration and which therefore vary during the course of a particular photolysis.7 These deviations from first-order kinetics have been discussed in terms of a collision-induced transition of an excited-singlet pyrimidine to a long-lived state.7 We shall say more about the probability of long-lived states later. 

Welsh suggested correctly that similar transitions take place even if the molecular pair is not bound. The energy of relative motion of the pair is a continuum. Its width is of the order of the thermal energy, Efree 3kT/2. Radiative transitions between free states occur (marked free-free in the figure) which are quite diffuse, reflecting the short lifetime of the supermolecule. In dense gases, such diffuse collision-induced transitions are often found at the various rotovibrational transition frequencies, or at sums or differences of these, even if these are dipole forbidden in the individual molecules. The dipole that interacts with the radiation field arises primarily by polarization of the collisional partner in the quadrupole field of one molecule the free-free and bound-bound transitions originate from the same basic induction mechanism. 

H. Harima. Some aspects of collision-induced transitions in spectral line shape experiments. In L. Frommhold and J. W. Keto, eds., Spectral Line Shapes 6, Am. Inst. Phys., N.Y., p. 269, 1990. 

The discrepancy may arise partly from the yet uncertain cis- to trn/i.v-1,2-dimethylcyclopropane ratio resulting from the triplet methylene addition to 2-butene and from the collision induced transition of methylene from singlet to triplet that may occur to a different degree depending on substrate molecules. 

A liquid chromatography/tandem mass spectrometry (LC/MS/MS) method was developed [33] and validated for the determination of donepezil in human plasma samples. Diphenhydramine was used as the IS. The collision-induced transition m/z 380 > 91 was used to analyze donepezil in selected reaction monitoring mode. The signal intensity of the m/z 380 —> 91 transition was found to relate linearly with donepezil concentrations in plasma from 0.1 to 20.0 ng/ml. The lower limit of quantification of the LC/MS/MS method was 0.1 ng/ml. The intra- and inter-day precisions were below 10.2% and the accuracy was between 2.3% and +2.8%. The validated LC/MS/MS method was applied to a pharmacokinetic study in which healthy Chinese volunteers each received a single oral dose of 5 mg donepezil hydrochloride. The non-compartmental pharmacokinetic model was used to fit the donepezil plasma concentration-time curve. Maximum plasma concentration was... 

Lebed , I.V., Nikitin, E.E. and Umansky, S.Ya. (1977). Collision-induced transitions between the rotational levels of diatomic molecules in II state, Optika i Spektroskopiya, 43, 636-644. [Opt. Spectrosc. (USSR),... 

Ottinger, Ch. and Schroder, M. (1979). Rate constants for collision-induced transitions in ground-state Li2 from two-laser spectroscopy, J. Phys. B At. Mol. Phys., 12, 3533-3551. 

Sudbp, Aa.S. and Loy, M.M.T. (1982). Measurements of absolute state-to-state rate constants for collision-induced transitions between spin-orbit and rotational states of NO (X2H,v = 2), J. Chem. Phys., 76, 3646-3654. 

Fig. 17. Energy levels of the rotation-inversion spectrum of ammonia. The quantum numbers (J,K) are given for each level. The heavy arrows indicate the inversion transitions detected in interstellar space and their frequencies in MHz. Thin arrows indicate the rotation-inversion transitions located in the submillimeter wave region. Dashed arrows indicate some collision induced transitions...

The relative intensities of the CN bands depend strongly on the nature of the species added to active nitrogen [145, 146], With halogenated hydrocarbons, red emission from the A 2II state predominates this was classified by Bayes [146] as the P2 emission. The v distribution is broad, peaking at v = 7, and the red system is accompanied by bands from B 2S+ v = 0) that is populated via A 2II (y = 10) because of perturbations and collision-induced transitions. The Pa emission from mixtures of active nitrogen with halogen-containing compounds is quite different, and the relative band intensities in the red system show that v = 0 is now the most populated level. 

It is suggested that the two electronic states fa and l °f noninteracting partners provide a good basis set to be used for constructing orthonormal adiabatic electronic functions fa and fa. At R — oo the functions fa and fa adiabatically correlate with fa and fa, so that the nonadiabatic transition probability calculated for a particular trajectory R(f) refers to the collision-induced transition between the two states of the partners. 

The observation in propynal of both internal conversion and intersystem crossing on the same time scale, together with collision-induced transitions on both pathways, make this... 

The interaction with the perturber leads to a mixing of the wavefunctions which makes the transition slightly allowed. Under these conditions the interpretation of experimental results is a little more complicated, but information on the value of the oscillator strength of the collision induced transition can be obtained and compared with the predictions of Pascale (6) and Czuchaj (7 ). 

The above discussion represents a satisfactory qualitative description of the effects of vibrational relaxation upon radiative decay rates. When s is a excited vibronic state, it can contribute directly to the vibrational relaxation. It may also be necessary in some cases to consider direct collision induced crossings. The collision induced transitions between the various components of s itself are, of course, of great interst. 

Experimental [23, 24] probabilities for the many possible collision-induced transitions in this molecule show no apparent dependence on energy gap between initial and final state. However, the probabilities fall exponentially with the magnitude of the AM gap measured as shown in Fig. 3. This static model (Fig. 3) of an asymmetric top 7ka kc AM vector is not wholly representative since the vector s natural precession creates an AM trajectory. Coupling of this vector to an external AM introduced on collision can cause the vector to hop to an adjacent trajectory of different y ka kc on the molecule s AM surface. When this dynamical picture is considered, the conclusions above remain valid [24, 25]. The energy gap generally becomes more dominant as initial j state increases [25], an effect also found in... 

Fig. 4 Plot of sin 9, where 9 is the most probable scattering angle, versus v-th/vI where vr is the most probable relative velocity and the (calculated) threshold relative velocity for the particular state-to-state collision-induced transition...

The use of classical mechanics to solve practical problems often involves development of an appropriate expression that combines simultaneous energy and AM conservation. This can be done for a limited number of cases of collision-induced transitions in molecular quantum states but rapidly becomes very complex when, for example, VRT or takes place. Furthermore, such equations often lack the transparency of the individual expressions for energy and AM conservation and key insights are lost. This is readily illustrated since the equations for AE and for Aj (in the limiting case l = Aj so that A/ /< v / /" ix) may both be plotted as velocity or... 

Perturbations affect the rate of absorption and emission of radiation in a fully understood and exactly calculable manner. They also affect the rates of chemical and collisional population/depopulation processes, but in a less easily estimated way. Perturbation effects on steady-state populations can be very large and level-specific. Although collision-induced transitions and chemical reactions are not governed by rigorous selection rules as are electric dipole transitions and perturbation interactions, some useful propensity rules have been suggested theoretically and confirmed experimentally. Gelbart and Freed (1973) suggested that the cross sections for collision-induced transitions between two different electronic states, E and E, are... 

Early optically detected microwave transition linewidth studies (Pratt and Broida, 1969) suggested that CN A2II(u = 10) —> B2E+(u = 0) collision-induced transitions through perturbed levels occur at gas-kinetic collision rates, faster than pure rotational relaxation. The pressure dependence of chemiluminescence in the Ba + N2O system also implied BaO b3II(u = 10) —> A1E+(u = 1) collisional transfer through spectroscopic doorways (Field, et al., 1974). 

Dentamaro and Katayama (1989) have also employed the OODR method to study A2II(u = 0) — X2E+(v = 10) transitions in the isoelectronic CO+ ion induced by collisions with He. In contrast to the He collision-induced transitions in Ng and CN, these transitions are much less efficient because of a poor Franck-Condon factor. Significant collisional transitions are observed only for perturbed F f initial levels. 

The propensity rules for collision-induced transitions between electronic states and among the fine-structure components of non-1E+ states depend on the identity of the leading term in the multipole expansion of the molecule/collision-partner interaction potential. Alexander (1982a) has considered the dipole-dipole term, which included both permanent and transition dipole contributions. In the limit that first-order perturbation theory applies (not the usual circumstance for thermal molecular collisions), the following collisional propensity rules for the permanent dipole term can be enumerated from the selection rules for both perturbations and pure rotational transitions... 

Propensity rules for collision-induced transitions with non-1E+ states have been discussed by Gottscho (1981), Nedelec and Dufayard (1984), Alexander... 

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