Excitation, vibrational

Excitation of a molecule to a higher vibrational state often can be described reasonably well as an elevation of an individual normal mode from quantum number to a higher number, /m,. If the frequencies of the normal modes do not change significantly when the molecule is excited, the excitation energy is (w, — n,) hvi where , is the vibration frequency of the mode. 

To investigate the selection mles and dipole strengths for vibrational excitations, we have to evaluate how the radiation field perturbs the vibrational energy and how this perturbation depends on the normal coordinate. Consider first a diatomic molecule so that we have only a single vibrational coordinate (x). The perturbation term in the Hamiltonian takes the form  

The leading term in Eq. (6.9), li 0) Xm Xt is zero for because of the orthogonality of the eigenfunctions. The term (dnldx)o xm x x, thus dominates the series, provided that (3/i/3x)o 0. Examination of the eigenfunctions of a harmonic oscillator shows that the integral Xm x Xn) in this term is non-zero only if m = n 1 (Box 6.2). The formal selection mles for excitation of a harmonic vibration are, therefore  

The magnitude of the integral xJx Xr) in Eq. (6.9) can be evaluated for harmonic oscillators by using the recursion expression for Hermite polynomials  

2K 8n n+i pertains to absorption (vibrational excitation), whereas ( /2jc) m,n-i pertains to emission. Equation (B6.2.2) is identical to the expression we developed for emission and absorption of photons (Eq. 5.45). But note that here quantum numbers m and n refer to the excitation level of the molecular vibration, that is, the number of phonons in the mode, not to the density of photons in the incident radiation. 

The paper is organized as follows we first discuss vibrational excitation through various mechanisms, including ionization, / -dependent depletion, and bond-softening. We then present evidence for electronic excitation and consider multiphoton excitation, inner orbital ionization, and excitation through recollisions. Several applications of these interactions are presented, followed by our conclusions. 

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Electrons interact with solid surfaces by elastic and inelastic scattering, and these interactions are employed in electron spectroscopy. For example, electrons that elastically scatter will diffract from a single-crystal lattice. The diffraction pattern can be used as a means of stnictural detenuination, as in FEED. Electrons scatter inelastically by inducing electronic and vibrational excitations in the surface region. These losses fonu the basis of electron energy loss spectroscopy (EELS). An incident electron can also knock out an iimer-shell, or core, electron from an atom in the solid that will, in turn, initiate an Auger process. Electrons can also be used to induce stimulated desorption, as described in section Al.7.5.6. 

Shen T-C, Wang C, Abein G C, Tucker J R, Lyding J W, Avouris P and Walkup R E 1995 Atomic-scale desorption through electronic and vibrational excitation mechanisms Science 268 1590... 

Unstable species such as O, FI and N atoms, molecular radicals and vibrationally excited diatomics can be injected by passmg the appropriate gas tluough a microwave discharge. In a SIFT, the chemistry is usually straightforward since there is only one reactant ion and one neutral present in the flow tube. 

The first mfonnation on the HE vibrational distribution was obtained in two landmark studies by Pimentel [39] and Polanyi [24] in 1969 both studies showed extensive vibrational excitation of the HE product. Pimental found that tire F + H2 reaction could pump an infrared chemical laser, i.e. the vibrational distribution was inverted, with the HF(u = 2) population higher than that for the HF(u = 1) level. A more complete picture was obtained by Polanyi by measuring and spectrally analysing tlie spontaneous emission from vibrationally excited HE produced by the reaction. This infrared chemiluminescence experiment yielded relative populations of 0.29, 1 and 0.47 for the HF(u =1,2 and 3)... 

An important further consequence of curvature of the interaction region and a late barrier is tliat molecules that fail to dissociate can return to the gas-phase in vibrational states different from the initial, as has been observed experunentally in the H2/CU system [53, ]. To undergo vibrational (de-)excitation, the molecules must round the elbow part way, but fail to go over the barrier, eitlier because it is too high, or because the combination of vibrational and translational motions is such that the molecule moves across rather than over the barrier. Such vibrational excitation and de-excitation constrains the PES in that we require the elbow to have high curvature. Dissociation is not necessary, however, for as we have pointed out, vibrational excitation is observed in the scattering of NO from Ag(l 11) [55]. 

The site specificity of reaction can also be a state-dependent site specificity, that is, molecules incident in different quantum states react more readily at different sites. This has recently been demonstrated by Kroes and co-workers for the Fl2/Cu(100) system [66]. Additionally, we can find reactivity dominated by certain sites, while inelastic collisions leading to changes in the rotational or vibrational states of the scattering molecules occur primarily at other sites. This spatial separation of the active site according to the change of state occurring (dissociation, vibrational excitation etc) is a very surface specific phenomenon. 

To detect tlie initial apparent non-RRKM decay, one has to monitor the reaction at short times. This can be perfomied by studying the unimolecular decomposition at high pressures, where collisional stabilization competes with the rate of IVR. The first successful detection of apparent non-RRKM behaviour was accomplished by Rabinovitch and co-workers [115], who used chemical activation to prepare vibrationally excited hexafluorobicyclopropyl-d2 ... 

Stock C, Li X, Keller H-M, Schinke R and Temps F 1997 Unimolecular dissociation dynamics of highly vibrationally excited DCO x-A t- I- Investigation of dissociative resonance states by stimulated emission pumping spectroscopy J. Cham. Phys. 106 5333-58... 

Faubel M and Toennies J P 1977 Scattering studies of rotational and vibrational excitation of molecules Adv. Atom. Mol. Phys. 13 229... 

Miller L A and Barker J R 1996 Collisional deactivation of highly vibrationally excited pyrazine J. Chem. Phys. 105 1383-91... 

Pibel C D, Sirota E, Brenner J and Dai H L 1998 Nanosecond time-resolved FTIR emission spectroscopy monitoring the energy distribution of highly vibrationally excited molecules during collisional deactivation J. Chem. Phys. 108 1297-300... 

Okamoto H, Nakabayashi T and Tasumi M 1997 Analysis of anti-Stokes RRS excitation profiles as a method for studying vibrationally excited molecules J. Phys. Chem. 101 3488-93... 

Keil and co-workers (Dhamiasena et al [16]) have combined the crossed-beam teclmique with a state-selective detection teclmique to measure the angular distribution of HF products, in specific vibration-rotation states, from the F + Fl2 reaction. Individual states are detected by vibrational excitation with an infrared laser and detection of the deposited energy with a bolometer [30]. 

Vaccaro P H 1995 Resonant four-wave mixing spectroscopy a new probe for vibrationally-excited species Molecular Dynamics and Spectroscopy by Stimulated Emission Pumping (Advances in Chemistry Series) vol 7, ed H-L Dai and R W Field (Singapore World Scientific) p 1... 

In contrast to the ionization of C q after vibrational excitation, typical multiphoton ionization proceeds via the excitation of higher electronic levels. In principle, multiphoton ionization can either be used to generate ions and to study their reactions, or as a sensitive detection technique for atoms, molecules, and radicals in reaction kinetics. The second application is more common. In most cases of excitation with visible or UV laser radiation, a few photons are enough to reach or exceed the ionization limit. A particularly important teclmique is resonantly enlianced multiphoton ionization (REMPI), which exploits the resonance of monocluomatic laser radiation with one or several intennediate levels (in one-photon or in multiphoton processes). The mechanisms are distinguished according to the number of photons leading to the resonant intennediate levels and to tire final level, as illustrated in figure B2.5.16. Several lasers of different frequencies may be combined. 

The chemical-activation step is between one and two orders of magnitude faster than the subsequent collisional deactivation of vibrationally excited O2. Finally, the population of individual vibrational levels v" of O2 is probed tluough LIF in the Schiunann-Runge band Oi X E") after exciting the oxygen... 

Related results of promotion (catalysis) and inliibition of stereonuitation by vibrational excitation have also been obtained for the much larger molecule, aniline-NHD (CgH NHD), which shows short-time chirality and stereonuitation [104. 105]. This kind of study opens the way to a new look at kinetics, which shows coherent and mode-selective dynamics, even in the absence of coherent external fields. The possibility of enforcing coherent dynamics by fields ( coherent control ) is discussed in chapter A3.13. 

McCoy A B and Siebert E L 1996 Canonical Van VIeck pertubation theory and its applications to studies of highly vibrationally excited states of polyatomic molecules Dynemics of Moiecuies end Chemicei Reections ed R E Wyatt and J Z H Zhang (New York Dekker) p 151... 

An important area that has yet to be fully explored is the effect of the flexibility of water molecules. The intennolecular forces in water are large enough to cause significant distortions from the gas-phase monomer geometry. In addition, the flexibility is cmcial in any description of vibrational excitation in water. 

The vibrationally excited states of H2-OH have enough energy to decay either to H2 and OH or to cross the barrier to reaction. Time-dependent experiments have been carried out to monitor the non-reactive decay (to H2 + OH), which occurs on a timescale of microseconds for H2-OH but nanoseconds for D2-OH [52, 58]. Analogous experiments have also been carried out for complexes in which the H2 vibration is excited [59]. The reactive decay products have not yet been detected, but it is probably only a matter of time. Even if it proves impossible for H2-OH, there are plenty of other pre-reactive complexes that can be produced. There is little doubt that the spectroscopy of such species will be a rich source of infonnation on reactive potential energy surfaces in the fairly near future. 

Hossenlopp J M, Anderson D T, Todd M W and Lester M I 1998 State-to-state inelastic scattering from vibrationally excited OH-Hj complexes J. Chem. Phys. 109 10 707-18... 

Actually, collisions in which tlie batli becomes vibrationally excited are relatively rare, occurring witli a typical probability of 1% per gas-kinetic collision [6, 8, H and 13]. More common are processes tliat produce rotational and translational excitation in tlie batli acceptor while leaving tlie molecule in its ground (vibrationless) OO O state. 

C3.3.4 DEDUCING ENERGY TRANSFER MECHANISMS FROM POPULATION AND VELOCITY DISTRIBUTIONS OF THE SCATTERED BATH MOLECULES ROTATIONAL STATE POPULATION DISTRIBUTIONS FOR VIBRATIONAL EXCITATION OF THE BATH... 

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