Distributions vibrational

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)... 

This function decreases monotonically with increasing vibrational quantum number n, and hence an inverted vibrational distribution can never be described with a temperature (except for degenerate vibrations). A P n) distribution that is thermal , or at least not inverted, is indicative of a well on the PES that is connected with little or no barrier to the product asymptote. 

In order to see the effect of the rotational excitation of the parent H2O molecules on the OH vibrational state distribution, the experimental TOF spectrum of the H atom from photodissociation of a room temperature vapor H2O sample has also been measured with longer flight distance y 78 cm). By integrating each individual peak in the translational energy spectrum, the OH product vibrational distribution from H2O photodissociation at room temperature can be obtained. 

The overall OD vibrational distribution from the HOD photodissociation resembles that from the D2O photodissociation. Similarly, the OH vibrational distribution from the HOD photodissociation is similar to that from the H2O photodissociation. There are, however, notable differences for the OD products from HOD and D2O, similarly for the OH products from HOD and H2O. It is also clear that rotational temperatures are all quite cold for all OH (OD) products. From the above experimental results, the branching ratio of the H and D product channels from the HOD photodissociation can be estimated, since the mixed sample of H2O and D2O with 1 1 ratio can quickly reach equilibrium with the exact ratios of H2O, HOD and D2O known to be 1 2 1. Because the absorption spectrum of H2O at 157nm is a broadband transition, we can reasonably assume that the absorption cross-sections are the same for the three water isotopomer molecules. It is also quite obvious that the quantum yield of these molecules at 157 nm excitation should be unity since the A1B surface is purely repulsive and is not coupled to any other electronic surfaces. From the above measurement of the H-atom products from the mixed sample, the ratio of the H-atom products from HOD and H2O is determined to be 1.27. If we assume the quantum yield for H2O at 157 is unity, the quantum yield for the H production should be 0.64 (i.e. 1.27 divided by 2) since the HOD concentration is twice that of H2O in the mixed sample. Similarly, from the above measurement of the D-atom product from the mixed sample, we can actually determine the ratio of the D-atom products from HOD and D2O to be 0.52. Using the same assumption that the quantum yield of the D2O photodissociation at 157 nm is unity, the quantum yield of the D-atom production from the HOD photodissociation at 157 nm is determined to be 0.26. Therefore the total quantum yield for the H and D products from HOD is 0.64 + 0.26 = 0.90. This is a little bit smaller ( 10%) than 1 since the total quantum yield of the H and D productions from the HOD photodissociation should be unity because no other dissociation channel is present for the HOD photodissociation other than the H and D atom elimination processes. There are a couple of sources of error, however, in this estimation (a) the assumption that the absorption cross-sections of all three water isotopomers at 157 nm are exactly the same, and (b) the accuracy of the volume mixture in the... 

Rotational state distributions of the OH(A) product for v = 0 to 3 have also been determined. Highly rotationally excited OH(A,v = 0,1) products are dominant as in the ground state, indicating that the angular anisotropy of the potential is also very important to the production of these product states on the H2O B lA state surface. The vibrational distribution... 

From the point of view of associative desorption, this reaction is an early barrier reaction. That is, the transition state resembles the reactants.46 Early barrier reactions are well known to channel large amounts of the reaction exoergicity into product vibration. For example, the famous chemical-laser reaction, F + H2 — HF(u) + H, is such a reaction producing a highly inverted HF vibrational distribution.47-50 Luntz and co-workers carried out classical trajectory calculation on the Born-Oppenheimer potential energy surface of Fig. 3(c) and found indeed that the properties of this early barrier reaction do include an inverted N2 vibrational distribution that peaks near v = 6 and extends to v = 11 (see Fig. 3(a)). In marked contrast to these theoretical predictions, the experimentally observed N2 vibrational distribution shown in Fig. 3(d) is skewed towards low values of v. The authors of Ref. 44 also employed the electronic friction theory of Tully and Head-Gordon35 in an attempt to model electronically nonadiabatic influences to the reaction. The results of these calculations are shown in... 

Fig. 8. Scattering the transition state from the surface. Measured vibrational distribution of NO resulting from scattering of laser-prepared NO(v = 15) from Au (111) at incidence = 5 kJ mol-1. Only a small fraction of the laser-prepared population of v = 15 remains in the initial vibrational state. The most probable scattered vibrational level is more than 150 kJ mol-1 lower in energy than the initial state. Vibrational states below v = 5 could not be detected due to background problems. These experiments provide direct evidence that the remarkable coupling of vibrational motion to metallic electrons postulated by Luntz et al. can in fact occur. (See Refs. 44 and 59.)...

In this system there is only one exothermic set of products and the problem consists of determining the vibrational distribution of the CO product in both its ground and first excited electronic states. The results can be compared with the experimental determination of Adams, Babcock, et al.,80 as well as the approximate treatment of Bates.79 Assuming some success in this endeavor, we propose to study reaction 33 to determine the HNC/HCN product ratio with potential surfaces from a French quantum chemistry group.81... 

Merged-beam measurements 23-26 have consistently shown that the measured recombination cross section depends on conditions in the ion source. The authors have ascribed the effect to differing vibrational distributions. In one of the later measurements,16 the Hj vibrational state was inferred from the threshold energy for electron-ion dissociative excitation,... 

Ex 35 Kcal/mole.15 We find that the CO product vibrational distribution calculated using the phase space model with Eav = 35-40 Kcal/mole is in good agreement with our experimental results (Figure 2). Thus, the measured CO vibrational distribution indicates that vibrational energy disposal to the photolysis products is determined at a point on the potential surface where the full reaction exoergicity is available. This suggests that the 351 nm excitation of W(CO)g results in the sequence of events, (2)-(4), where the asterisk denotes vibrational excitation. 

Developed into a power series in R 1, where R is the intermolecular separation, H exhibits the dipole-dipole, dipole-quadrupole terms in increasing order. When nonvanishing, the dipole-dipole term is the most important, leading to the Forster process. When the dipole transition is forbidden, higher-order transitions come into play (Dexter, 1953). For the Forster process, H is well known, but 0. and 0, are still not known accurately enough to make an a priori calculation with Eq. (4.2). Instead, Forster (1947) makes a simplification based on the relative slowness of the transfer process. Under this condition, energy is transferred between molecules that are thermally equilibriated. The transfer rate then contains the same combination of Franck-Condon factors and vibrational distribution as are involved in the vibrionic transitions for the emission of the donor and the adsorptions of the acceptor. Forster (1947) thus obtains... 

Using fs laser excitation at 620 nm, a 2PC in Y of 0.5ps [399] implicates hot electrons, probably thermalized at Te, as the mechanism for desorption induced by the fs laser (Section 2.6.2). Rotational state distributions are nearly Boltzmann characterized by Tf. The 2PC of internal state distributions was also obtained. Rather surprisingly, significant differences in these 2PC were obtained for T and the state-resolved yield for the two spin-orbit states and this was qualitatively rationalized by a DIMET picture [399]. Where overlap in experiments exist, the qualitative results are similar to those for fs laser induced desorption of NO/Pd(lll) [400,401]. For this latter system, the absolute yield Y is large at typical fluencies used in the experiments and a very hot vibrational distribution was observed (Tv = 2900 K). 

For the vibrational term qivib, a classical high-T continuum approximation is seldom valid, and evaluation of the discrete sum over states is therefore required over the quantum vibrational distribution. (As pointed out in Sidebar 5.13, accurate treatment of molecular vibrations is crucial for accurate assessment of entropic contributions to AGrxn.) A simple quantum mechanical model of molecular vibrations is provided by the harmonic oscillator approximation for each of the 3N — 6 normal modes of vibration of a nonlinear polyatomic molecule of N atoms (cf. Sidebar 3.8). In this case, the quantum partition function can be evaluated analytically as... 

V. S. Letokhov Let me make two comments. My first comment is about terminology and the second about the possibility to laser control the intramolecular vibrational distribution (IVR) rate. 

The temporal resolution of both methods is limited by the risetime of the IR detectors and preamplifiers, rather than the delay generators (for CS work) or transient recorders (SS) used to acquire the data, and is typically a few hundred nanoseconds. For experiments at low total pressure the time between gas-kinetic collisions is considerably longer, for example, approximately 8 /is for self-collisions of HF at lOmTorr. Nascent rotational and vibrational distributions of excited fragments following photodissociation can thus be obtained from spectra taken at several microseconds delay, subject to adequate SNR at the low pressures used. For products of chemical reactions, the risetime of the IR emission will depend upon the rate constant, and even for a reaction that proceeds at the gas-kinetic rate the intensity may not reach its maximum for tens of microseconds. Although the products may only have suffered one or two collisions, and the vibrational distribution is still the initial one, rotational distributions may be partially relaxed. 

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