Vibration, H atom

J.J. Rush, R.R. Cavanagh, R.D. Kelley J.M. Rowe (1985). J. Chem. Phys., 83, 5339-5341. Interaction of vibrating H-atoms on the surface of platinum particles by isotope-dilution neutron spectroscopy. 

It is beyond the scope of these introductory notes to treat individual problems in fine detail, but it is interesting to close the discussion by considering certain, geometric phase related, symmetry effects associated with systems of identical particles. The following account summarizes results from Mead and Truhlar [10] for three such particles. We know, for example, that the fermion statistics for H atoms require that the vibrational-rotational states on the ground electronic energy surface of NH3 must be antisymmetric with respect to binary exchange... 

The hydrogen atom attached to an alkane molecule vibrates along the bond axis at a frequency of about 3000 cm. What wavelength of electromagnetic radiation is resonant with this vibration What is the frequency in hertz What is the force constant of the C II bond if the alkane is taken to be a stationary mass because of its size and the H atom is assumed to execute simple harmonic motion ... 

The temperature dependences of k, calculated by Hancock et al. [1989], are given in fig. 48. The crossover temperature equals 25-30 K. The weak increase of k T) with decreasing temperature below is an artefact caused by extending the gas-phase theory prefactor to low temperatures without taking into account the zero-point vibrations of the H atom in the crystal. For the same reason the values of the constants differ by 1-2 orders of magnitude from the experimental ones. 

B synchronously moving away from and toward H the H atom does not move (if A and B are of equal mass). If H does not move in a vibration, its replacement with D will not alter (he vibrational frequency. Therefore, there will be no zero-point energy difference between the H and D transition states, so the difference in activation energies is equal to the difference in initial state zero-point energies, just as calculated with Eq. (6-88). The kinetic isotope effect will therefore have its maximal value for this location of the proton in the transition state. 

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.

By repeating the experiment with molecules having different speeds and different states of rotational or vibrational excitation, chemists can learn more about the collision itself. For example, experimenters have found that, in the reaction between a Cl atom and an HI molecule, the best direction of attack is within a cone of half-angle 30° surrounding the H atom. 

For a useful separation of pathways, the variation in final state distributions within each pathway must be at least somewhat smaller than the variation between pathways. The aforementioned dissociation of H2CO provides a perfect example of this technique, in which the H2 produced through the three-center ehmination leads to extensive rotational excitation of CO, with only moderate vibrational excitation of H2. By contrast, the competing pathway involving roaming of one H atom leaves much less energy in CO rotation, with very significant vibrational excitation of H2 [8]. 

The factor Dg can either be determined from the dissociation energy and the ground state vibration energy or from thermodynamic data. The heat of formation of H atoms from H2 molecules can be found in the literature, but some care should be exercised in considering the total energy content of H atoms and H2 molecules under standard conditions. 

The time-of-flight spectrum of the H-atom product from the H20 photodissociation at 157 nm was measured using the HRTOF technique described above. The experimental TOF spectrum is then converted into the total product translational distribution of the photodissociation products. Figure 5 shows the total product translational energy spectrum of H20 photodissociation at 157.6 nm in the molecular beam condition (with rotational temperature 10 K or less). Five vibrational features have been observed in each of this spectrum, which can be easily assigned to the vibrationally excited OH (v = 0 to 4) products from the photodissociation of H20 at 157.6 nm. In the experiment under the molecular beam condition, rotational structures with larger N quantum numbers are partially resolved. By integrating the whole area of each vibrational manifold, the OH vibrational state distribution from the H2O sample at 10 K can be obtained. In... 

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... 

Fig. 12. Internal energy spectrum of the CH2 fragment from photolysis of the CH3 radical at 216.3 nm. The combs above the figure indicate the expected TOFs of H atoms formed, in association with triplet methylene CH2(X3Bi) or singlet CH2( i1Ai) respectively as a function of V2, the vibrational quantum number for their respective bending mode. (From Wilson et al,113)...

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