Rotation population

Figure B2.3.14. Experimentally derived vibration-rotation populations for the NO produet from the H + NO2 reaetion [43], The fme-stnieture labels and refer to the two ways that the projeetions 2 and A of the eleetron spin and orbital angular momenta along the intemuelear axis of this open-shell ean be eoupled (D =...

If the spectrum is observed in emission it is the rotational populations in the upper state which determine relative intensities. They may or may not be equilibrium Boltzmann populations, depending on the conditions under which the molecule got into the upper state. 

The resolution of the ZEKE-PE spectmm of 1,4-difluorobenzene can be compared with, for example, that of the ultraviolet photoelectron spectmm of benzene in Figure 8.12. The greatly increased resolution in the ZEKE-PE spectmm is attributable mostly to the fact that only photoelectrons with zero kinetic energy are being detected. It is also partly attributable to the molecules being in a supersonic jet this has the effect of sharpening the bands because of the restricted rotational populations in the ground state of the molecule. 

That means the frequency exchange operator in the Q-branch coincides with that ruling relaxation of rotational populations Nj = J2m Njm in the ground state ... 

Fig. 9. Incidence energy dependence of the vibrational state population distribution resulting when NO(u = 12) is scattered from LiF(OOl) at a surface temperature of (a) 480 K, and (b) 290 K. Relaxation of large amplitude vibrational motion to phonons is weak compared to what is possible on metals. Increased relaxation at the lowest incidence energies and surface temperatures are indicators of a trapping/desorption mechanism for vibrational energy transfer. Angular and rotational population distributions support this conclusion. Estimations of the residence times suggest that coupling to phonons is significant when residence times are only as long as ps. (See Ref. 58.)...

The rotational population distributions were Boltzmann in nature, characterized by 7Ji = 640 35 K. This seems substantially lower than yet somewhat larger than the temperature associated with the translational degree of freedom. The lambda doublet species were statistically populated. The population ratio of i =l/t =0 was roughly 0.09, consistent with a vibrational temperature Ty— 1120 35K. The same rotational and spin-orbit distributions were obtained for molecules desorbed in t = 1 as for f = 0 levels. Finally, there was no dependence in the J-state distributions on desorption angle. 

Repeating these experiments using the YAG laser fundamental (1064nm, 1.17 eV), adjusting the energy to achieve the same calculated temperature jump, gave essentially identical (Q, J, A)-state distributions. The inversion of population in the two spin-orbit levels, the population plateau for internal energies below 300 cm and the rapid fall-off of rotational population for... 

Two components were observed in the LID TOP spectra. The slower component was found to have a cosine angular flux distribution and an average kinetic energy 250 K, approximately the value of T . This component was also characterized by a rotational population distribution described by a rotational temperature T t = 170 20K. These results are comparable to the thermal LID results for Pt(lll), Pd(lll) and Pt(foil) discussed in the previous sections. 

The visible and near-infrared LID results for NO/Pt were discussed in terms of hot electrons combined with a charge transfer mechanism. For the 193 nm LID result considered here, the photon energy is above the substrate work function, thereby providing a direct source of electrons to bathe the adsorbed NO species. Comparison of translational energy and vibrational state distributions for NO/Pt(lll), NO/Pt(foil), and N0/Ni(100)-0 suggests that the mechanisms driving the desorption processes in these systems might be related. However, the details of the specific interaction potentials must be substantially different to account for the disparate spin-orbit and rotational population distributions. 

The exponential energy factor in Eq. (H) gives decreasing populations with increasing 7, but the degeneracy factor (27 + 1) works in the opposite direction. As a result, rotational populations increase initially with increasing 7, reach a peak, and subsequently decrease. 

Figure 10.1 Numerically calculated distribution of rotational population in before and after the interaction with a single linearly polarized femtosecond pulse of duration 120 fs and peak intensity 10 3 W/cm. (a) Zero temperature, (b) Room temperature.

Figure 10.2 Experimentally measured rotational population (color coded) of the first eight rotational levels in (a) and (b). For a pulse train period equal to the revival time (white vertical hnes) the population is efficiently transferred from the initial states N = 0,1,2 to higher states N = 3,4,..., 7. Part of Fig. 4 in Ref. 25. Copyright 2012, American Physical Society.

Figure 3.15. Rotational state distributions of NO produced in direct scattering from Ag(lll) at Ts 600 as a function of incident normal energy En. Rotational populations Nj are plotted in such a way that a Boltzmann distribution characterized by a temperature T is a straight line. The different symbols correspond to rotational populations derived from the different rotational transitions as listed. From Ref. [160].

A model of the randomly colling form of polylrll) based on minimum-energy conformers of UpU is described. The blend of conformers is chosen to fit the C—C rotational populations derived in NMR studies of UpU and poly(rU) and to match the experimental unperturbed dimensions of the poly(rU) chain. In addition, estimates of loop closure based on the model are comparable to the sizes of loops most frequently seen In the model oligonucleotides. Approximately 60% of the conformers constituting the model are characterized by stacked, extended C2 -endo ra cmy = tg g+ rotations. 

Using a tunable laser as a probe they have observed that CN(X2E) radicals produced at this wavelength are vibrationally and rotationally excited. The rotational distribution follows the Boltzmann law, indicating that dissociation is not immediate but occurs after many vibrations of the electronically excited molecule. Thus, the distribution of the rotational population reflects (lie statistical nature of the dissociation processes. The distribution of the excess energy beyond that required to break the C—C bond is 54% in electronic, 20% in translational, 14% in vibrational, and 11% in rotational energies. See also p. 87. 

Vibrational Population in Diatomic Molecules, 18 I 4.2 Rotational Population in Diatomic Molecules, 19 I 4.3 Thermal Contribution to Photolysis and Fluorescence. 21)... 

REACTION INCIDENT-ION TRANSLATIONAL ENERGY EMITTING SPECIES wavelengths and/or TRANSITIONS OBSERVED VIBRATIONAL AND ROTATIONAL POPULATIONS OF EMITTING STATE REFERENCE... 

The depopulation cross sections of the Rb nd states of 25 < n < 40 are 1000 A2, which is the same as the cross section of the Rb ns state if the ns —> (n - 3)1,1 > 3 contribution is subtracted. For the Rb nd states the calculated contribution of the scattering of the nd state to nl S 3 and (n—1)1 s 3 states with no change in the rotational state of the CO is <100 A2, so 90% of the cross section is due to the inelastic transitions leading to rotational excitation. Presumably it is because the resonant transfer accounts for 90% of the observed cross section that the structure in the cross section is more visible in the nd cross sections than in the ns cross sections. For both the ns and nd states minimal collisional ionization is observed and calculated in this n range, principally because there are too few CO molecules with energetic enough A/ = -1 rotational transitions. For example, only CO 7 > 18 states can ionize an n = 42 Rydberg state by a A7 = -1 transition, and only 3% of the rotational population distribution is composed of 7 > 18 states. 

A CARS experiment has recently been done to determine the amount of vibrational and rotational excitation that occurs in the O2 (a- -A) molecule when O3 is photodissociated (81,82). Valentini used two lasers, one at a fixed frequency (266 nm) and the other that is tunable at lower frequencies. The 266 nm laser light is used to dissociate O3, and the CARS spectrum of ( (a A), the photolysis product, is generated using both the fixed frequency and tunable lasers. The spectral resolution (0.8 cm l) is sufficient to resolve the rotational structure. Vibrational levels up to v" = 3 are seen. The even J states are more populated than the odd J states by some as yet unknown symmetry restrictions. Using a fixed frequency laser at 532 nm (83) to photolyze O3 and to obtain the products 0(3p) + 02(x3l g), a non-Boltzmann vibrational population up to v" = k (peaked at v" = 0) is observed from the CARS spectrum. The rotational population is also non-Boltzmann peaked at J=33, 35 33, 31 and 25 for v" = 0,1,2,3, and k, respectively. Most of the available energy, 65-67%, appears in translation 15-18% is in rotation and 17-18% is in vibration. A population inversion between v" = 2 and 3 is also observed. 

Recent work (161) with a tunable VUV flash lamp has shown that the CN(A2II) can be detected directly using the LIF technique. Thus one is able, in principle, to determine the vibrational and rotational population of each of the fragments (CN(X2E), (A2n)). The tunable UV flash lamp allows one to measure these quantum state distributions as a function of the vibrational frequency of the upper electronic state. The results from these studies thus far are summarized in Table 8. 

Butler et al. (175) measured the LIF spectra of the ground state of the CS radical, and found that it was produced vibra-tionally excited. Their vibrational distribution curve peaks at v" = 3 and extends to v" = 6 (see Figure 10). Their high resolution studies indicated that the rotational population could be described with a "temperature" of about 700 K. Addison et al. (176) directly measured the S(4i) concentration change in time using resonance fluorescence detection. From the time dependence they extrapolated the concentration back to zero time and determined the nascent atom concentration for the 4). The yield of the S(3p)/S(4)) ratio was obtained by measuring the... 

Rotational Population Distributions. As expected, there is an overpopulation in the A state level and an underpopulation in the X state level connected by the laser, compared to a thermal distribution (see Fig. 1). Higher rotational levels (N 6) in the A-state are described by a Boltzmann distribution with T 940°K, well less than the gas temperature and reflecting the energy dependence of the or. The high-N levels of the X-state are described by a Boltzmann distribution with very high T (3200°K) but this may be an artifact of the model, due principally to the assumed... 

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