Spin-orbit states

For molecules with an even number of electrons, the spin function has only single-valued representations just as the spatial wave function. For these molecules, any degenerate spin-orbit state is unstable in the symmetric conformation since there is always a nontotally symmetric normal coordinate along which the potential energy depends linearly. For example, for an - state of a C3 molecule, the spin function has species da and E that upon... 

Several characteristics of the metal beam have been studied in detail. It is well known that metal clusters and metal oxides are formed as a result of the ablation process. However, these potentially interfering species have been studied in detail130 and it has been concluded that they do not introduce any doubt as to the validity of the experimental results. Much more important than cluster or oxide formation are the atomic electronic state populations of the metal beams. For each metal reactant, these have been characterized using laser-induced fluorescence (LIF) excitation spectroscopy. For Y, only the two spin-orbit states of the ground electronic state (a Dz/2 and a D-3,/2) were observed.123... 

Table 4. The percent population of On from the triplet channel in v > 26 as a function of photolysis wavelength and spin-orbit state of the counter fragment. Note that the thermodynamic threshold for the generation of 02(v = 26) is at 241.6nm.

Table 5. The branching ratios into the three spin-orbit states of the oxygen atom fragment as a function of photolysis wavelength in the Hartley band. Note that a statistical yield would give a branching ratio of 5 3 1, or as percentages, 55.5 33.3 11.1.

Third, there are clear differences in the images for dissociation at the same wavelength while probing different spin-orbit states. Two effects contribute to these differences. One is the slight difference in energy in the atomic states, most easily seen in the data at 234 nm where the 0(3P2) data clearly has the strong contribution from vibrationally-excited O2 while the other spin-orbit states do not. In this case the threshold for the dynamical process that forms the vibrationally-excited products has been crossed by the 158.265 cm-1 of the spin-orbit excitation. The second effect is that due to the nature of the J-level. It is known that there is a v—J correlation from the angular fits as well as from the fact that when the polarization of the... 

Thermal distributions of NO(u 2, J, A Ej,) states were observed, wherein the population in any level was determined by the internal energy and the parameter Tr. and independent of spin-orbit state or lambda doublet species. This is in contrast to the rotational rainbows, the propensities for preferential population in the Il(A ) lambda doublet species and the Fj spin orbit state which were observed in direct inelastic scattering of NO/Ag(l 11). 

Fig. 11. Population distributions observed in the non-Boltzmann laser-induced desorption channel for NO/Pt(l 11). Populations in the higher (open cirdes) Fj and lower energy ( + ) F] spin-orbit states are distinguished. The heating laser wavelength was 532 nm.

The electronic spectra of large molecules, particularly when continuous in nature, do not always allow the confident prediction of spin orbit states... 

Figure 3.16. Population distribution b0 (a) and rotational alignment b2/b0 (b) plotted vs. the internal energy. As in Figure 3.15, Boltzmann population distributions are linear in such plots. The different symbols correspond to different spin-orbit states of NO. From Ref. [170].

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). 

Amount by which lower energy spin-orbit state lies below unsplit term, see Moore, C. Natl. Bur. 

There are also charge-transfer characteristics within the electronic transitions between the spin-orbit states of the pentaammine complexes. This is evidenced by order of magnitude increases in the intensities of these transitions when an ammine or aqua ligand is replaced by a 77-base (e.g., Cl ) or a 7r-acid (e.g., N heterocycle) (67). 

Recently Shokoohi et al. (14) obtained high resolution LIF spectra from the photolysis of ICN at 266 nm. Using these spectra, they were able to show that the population of the and F2 spin components associated with each rotational level varied with both rotational and vibrational quantum number. For CN radicals with v" = 0 and N" < 43 the population of F- level < F level, for N" = 43 the population of F- level F level, and for N" > 43 the population of F- level > F2 level. In the v" = 1 level more of the CN radicals are produced in the upper N" levels than in the lower levels and for these upper levels the population of F-l level > F2 level. In the v" = 2 level, no radicals are observed below N" = 17, and the population of Fj level > F level. These results can be qualitatively understood in the following manner. The iodine atom can be produced in the /2 and the spin-orbit states. Spin-orbit interaction between... 

The luminescence spectrum predominantly originates from a single spin-orbit state, but the Raman and absorption spectra are influenced by other spin-orbit states and by nearby charge transfer states. The results reported here are based on pre-resonance Roman data obtained as close to the experimentally determined orgin of the lowest excited state as possible. 

We derive from the earlier relations the results of Table 3 for Hermitian conjugation of the operators (in the ordinary sense this Hermitian conjugation action does not conjugate elements of the quasispin matrices), time reversal and their combination. It is necessary where time reversal is involved to assume one-particle spin-orbital states with yl = — 1, so as to use anticommutation relations to reorder the operators this case is taken for the whole table. This shows that for a one-particle state Q(X)a is Hermitian, while time reversal performs a nt rotation about the y-axis of quasispin space. 

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