Spin-orbit constant

Figure 3. Low-energy vibronic spectrum in a. 11 electronic state of a linear triatomic molecule, computed for various values of the Renner parameter e and spin-orbit constant Aso (in cm ). The spectrum shown in the center of figure (e = —0.17, A o = —37cm ) corresponds to the A TT state of NCN [28,29]. The zero on the energy scale represents the minimum of the potential energy surface. Solid lines A = 0 vibronic levels dashed lines K = levels dash-dotted lines K = 1 levels dotted lines = 3 levels. Spin-vibronic levels are denoted by the value of the corresponding quantum number P P = Af - - E note that E is in this case spin quantum number),...

Spin-spin and spin-orbit constants for CO have been investigated using semi-empirical methods, for states which can be described by a single configuration.323... 

Lichten [3 5] studied the magnetic resonance spectrum of the para-H2, N = 2 level, and was able to determine the zero-field spin-spin and spin-orbit parameters we will describe how this was done below. Before we come to that we note, from table 8.6, that in TV = 2 it is not possible to separate Xo and X2. Measurements of the relative energies of the J spin components in TV = 2 give values of Xo + fo(iX2, and the spin-orbit constant A the spin rotation constant y is too small to be determined. In figure 8.18 we show a diagram of the lower rotational levels for both para- and ortho-H2 in its c3 nu state, which illustrates the difference between the two forms of H2. This diagram does not show any details of the nuclear hyperfine splitting, which we will come to in due course. 

A further refinement in the analysis of the case (a) spectra was described by Carrington and Howard [28] in their study of the CF radical. We have already pointed out that in CIO, for example, it is only possible to determine the total axial magnetic hyperfine constant A 3/2 from studies of the J = 3/2 level alone. In CF, however, the rotational constant Bo is relatively large and the spin-orbit constant A is relatively small. This means that the ratio B0/A is considerably larger for CF (0.0183) than for CIO (0.0022), so that the rotational mixing of the 2n3/2 and 2ni/2 states (equation (9.38)) is more important. This fact, taken with additional measurements of the J = 5/2 level in the 2 n3/2 state, enables both /i3/2 and b to be determined uniquely, though with less accuracy than one would wish. 

Klisch, Belov, Schieder, Winnewisser and Herbst [157] have combined all of the data for NO to produce a current best set of molecular constants for three isotopomers, presented in table 10.15. The data used, apart from their own terahertz studies, included the A-doubling of Meerts and Dymanus [156, 158], the sub-millimetre transitions of 15N160 and 14NlsO, and Fourier transform data from Salek, Winnewisser and Yamada [159]. These last authors were able to study the magnetic dipole transitions between the two fine-structure states. The values of the spin orbit constant A for the less common isotopomers come from Amiot, Bacis and Guelachvih [160]. 

The experimental separation of the 2F pair of levels in Ce3+ has been found by Lang [333] to be 2253 cm-1 which gives a free-ion value for the spin-orbit constant parameter of 644 cm-1. 

For carbon, the spin orbit constant X(so) is very small and the contribution to line broadening is normally negligible. But the significantly larger X so) leads to substantial g shift in silicon. The interactions between the spin system and its environment are also directly related to X(so). Both intrinsic g shifts and lifetime broadening effects are less than 15 G for carljon, but 15 G is a typical broadening for silicon at the X band. Broadening is, therefore, more apparent in silicon than in carbon radicals [10]. 

A B , where A is the spin-orbit constant (assumed to be positive Because of the spin-orbit splitting in the C state, each v v") band shows four band heads. Since the bands are degraded to the red, the band heads are formed by the Qi + R12 and Rj branches in the subband and by the Rj + Q21 and R21 branches in the... 

Table 1. MRCI + Q adiabatic transition energy (To, including zero-point vibrational energy correction computed variationally, in eV), equilibrium distances (Re in A), spin-orbit constant at Re (Aso,e in cm-1) and the spectroscopic parameters (in cm-1) of S2 and of S2(X3 g). 

Thus this model maps density over atoms rather than spatial coordinates. If overlap is included some other definition of charge density such as Mulliken s17 may be employed. Eq. (30) and (31) are then used with this wave function to calculate the hyperfine constants as a function of the pn s. If symmetry is high enough, there will be enough hyperfine constants to determine all the p s, otherwise additional approximations may be necessary. For transition metal complexes, where spin-orbit effects are appreciable, it is necessary to include admixtures of excited-state configurations that are mixed with the ground state by the spin-orbit operator. To determine the extent of admixture, we must know the value of the spin-orbit constant X and the energy of the excited states. 

Using this model, a least squares refinement of the data Was performed, taking the free ion value for the spin-orbit constant ] , = 360 K) and k = 0.8 as orbital reduction parameter. We obtain Jj = —13,5 K and D = 3000 K + 200 K... 

The O2 3nu Rydberg state with a 4n core and an outer 3sct9 electron (the H3nu state, see the end of Section 3.2.3), for which the wavefunction is specified in Eq. (3.2.111a), has a spin-orbit constant ... 

Thus, an approximate value for the unknown 3E 1E+ interaction can be obtained from an observable diagonal spin-orbit constant. As will be discussed later (Sections 3.4.4 and 5.3.3), second-order spin-orbit effects of this type contribute significantly to the effective spin-spin interaction in 3E states. 

The utility of Eq. (4.4.22) may be illustrated very simply. At very high J-values, a 2n state will approach the case (b) limit, at which point there is essentially no information in the spectrum from which the spin-orbit constant, A, may be determined. The U matrix for the case (a)—>(b) transformation at the high-J limit is... 

The difference between the spin-orbit constants of the main constituent atomic orbital, A(atom, nl), in the Rydberg molecular orbital and that of the molecular Rydberg state, Ar, is due to penetration of the Rydberg MO into the molecular core, i.e., to the contribution of the (n — l) atomic orbital responsible for the orthogonality between the Rydberg MO and the molecular core orbitals. 

Consequently, the spin-orbit constants for A 0 Rydberg states will be smaller than those of the valence states constructed from orbitals of smaller n values. In Table 5.3, spin-orbit constants of valence and Rydberg states of the same molecule are compared. 

In Section 3.4.2, spin-orbit matrix elements are expressed, in the single-configuratioi approximation, in terms of molecular spin-orbit parameters. These molecular parameters can also be related to atomic spin-orbit parameters. In Table 5.6, some values are given for atomic spin-orbit constants, (nl). Sections 5.3.1 and... 

Table 5.6 Spin-Orbit Constants of Atoms and Ions (cm X)Q...

A semiempirical calculation of molecular spin-orbit constants can be made, using the method of Ishiguro and Kobori (1967). 

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