Factors. Spin-Orbit Coupling

The following electron spin g factors were obtained from ESR spectra of the PH2 radical isolated in various solid matrices  

Rotational g factors g have been derived from an expression due to [10] for the electronic contribution to these factors, i.e., g = - eqq /Aso with Ago = spin-orbit coupling constant. Using available data for 8qq and an atomic P value for Ago (299 cm given in [11 ]), the following factors were obtained [12]  

The isotropic or Fermi contact hyperfine (hf) coupling constant ap was first obtained for both nuclei ip and from ESR spectra of ground-state PHg isolated at low temperature in rare-gas matrices (see the second table below). Anisotropic or dipolar features were first detected for 3 P with PHg anchored by H bonding in a frozen aqueous solution of sulfuric acid [1 ]. Complete sets of ap and the anisotropic components Tqq (q = inertial axes a, b, c XTqq=0) for both nuclei of ground-state PHg were later determined by far-IR laser magnetic resonance (FIR, LMR) [2] and microwave (MW) [3, 4] spectra. The latter [3, 4] also yielded data for the interaction constants Cqq(3ip). Interaction constants were also obtained for the electronically 

Two sets of hf coupling constants (all in MHz) measured in the vapor phase are given below  

Five rotational transitions were measured. The analysis [4] included earlier hf data from MW [3] and FIR LMR [2, 7] spectra. T c was derived from the sum rule XTqq = 0. Very similar values were given in [3] (see also [6]). - Eight rotational transitions were measured. 1 2 for ip (and the absolute values of Tgg and were in the order of magnitude of B( P)=287 MHz calculated [8] for the P3p orbital in the ground state of the free atom [2]. In a preliminary FIR LMR study [7] ap(3ip) = 224 MHz from a matrix ESR spectrum (see the next table) and Tcc/2(3ip) = 287 MHz [8] were used to interpret the observed ip hf structure. 

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A third possible channel of S state deexcitation is the S) —> Ti transition -nonradiative intersystem crossing isc. In principle, this process is spin forbidden, however, there are different intra- and intermolecular factors (spin-orbital coupling, heavy atom effect, and some others), which favor this process. With the rates kisc = 107-109 s"1, it can compete with other channels of S) state deactivation. At normal conditions in solutions, the nonradiative deexcitation of the triplet state T , kTm, is predominant over phosphorescence, which is the radiative deactivation of the T state. This transition is also spin-forbidden and its rate, kj, is low. Therefore, normally, phosphorescence is observed at low temperatures or in rigid (polymers, crystals) matrices, and the lifetimes of triplet state xT at such conditions may be quite long, up to a few seconds. Obviously, the phosphorescence spectrum is located at wavelengths longer than the fluorescence spectrum (see the bottom of Fig. 1). 

If the spin-orbit coupling is small, as it is in helium, the total electronic wave function J/ can be factorized into an orbital part J/° and a spin part pl ... 

Mixing of LS-states by spin orbit coupling will be stronger with an increasing number of f-electrons. As a consequence, intermediate values of Lande g factor and reduced crystal field matrix elements must be used. 

The expressions (4.22)-(4.23) found in chap. 4 for the isomer shift 5 in nonrelativ-istic form may be applied to lighter elements up to iron without causing too much of an error. In heavier elements, however, the wave function j/ is subject to considerable modification by relativistic effects, particularly near the nucleus (remember that the spin-orbit coupling coefficient increases with Z ). Therefore, the electron density at the nucleus l /(o)P will be modified as well and the aforementioned equations for the isomer shift require relativistic correction. This has been considered [1] in a somewhat restricted approach by using Dirac wave functions and first-order perturbation theory in this approximation the relativistic correction simply consists of a dimensionless factor S (Z), which is introduced in the above equations for S,... 

In simple crystal field theory, the electronic transitions are considered to be occurring between the two groups of d orbitals of different energy. We have already alluded to the fact that when more than one electron is present in the d orbitals, it is necessary to take into account the spin-orbit coupling of the electrons. In ligand field theory, these effects are taken into account, as are the parameters that represent interelectronic repulsion. In fact, the next chapter will deal extensively with these factors. 

It should be pointed out that a somewhat different expression has been given for the Knight shift [32] and used in the analysis of PbTe data that in addition to the g factor contains a factor A. The factor A corresponds to the I PF(0) I2 probability above except that it can be either positive or negative, depending upon which component of the Kramers-doublet wave function has s-character, as determined by the symmetry of the relevant states and the mixing of wavefunctions due to spin-orbit coupling. 

The ligand field was parameterised in terms of ea only, and values of this parameter, together with the spin-orbit coupling constant X, the orbital reduction factor k and the Racah parameter B were obtained by fitting the d-d spectra, zero-field splittings, principal magnetic susceptibilities and e.s.r. g-values. 

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