Ground spin multiplet

As seen in Section 1.6, this approximation holds when the spin multiplet ground state is well isolated from excited electronic states, and ZFS is negligible. If 5 = lh, the g values can easily be measured through EPR spectroscopy and the g directions can be determined by single-crystal EPR measurements. When the latter measurements are not available, sometimes the principal g directions can be guessed from the symmetry of the molecule, and an independent estimate of the pseudocontact shift can still be attempted. 

If the ground state is an orbital singlet, and so only has one multiplet component J, or if the ground-state multiplet splitting is so small that multiplet components are thermally occupied in proportion to their degeneracies, the spin-orbit factor in Eq. (29) becomes simply ... 

DFT formalism describe the electronic ground state in a single determinant scheme. While this method was well established for the ground state and the lowest states within a symmetry class from its early days, its extension to excited-state description is still in development. The first option proposed in 1977 by Ziegler and Baerends, within the framework of the time-independent formalism, and generalized in 1994 by Daul (so-called A-SCF method) is based on symmetry-dictated combinations of determinants able to evaluate in a nonambiguous way the space and spin multiplets. It has been applied with success to a variety of highly symmetric molecules. However, several limitations make this approach only accessible to experts in the subject. 

Without spin-orbit coupling, atomic ground state multiplet energies can be calculated in DFT from D h determinants see EJ Baerends, V Branchadell, M Sodupe. Chem Phys Lett 265 481-489, 1997. 

Fig. 27. Temperature dependence of the spontaneous muon spin precession frequency in single-crystalline TbNij with a Curie temperature of 23 K. The dashed curve is the appropriate fiee-ion Brillouin function. Inclusion of CEF interaction in the ground-state multiplet gives the solid curve which fits the data well. The behavior around the critical temperature is typical for a second-order magnetic phase transition. After Dalmas de Reotier et al. (1992).

The ESR measurements on lanthanide ions in Lap3 indicate six magnetically inequivalent sites having Cj/, symmetry or lower [Baker and Rubins (1961)]. This result is not in agreement with the NMR measurements of Andersson and Proctor (1968) which indicate only three inequivalent sites (see section 2.3.2). In any event, each of the six ESR sites is described by identical spin Hamiltonian parameters, the only difference being in the orientation of the principal axes of the g-tensor with respect to the crystalline c axis. Because of the low symmetry of the CEF, one expects that all degeneracy in the ground state multiplet will be completely lifted in the case of non-Kramers ions so that in these cases ESR will not be detectable [Schulz and Jeffries (1966)]. The measured g-tensor components are listed in table 18.28. 

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