Spin dimer

Hamiltonian, spin, dimer species, 31 95 Hamiltonian matrix elements, 25 4, 5, 7, 8, 10 Hammett acidity... 

A triplet state dimer of a benzofused 1,2,3-trithiole dication was postulated. However the occurrence of this high-spin dimer is strongly dependent on the nature of the solvent and the oxidant129. The 2,5-dimethoxy-4-methylphenyl moiety in which the additional charge and the single electron are stabilized in a quinoidal structure after one-electron oxidation has been utilized as a probe for electron delocalization when two of these moieties were connected either by a trimethylene, a 1,4-disubstituted phenylene or a biphenyl bridge130. 

If several exchange pathways exist in polynuclear coordination complexes, ferromagnetic and antiferromagnetic pathways can compete for a given spin dimer, usually resulting in a dominant antiferromagnetic exchange. 

An antiferromagnetically coupled spin dimer of two s=l/2 has a spin singlet as its lowest energy state. The first excited state is a spin triplet and the energy between these two states is denoted as the spin gap A. If such dimers are coupled in one dimension a dimerized spin chain is formed. Such spin chains exist in several spin systems, e.g. in CuGeC>3 [5], Properties of this and related compounds are further discussed in Ref. [3],... 

Dendritic-macrocyclic polyradicals consist of small dendritic branches which may be connected to calix[4]arene macrocyclic cores via 3,4 -biphenylene linkers. Polyradicals 45-50 correspond spin dimers, trimers, and pentamers, as illustrated in Fig. 28. Their connectivity is consistent with ferromagnetic coupling scheme. 

Temperature of maximum susceptibility for antiferromagnetically coupled spin dimers... 

A second term in Eq. (18.10) is the SCE in the S-T gap, and, consequently, a second term in a denominator of Eq. (18.8) projects the spin contamination in the BS singlet solution. In this way, Eq. (18.8) gives approximately spin-projected (AP) Jab values. Equation (18.8) can be easily expanded into any spin dimers, namely, the lowest spin state (LS) and the highest spin state (HS), e.g., singlet-quintet for S = Sh = 2/2 pairs, singlet-sextet for 5a = Sb = 3/2 pairs, and so on, as follows ... 

A high spin concentration is usually observed in the case of nondegenerate conducting polymers at the first redox potential compatible with a substantial stability of the polaron state. Thus PP reaches a level of about one spin for 12 rings PT, at the first redox potential, displays a low spin content (about one spin per 40 rings), which may be attributed to spin dimerization. This will be clarified in a later section. 

As a final comment, it is important to note that the application of the BS method to high spin dimers, i.e. the use of equation (8), is bound to the validity of the SH approach to describe the relative spacing of the spin multiplets. Independent evaluation of the energies of the various spin multiplets would allow one to test this hypothesis, which, up to now, has only found experimental verifications, Sections 2.2 and 2.3 present methods that can, in principle, address this problem, which should also be a major challenge of any post-We treatment. In any case it should be mentioned that the actual value of the computed J value is expected to depend on the overlap integral appearing in (3) [34,35] and the proper use of equation (8) allows to estimate an upper limit for J [5n]. 

The parameters of these spectra are calculated on a six-spin dimer model , and are as follows for the polymers in o-dichlorobenzene at 110°. 

In (d) is shown the spectrum in this region calculated using the six-spin dimer model and essentially the same chemical shift parameters as obtained for the atactic 5-polymers, which are very close to the chemical shifts obtained from the isotactic and syndiotactic polymer spectra. It must be emphasized that there are thus no arbitrary chemical shift adjustments in these calculations. The vicinal couplings of a and jS protons are likewise close to those observed for the stereoregular polymers. The parameters used are summarized in Table 2 below. 

The catalytic activity of the VO(stearate)2-L/o tartrate system with the suggested presence of a dinuclear oxidovanadium(IV) tartrato complex leads to an enanti-oselective oxidative coupUng polymerization of 2,3-dihy-droxynaphthalene [13]. Very recently, the second harmonic generation and spin-dimer behavior were observed for oxovanadium(IV) tartrates [14], In addition, a study appeared on an interaction of tartratovanadates with chiral Fe(II) and Ni(II) tris(2,2 -bipyridine) complexes manifesting itself with the solid state by packing into homochiral layers in the crystal structure [15]. 

A partial explanation for this surprising difference is provided by a combination of an analysis of the role of magnetic site coordination polyhedron in determining the electronic structure and application of the Spin Dimer Model.The octahedron about Os in Li50s06 is subject to a much stronger psuedo-tetragonal compression, 4 Os - O bonds at 1.908 A... 

Table 2.4 Relative values for the exchange pathways Ji -J5 (Figure 2.13) calculated on the Spin Dimer Model for occupation of only and equal occupation of dxy, dxz and dy for Li50s06. The values for Li4MgRe06 follow the same pattern...

Analysis of the effect of O disorder on the Mo - O - Mo superexchange interaction, using spin dimer analysis, shows a significant perturbation to the average structure value. This observation fits well with the Saunders-Chalker model for the appearance of the spin glass state for systems with... 

Calvo, R, Isaacson, RA, Abresch, EC, Okamura, MY and Feher, G. 2002. Spin-lattice relaxation of coupled metal-radical spin dimers in proteins application to Fe " -cofactor (Qa > Qb > < > ) dimers in reaction centers from photosynthetic bacteria. Biophys J 83(5) 2440-2456. 

Detailed electrochemical studies on nTs have also provided new insights into the redox properties of PTs and the charged species responsible for the electrical conduction in PTs. Thus, in the case of 74, first evidence of reversible reduction to the mono- and dianion states was obtained (Fig. 12.11). On the other hand, analyses of the redox behavior of nTs by ESR, UV-vis absorption, and cyclic voltammetry provided evidence for the dimerization of oligomeric cation radicals (polarons) into spin-dimerized polarons, which have been propo.sed as... 

Dependence of the orbital interactions between two spin sites in a spin dimer on the (a) FM and (b) AFM spin arrangements. Each spin site is assumed to have one electron and one orbital. 

To gain insight into the meaning of the symmetric (or Heisenberg) spin exchange interaction, we consider a spin dimer consisting of two equivalent spin-1/2 spin sites, I and 2, with one electron at each spin site (24.7) [1,26]. The energy of the spin... 

In principle, the spin at site (= 1,2) of the spin dimer can have either up-spin a or down-spin p state. For a single spin S= V2 and = 1/2 so that, in terms of the S, Sz) notations, these states are given by... 

The eigenstates of Hspin allowed for the spin dimer are the singlet state S) and triplet state IT),... 

We now examine how the triplet and singlet states of the spin dimer are described in terms of electronic structure calculations. This closely follows the material in Sections 8.5 and 8.8. The electronic Hamiltonian Heiec for this two-electron system can be written as... 

With DFT calculations, the energy-mapping between the energy spectra of Heiec and Hspin is carried out by using high-spin and broken-symmetry states ( HS) and BS), respectively) [1,34-37]. For example, let us reconsider the spin dimer shown in 24.10, for which the pure-spin HS) and 6S) states are given by... 

Effect of magnetic field on the energy levels of an AFM spin dimer made up of two 5=1/2 ions for (a) a large and (b) a small energy difference between the singlet and triplet states. 

---