Spin-Hamiltonian approach

Orbitally degenerate grormd states, in general, cannot be treated in the spin-Hamiltonian approach. In this case, SOC has to be evaluated explicitly on an extended basis of spin-orbit functions. However, in coordination chemistry and bioinorganic chemistry, this is only of marginal importance, because the metal centers of... 

Let us consider that a transition metal ion in a crystal is subjected to an external magnetic field. The energy states of the system are calculated using the so-called the spin Hamiltonian approach ... 

Now we come to the part we have been working toward ever since we noted the spin-Hamiltonian approach needed a way to find the coupling constants. COSY has revolutionized the use of NMR because it is no longer necessary to worry about the values of the coupling constants and there is... 

MMVB is a hybrid force field, which uses MM to treat the unreactive molecular framework, combined with a valence bond (VB) approach to treat the reactive part. The MM part uses the MM2 force field [58], which is well adapted for organic molecules. The VB part uses a parametrized Heisenberg spin Hamiltonian, which can be illustrated by considering a two orbital, two electron description of a sigma bond described by the VB determinants... 

If the electric quadrupole splitting of the 7 = 3/2 nuclear state of Fe is larger than the magnetic perturbation, as shown in Fig. 4.13, the nij = l/2) and 3/2) states can be treated as independent doublets and their Zeeman splitting can be described independently by effective nuclear g factors and two effective spins 7 = 1/2, one for each doublet [67]. The approach corresponds exactly to the spin-Hamiltonian concept for electronic spins (see Sect. 4.7.1). The nuclear spin Hamiltonian for each of the two Kramers doublets of the Fe nucleus is ... 

The EPR spectrum is a reflection of the electronic structure of the paramagnet. The latter may be complicated (especially in low-symmetry biological systems), and the precise relation between the two may be very difficult to establish. As an intermediate level of interpretation, the concept of the spin Hamiltonian was developed, which will be dealt with later in Part 2 on theory. For the time being it suffices to know that in this approach the EPR spectrum is described by means of a small number of parameters, the spin-Hamiltonian parameters, such as g-values, A-values, and )-values. This approach has the advantage that spectral data can be easily tabulated, while a demanding interpretation of the parameters in terms of the electronic structure can be deferred to a later date, for example, by the time we have developed a sufficiently adequate theory to describe electronic structure. In the meantime we can use the spin-Hamiltonian parameters for less demanding, but not necessarily less relevant applications, for example, spin counting. We can also try to establish... 

Recently similar doublet structures have been observed in other systems with inversion symmetry58,66). Fujimoto et al.58) used a somewhat different perturbation approach for the explanation of the 14N-ENDOR spectra in copper-doped a-glycine, whereas Brown and Hoffman66) determined the nitrogen ENDOR frequencies of Cu(TPP) and Ag(TPP) by numerical diagonalization of the spin Hamiltonian matrix for an electron interacting with a single pair of equivalent 14N nuclei. 

Except for coi (transition frequencies of the nuclear spin Hamiltonian) all values are temperature-dependent. From the previous subsection the behaviour of a>s is known. From the anomalous contribution to the birefringence which is proportional to (Sp ) we get the information concerning Ai. If we assume that the damping of the soft mode is non-critical (which is generally accepted), Eq. 10 describes a transition from an under-damped mode to an over-damped one as Tc is approached from either side. 

Before turning to the problem of calculating the spin Hamiltonian, we should consider how the results can be interpreted with respect to the bonding. From the spin Hamiltonian parameters, we shall obtain the values for Cji of the antibonding orbitals, and we need to know what relation these have to the Cj, of the bonding states. One approach to this problem, which seems fruitful, is the gross-population analysis developed by Mulliken (26). Consider first our three-electron example. In this case we split up the term... 

A combination of the two techniques was shown to be a useful method for the determination of solution structures of weakly coupled dicopper(II) complexes (Fig. 9.4)[119]. The MM-EPR approach involves a conformational analysis of the dimeric structure, the simulation of the EPR spectrum with the geometric parameters resulting from the calculated structures and spin hamiltonian parameters derived from similar complexes, and the refinement of the structure by successive molecular mechanics calculation and EPR simulation cycles. This method was successfully tested with two dinuclear complexes with known X-ray structures and applied to the determination of a copper(II) dimer with unknown structure (Fig. 9.5 and Table 9.9)[119]. 

The Spin Hamiltonian Effective Approach to the Vibronic Effects - Selected Cases... 

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