Spin-coupling scheme

Table 7.1 Number of possible spin coupling schemes for achieving an overall singlet state...

Figure 7.4 Representations of important spin coupling schemes in benzene...

FIGURE 26 (a) MP2/6-31G(d) geometry of the cyclopropyl radical 40 according to Reference 246. (b) Spin-coupling scheme of the cyclopropyl radical according to the intra-atomic Hund rule and spin coupling within bonds. Hyperfine splitting aN at nucleus N will be > 0 ( < 0) if valence electrons at N possess oc (/ ) spin... 

This system has been chosen just to pinpoint the variety of systems and of spin coupling schemes available in heteropolymetallic systems. 

We deal first with the 14N quadrupole interaction, using the first term in (10.88), and making use of the results described in chapter 8 for the weak field coupled basis in CsF. The nuclear spin coupling scheme is... 

Despite the fact that it may be very difficult to find spin coupling schemes that correspond to realistic value landscapes and can be directly analyzed, the analogy to spin lattices is of great heuristic value. It provides a straightforward explanation of the existence of well-defined error thresholds that sharpen with increasing chain length v, just as cooperative transitions do in linear biopolymers. 

SCVB calculation of CH4 gives as a result that one of the spin coupling schemes completely dominates thejwave functinn, namely that cniTRsponding to the electron... 

Treatments based on particular spin coupling schemes, such as GUGA, often include also the non-interacting conrigurations or part of them. 

The Hartree-Fock method is an orbital approximation in that we attempt to calculate the motion of each individual electron in the averaged field of the other electrons. No allowance is made for the correlation of the motion of different electrons with each other. As we will see below, the Hartree-Fock method is not the most general orbital approximation. This is because it imposes the unnecessary but highly convenient condition that the orbitals be orthogonal to each other, and also imposes a specific spin-coupling scheme on the wavefunction. 

It is useful at this juncture to point out that some forms of Fe, as well as other transition elements, can exist in diamagnetic forms as well as in forms containing an even number of electrons. For the first there can be no EPR since there is no magnetic moment. For the latter situation, exemplified by high-spin Fe(II) and Mn(III), EPR may be observable using special methods, or may not be observable at the conventional frequencies. (For details, see [22].) In the case of Fe, however, one has the option of employing Mossbauer spectroscopy. It is useful in all oxidation states and spin-coupling schemes. 

Nuclear spin coupling scheme J + 1 =F where I refers to the outer N nucleus. 

Nuclear spin coupling scheme /+/j = F where /] refers to the N nucleus. 

In this chapter, we reviewed different quantum chemical approaches to determine local quantities from (multireference) wave functions in order to provide a qualitative interpretation of the chemical bond in open-shell molecules. Chemical bonding in open-shell systems can be described by covalent interactions and electron-spin coupling schemes. For different definitions of the (effective) bond order as well as various decomposition schemes of the total molecular spin expectation value into local contributions, advantages and shortcomings have been pointed out. For open-sheU systems, the spin density distribution is an essential ingredient in the... 

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