Spin-pairing parameter

The results of the derivation (which is reproduced in Appendix A) are summarized in Figure 7. This figure applies to both reactive and resonance stabilized (such as benzene) systems. The compounds A and B are the reactant and product in a pericyclic reaction, or the two equivalent Kekule structures in an aromatic system. The parameter t, is the reaction coordinate in a pericyclic reaction or the coordinate interchanging two Kekule structures in aromatic (and antiaromatic) systems. The avoided crossing model [26-28] predicts that the two eigenfunctions of the two-state system may be fomred by in-phase and out-of-phase combinations of the noninteracting basic states A) and B). State A) differs from B) by the spin-pairing scheme. 

Subsequently, LFMM was extended with an explicit spin-pairing energy (18). This is an empirical term with the same functional form as the AOM parameters (Eq. 7) and is significantly easier to implement than to express the ligand field stabilization energy as a function of the many-electron Russell-Saunders terms (60). Preliminary indications (61) for Fe(II) species suggest the approach is satisfactory and we expect to be able to use LFMM to study phenomena like spin crossover. 

Figure 4. (a,b) The 89Y spin cut-off parameter, a1, vs E, and the spin distribution, P(J), obtained from 60 discrete levels and from calculations with k values of 0.146 and 0.24. At energies below the pairing energy, the value of a2 is arbitrarily held constant and equal to (6/tt2) (A A2/3). (c,d) The MY spin cutoff parameter and the spin distribution obtained from 25 discrete levels and from calculations with k values of 0.146 and 0.29. 

In order to reduce the dimension of the model space, several attempts have been made to find associated topological quantum numbers which would allow to separate the covalent VB space into non-mixing different subspaces (see Ref. 30 and references therein). For the linear chain, preliminary attempts were made early in 1979 [31], when a parameter measuring the spin-pairing long-range order was suggested,... 

Since the specific form of the existing and missing multiplets in the wave function (26) on each of the two nearest neighbor spin pairs depends on the parameters x and y, the projectors in (29) also depend on x and y. Each projector can be written in the form... 

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