High-spin molecules degenerate orbitals

The question of how to design high-spin organic molecules now reduces to the problem of how to arrange within a molecule many singly occupied degenerate orbitals that are orthogonal to one another. 

Both in atomic spectroscopy (describing gaseous atoms and ions sufficiently isolated from each other to be considered as free) and in M.O. theory, the approximation of configurations is introduced. In this approximation, each electron has an orbital y>, and each orbital may contain zero, one, or two electrons (with opposite spin-directions). However, in atoms and in molecules having a sufficiently high symmetry, systematically degenerate sets of orbitals may occur. In the case of such a partly filled set of orbitals, more than one energy level is often produced. The main reason for this is the interelectronic repulsion between the... 

Consider a free atom or molecule in which several electrons occupy but do not fill a set of orbitals, which need not all be degenerate. There will usually be many ways in which the electrons can be distributed, some of which will be of lower energy than others. The differences in energy will be determined by electron repulsion and the more stable arrangements will be those with the least electron repulsion destabilization. So, electron-electron repulsion will be relatively small if the electrons occupy orbitals which are spatially well separated it will be reduced yet more if the electrons have a high spin multiplicity, i.e. have parallel spins, because two electrons with parallel spins can never be in the same orbital. 

Only spatially degenerate states exhibit a first-order zero-field splitting. This condition restricts the phenomenon to atoms, diatomics, and highly symmetric polyatomic molecules. For a comparison with experiment, computed matrix elements of one or the other microscopic spin-orbit Hamiltonian have to be equated with those of a phenomenological operator. One has to be aware of the fact, however, that experimentally determined parameters are effective ones and may contain second-order contributions. Second-order SOC may be large, particularly in heavy element compounds. As discussed in the next section, it is not always distinguishable from first-order effects. 

Theory can now provide much valuable guidance and interpretive assistance to the mechanistic photochemist, and the evaluation of spin-orbit coupling matrix elements has become relatively routine. For the fairly large molecules of common interest, the level of calculation cannot be very high. In molecides composed of light atoms, the use of effective charges is, however, probably best avoided, and a case is pointed out in which its results are incorrect. It seems that the mean-field approximation is a superior way to simplify the computational effort. The use of at least a double zeta basis set with a method of wave function computation that includes electron correlation, such as CASSCF, appears to be imperative even for calculations that are meant to provide only semiquantitative results. The once-prevalent degenerate perturbation theory is now obsolete for quantitative work but will presumably remain in use for qualitative interpretations. 

For high rotational levels, or for a molecule like OH, for which the spin-orbit splitting is small, even for low J, the pattern of rotational/fme-structure levels approaches the Hund s case (b) limit. In this situation, it is not meaningful to speak of the projection quantum number Q. Rather, we first consider the rotational angular momentum N exclusive of the electron spin. This is then coupled with the spin to yield levels with total angular momentum J = A-I- land A -1. As before, there are two nearly degenerate pairs of levels associated... 

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