S-T energy separations

Table 30.2. S-T energy separations (negative, in kJ/m), at a) TCSCF/ECP-31g(d) (ECP from Stevens, Basch, and Krauss) and b) UDFT (B3LYP/6-31g(d)) level on the various biradicals in silsesquioxanes.

The values ( 1) reflect the biradical character in the silsesquioxanes (the lowest singlet and triplet energies strongly mixed in the unrestricted wavefunction), in agreement with the fairly small S-T energy separations. In fact, the S-T separations are smaller than in trimethylene (see Table 30.1). This indicates that these species, exemplified here by the various cube structures, behave as electronic isolators , as witnessed in the experimental investigations. At least this is strongly dictated for the 1.4-biradical structure-type. 

The value is consistant with the previous considerations on the 1.2- to 1.4-biradical structures, with fairly small S-T energy separations. It indicates that in the TM-substituted silsesquioxanes the transition metal fragment can be readily oxidized at the metal center, but a delocalization over the cube does not take place. More generally, spin-delocalization is interrupted by the electronegative atoms linking the silicon centers. A similar phenomenon is observed for the spin-spin interactions in the resulting cubes with phosphaneiminato ligands. 

Table 11. Electronic origins, S,—T, energy separations, barrier heights, and out-of-plane angles of the Sj states of XjC = Y and XZC=Y molecules. ...

The origin of postulate (iii) lies in the electron-nuclear hyperfine interaction. If the energy separation between the T and S states of the radical pair is of the same order of magnitude as then the hyperfine interaction can represent a driving force for T-S mixing and this depends on the nuclear spin state. Only a relatively small preference for one spin-state compared with the other is necessary in the T-S mixing process in order to overcome the Boltzmann polarization (1 in 10 ). The effect is to make n.m.r. spectroscopy a much more sensitive technique in systems displaying CIDNP than in systems where only Boltzmann distributions of nuclear spin states obtain. More detailed consideration of postulate (iii) is deferred until Section II,D. 

For T i-S mixing in a system with only one proton, S(a) and S(j3) T i(a) are the only allowed transitions. The energy separation (and hence the transition probability) between these states depends critically upon the values of a-s, and the magnetic field Hj) in which the reaction is conducted. Qualitative conclusions concerning the effects of T i-S mixing on the observed polarization, applicable to a single group of nuclei, can be summarized as follows ... 

However, there are as yet no complete theories of solids and liquids from which A H, and A S, can be separately calculated. Because of this Bunn (1955) turned to the cohesive energy, E, A Hv— R T, where A Hv is the heat of vaporization per mole at the boiling point) for a property with which to compare melting points. He obtained many remarkable correlations in the case of monomeric substances after he had classified the monomers with respect to shape and flexibility. Prigogine and Defay (1954), have summarized generalizations with respect to AS, as follows ... 

---