Orbital equivalent

A suitable frame for the discussion places the tetrahedral molecular ion so that the two-fold rotation axes are the coordinate axes. We choose to represent the three degenerate ti-orbitals by their/-orbital equivalents ... 

A In fully ionic oxides the oxygen species present is O therefore the oxidation slate of the oxygen is equal to the charge, i.e. 2. This value is taken to he the oxidation stale of oxygen in compounds that are not necessarily ionic. The oxide ion has the fully occupied valence orbitals equivalent to the electronic eonliguralion ol neon. 2j 2p<. the Group IS element at the end of the same period. 

Localized orbitals Equivalent molecular orbital method31 32) Group orbital method34) Two-center molecular orbital method27) Second-order perturbation method124) ... 

It is possible to analyse the preceding results in terms of chemical concepts, provided that the ground and excited configurations of the perturbation calculation are built from localized orbitals equivalent to the standard molecular orbital. The various t3q>es of excitations are indicated in Table 1. 

In the general case there is degeneracy at the non-relativistic level, which is split by relativity. Then one must, after having performed the nonrel-ativistic calculation, extend the active space at orbital level by including all spin orbitals equivalent by symmetry. One then needs a matrix representation of the operator H2 in this basis to get the perturbation-adapted unperturbed states by diagonalizing this matrix representation. 

In quantum terms, we may describe the phenomena as follows (see Fig. 14). In the acceptor layer, for example, there would be an anion radical with neighbors on either side with vacant orbitals equivalent to the one occupied by the extra electron. This electron in its migration, i.e., when it moves from one molecule to the next one, produces a state after the reaction [as in (1), Fig. 14] shown in the top row of Fig. 14 which is identical in energy with the starting point. The same thing can be said of the donor layer with its hole, which can have electron migra-... 

The character of the representation induced by three v-bond orbitals equivalently disposed in a plane, as in BF3 or NO7, is as follows (D symmetry) ... 

It took a little while for the full power of the WE theorem to be appreciated. In its most obvious applications, it allows any vector operator to be replaced by another provided a proportionality constant is included. For example, we can write L+2S = gJ since L, S and J all satisfy similar commutation relations with respect to J. The spin-orbit equivalence. 

Valence-bond structures with Pauling 3-electron bonds between pairs of atoms may be constructed for a number of triatomic radicals. Here we shall examine these types of structures for some radicals with either 17 or 19 valence-shell electrons. For these systems, it is necessary to involve the participation in resonance of two Pauling 3-electron bond structures. The delocalized molecular orbital equivalent of this resonance involves the construction of three 3-centre molecular orbitals to accommodate five electrons this is described in Section 6-4. 

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