NPSO structures

Figure 3. Lewis-Kekule and npso structures for C3H5+, C3H5 and C3H5".

The (primarily) minimal basis set calculations of Linnett and co-workers [19] demonstrate clearly that the npso structures with one-electron bonds... 

If we want to use one valence-bond structure to summarize resonance between the long-bond structure (2) and other canonical stiuctures, in Section 23-4 we have found that we may also use the NPSO structure (10). Because this structure summarizes resonance between the canonical structures (1), (2), (3) and (4), T (NPSO) must generate a lower energy than do the wave-functions for either... 

After the CASSCF calculation with the above choice of orbitals, in order to perform an efficient VB analysis, it is better in this case to resort to an overcomplete non-orthogonal hybrid set. The five active orbitals, in fact, can be split into ten hybrids, in term of which the VB transcription of the wavefunction turns out to be the simplest and the most compact. Such kinds of overcomplete basis sets are commonly used in constructing the so called non-paired spatial orbital structures (NPSO, see for example [35]), but it should be remarked that their use is restricted to gradient methods of wavefunction optimization, such as steepest descent, because other methods, which need to invert the hessian matrix (like Newton--Raphson) clearly have problems with singularities. 

Both T (IVHL) and T (IVBO) include the standard and long-bond structure wavefimctions Tj and Tu. In Table 23-3, the P(TVHL) and the T(NPSO) are the low-energy functions in each case, with T(NPSO) being the slightly better function. 

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