SCVB treatment

These Li atom calculations used Huzinaga s (10/73) basis set[48], further split to (10/73/5221) to yield four basis functions. This is an 5 only basis, so our treatments will not produce any angular correlation, but the principles are well illustrated, nevertheless. 

There is no added symmetry in this example to cause one of the standard tableaux functions to disappear. Thus, the SCVB wave function is 

In terms of the primitive split Gaussian basis, we obtain for the three SCVB orbitals 

10 Four simple three-electron systems Table 10.13. Results ofMCVB calculation for Li. 

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The HeJ ion has the archetype three-electron bond originally described by Pauling [1], and this section gives a description of MCVB calculation and SCVB treatments for this system. All of these use a Huzinaga 6-G Is function split (411), a 4-G 2s function and a pz function with the scale set to 0.9605. We take up the MCVB treatment first. 

In this section we give the results of MCVB and SCVB treatments of BeH using a conventional 6-3IG basis. Although there are some similarities to the HeJ ion, the lack of g-u symmetry in this case introduces a number of interesting... 

The allyl radical and the He ion both have end-for-end s mimetry and thus the corresponding orbital SCVB treatment is applied. Consequently, there was only one tableau function in each of those cases. BeH is different in this regard. In the... 

Table 10.11. Coefficients and tableaux for standard tableaux functions and HLSP functions for SCVB treatment of BeH.

We have so far emphasized the nature of the wave function. We now examine the energies of some different arrangements ofthe bases. In Table 15.2 we show energies for five levels of calculation, Kekule-only, Kekule plus Dewar, SCF, SCVB, and full TV structures, where energies are given as the excess energy due to the tv system over that from the core. Cooper eta/. [61] gave the SCVB treatment of benzene. 

As the SCVB treatment had already shown [22], the 71 system of benzene is correctly described by a one configuration (one chemical structure ) of singly occupied atomic-localized non-orthogonal orbitals, making a six-electron bond, with no resonance. 

Another alternative to the SCVB approach is provided by the SCVB treatment,in which one generates one or more optimal virtual orbitals for each occupied SC orbital and then employs these virtuals to construct a non-orthogonal Cl expansion. The simplest case involves the calculation of one optimal virtual orbital for each SC orbital i/. If the SC wavefunction (3.9) is augmented with all vertical double excitations into these virtuals. 

A SCVB wavefunction incorporating just 25 structures has been shown to produce highly accurate results for the He- -LiH van der Waals system, with marked improvements over a SCVB treatment making use of a much larger number of structures. 

In this chapter we describe four rather different three-electron systems the it system ofthe allyl radical, the HeJ ionic molecule, the valence orbitals ofthe BeHmolecule, and the Li atom. In line with the intent of Chapter 4, these treatments are included to introduce the reader to systems that are more complicated than those of Chapters 2 and 3, but simple enough to give detailed illustrations of the methods of Chapter 5. In each case we will examine MCVB results as an example of localized orbital treatments and SCVB results as an example of delocalized treatments. Of course, for Li this distinction is obscured because there is only a single nucleus, but there are, nevertheless, noteworthy points to be made for that system. The reader should refer back to Chapter 4 for a specific discussion of the three-electron spin problem, but we will nevertheless use the general notation developed in Chapter 5 to describe the results because it is more efficient. 

Table 10.10. Energy differences between SCVB andMCVB treatment of BeH.

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