MCVB calculation

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. 

The basis described was used to generate one Is occupied and four virtual RHF orbitals. Using these afull calculation yields 250 standard tableaux functions, which may be combined into 125 functions of symmetry. The results for energy, bond distance, and vibrational frequency are shown in Table 10.5. We see that the agreement for is within 0.1 eV, for Re is within 0.01 A, and for cOe is within 20 cm . Even at the equilibrium nuclear separation, the wave function is dominated 

The three orbitals we use are two we label I q and l , that are symmetrically equivalent and one 2 that has the symmetry indicated. Thus if a is the horizontal 

When these orbitals are optimized, the energies of the SCVB wave functions are higher, of course, than those of the full MCVB wave functions. We show the differences at the equilibrium and infinite intemuclear separations in Table 10.6. The energy curves are parallel within s 0.1 eV, but the SCVB energy is about 1.1 eV higher. 

Because of the spatial symmetry there is only one configuration (as with allyl), and in this case the HLSP function function is the simpler of the two. We have for 

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In Table 2.8 we show a comparison of the EGSO weights for the two full MCVB calculations we have made with orthogonalized Gaussian bases. These are quite close to one another. We have only listed functions with weights > 0.001, and in each case there are five. 

The SCVB method can also be used to study the tt system of the allyl radical. As we have seen already, only one of the two standard tableaux ffinctions is required because of the symmetry of the molecule. We show the results in Table 10.4, where we see that one arrives at 85% of the correlation energy from the largest MCVB calculation in Table 10.2. There is no entry in Table 10.4 for the EGSO weight, since it would be 1, of course. 

A full MCVB calculation on BeH with the above basis yields 504 doublet standard tableaux functions, and these combine into 344 symmetry functions. In Table 10.7 we give some details of the results with experimental values for comparison. The calculated is within 0.1 eV of the experimental value, the values of... 

Figure 10.5. The dipole moment function from the MCVB calculation of BeH. The vertical dotted line marks the calculated equihbrium intemuclear distance.

The author and his students have used the term multiconfiguration valence bond (MCVB) to describe a linear variation calculation involving more than one VB structure (function). This practice will be continued in the present book. Other terms have been used that mean essentially the same thing[34]. We defer a fuller... 

It will be recalled by examining Table 2.3 that there are 12 independent cr-AO-only VB functions in the MCVB. Our complementary orbital function has only five independent parameters, so it certainly cannot duplicate the MCVB energy, but it reproduces 96.8% of the binding energy of the latter calculation. 

In Table 10.3 we give data for smaller calculations of the allyl tv system. As expected, the MCVB energies increase as fewer basis functions are included, the... 

In these discussions of benzene and cyclobutadiene we have compared MCVB level calculations of the n system with SCF level calculations of the core. We do not expect that using correlated wave functions for core energies would change the results enough to give a different qualitative picture. 

Table 15.12. Core, it SCF, and tv MCVB energies for various calculations of naphthalene. An ST03G basis is used, and all energies are in hartrees.

The addition of the doubly ionic structures to the MCVB wave function produces an energy only 0.15 eV above the full calculation and, therefore, has produced just about all the necessary delocalization. 

At the same time molecular orbital (MO) methods were seeing a rapid development, also because of increased computational ability. These, at least on the surface, appear to provide a simpler approach to molecular structure calculations. Nevertheless, Matsen and Browne[32] made a forceful case for the use of MCVB methods, indicating the difficulties... 

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