Valence bond calculation

Raimondi, M., Campion, W. and Karplus, M. (1977) Convergence of the valence bond calculations... 

We discuss all of the key features of our current CASVB methodology for modem valence bond calculations on ground and excited states. The CASVB strategy may be used to generate compact representations of CASSCF wavefunctions or, alternatively, to perform the fully-variational optimization of various general types ofVB wavefunction. We report also a new application, namely to the fourteen % electrons of a planar dimethylenecyclobu-tadiene chain with three rings. 

An Overview of the CASVB Approach to Modem Valence Bond Calculations... 

T. Thorsteinsson, D.L. Cooper, J. Gerratt and M. Raimondi A New Approach to Valence Bond Calculations CASVB, in R. McWeeny, J. Mamani, Y.G. Smeyers and S. Wilson (Eds.), Quantum Systems in Chemistry and Physics Trends in Methods and Applications, Kluwer Academic Publishers, Dordrecht (1997). 

Special attention has been dedicated to the study of the basis set superposition error (BSSE). The SCF-Ml algorithm which excludes the BSSE from the SCF function was employed. A multi configuration version of it, particularly suited to study proton transfer effects, has been formulated. The use of these techniques has led to binding energy values which show a better stability against variation of the basis set, when compared with standard SCF results. For a more complete evaluation of the advantages of the a priori strategy to avoid BSSE see references [47-50], where applications to the study of the water properties are reported, and reference [51], where the Spin Coupled Valence Bond calculations for the He-LiH system are presented. 

An overview of the CASVB approach to modern valence bond calculations 303... 

Valence bond calculations indicate that the M-C intermediate is more stable than the M-O-C intermediate by 7 kcal/mol. This reinforces the ideas presented earlier. The lack of ready decomposition pathways in conjunction to their intrinsic stability renders M-C intermediates susceptible to oxidative dehydrogenation. They stay on the surface until they are completely oxidized to CO,. 

Use of this wave function with Eq. (19) then yields a theoretical value for Ahh in CH4 of 12.5 cps which is to be compared with the experimental value of 12.3 0.6 cps. Valence bond calculations of this nature have successfully accounted for the variation with H—C—H angle of the proton-proton coupling constants in substituted methanes (45) (Fig. 3), for the difference between AHwcls and AHwran across double bonds in ethylenes, and for the difference between AHH [Pg.241]

The valence bond calculation as carried out on the allyl radical, however, gives the spin density distribution (75)... 

An experimental determination of the spin density distribution in the allyl radical recently has become available (30) and is in fair agreement with the results of the valence bond calculation and in somewhat better agreement with an extended Hartree-Foek calculation to be described below. It is seen that although the allyl radical possesses only a single unpaired electron, the total calculated ir-electron spin density on the molecule is % to % units depending on the approximation employed. However, the relationship (75)... 

In both the extended Hartree-Fock calculation and the valence bond calculation effects of spin correlation are included, but not in the simple Huckel scheme. The x-energy levels for the allyl radical arc shown schematically below. 

Qualitatively, the resonance picture is often used to describe the structure of molecules, but quantitative valence-bond calculations become much more difficult as the structures become more complicated (e.g., naphthalene, pyridine, etc.). Therefore the molecular-orbital method is used much more often for the solution of wave equations.5 If we look at benzene by this method (qualitatively), we see that each carbon atom, being connected to three other atoms, uses sp1 orbitals to form a bonds, so that all 12 atoms are in one plane. Each carbon has a p orbital (containing one electron) remaining and each of these can overlap equally with the two adjacent p orbitals. This overlap of six orbitals (see Figure 2.1) produces six new orbitals, three of which (shown) are bonding. These three (called it orbitals) all occupy approximately the same space.6 One of the three is of lower energy than... 

Valence-bond calculations of 13C chemical shift parameters of alkanes permit the following general conclusions [204]. 

TABLE 2. Hybridization and overlap values obtained with non-orthogonal hybrid orbitals within a valence bond calculation of cyclopropane"... 

TABLE 3. Overlap values calculated using non-ortliogonal hybrid orbitals within valence bond calculations of propane, cyclopropane and cyclobutane"... 

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