Valence-bond orbitals

Several methods of quantitative description of molecular structure based on the concepts of valence bond theory have been developed. These methods employ orbitals similar to localized valence bond orbitals, but permitting modest delocalization. These orbitals allow many fewer structures to be considered and remove the need for incorporating many ionic structures, in agreement with chemical intuition. To date, these methods have not been as widely applied in organic chemistry as MO calculations. They have, however, been successfully applied to fundamental structural issues. For example, successful quantitative treatments of the structure and energy of benzene and its heterocyclic analogs have been developed. It remains to be seen whether computations based on DFT and modem valence bond theory will come to rival the widely used MO programs in analysis and interpretation of stmcture and reactivity. 

Pauling, L., Herman, Z.S., Kamb, B.J. Reliability of the Pair-Defect-Sum Approximation for the Strength of Valence-Bond Orbitals Proc. Natl. Acad. Sci. (USA) 1982, 79, 1361— 1365. 

Such a spin-coupled wavefunction is optimized with respect to the core wavefunction (if applicable), as well as to the nonorthogonal valence bond orbitals,... 

We have outlined in the previous Section an efficient solution to the problem posed in (1). For the second point, one quickly realizes that the space 0 0 must take a full Cl (or, CASSCF) form, if no particular restrictions are to be placed on the valence bond orbitals. For the single-configuration spin-coupled wavefunction, there is for this reason an important link to N, N, A) CASSCF wavefunctions. 

We shall consider first the case of a spin-coupled wavefimction, as the requirements for an MCSC wavefimction may be easily derived from this. Our key assumption will be that the operators R induce permutations of the valence bond orbitals ... 

For the valence bond orbitals themselves, it is generally natural to specify a starting guess in the AO basis. Such a guess might, of course, not lie entirely inside the space spanned by the active space, and it must therefore be projected onto the space of the active MOs. This is achieved trivially in CASVB, by multiplication by the inverse of the matrix of MO coefficients. 

Figure 6-22 Generalized valence-bond orbitals calculated for ethene by the ab initio method. The nuclei are located in the x,y plane of the coordinate system at the positions indicated by crosses. The long dashes correspond to locations of change of phase. The dotted lines are contour lines of electron amplitude of opposite phase to the solid lines. Top shows both m-bonding carbon orbitals (almost sp2), middle-left is the carbon orbital and middle-right the hydrogen orbital of one of the C-H bonds, and bottom represents a side view of the ir orbitals in perpendicular section to the x,y plane. (Drawings furnished by Dr. W, A. Goddard, III.)...

Describe the bonding in [Mn(CN)g]3-, using both crystal field theory and valence bond theory. Include the appropriate crystal field d orbital energy-level diagram and the valence bond orbital diagram. Which model allows you to predict the number of unpaired electrons How many do you expect ... 

In this expansion, each of the are separate valence bond orbital (VBO) structures in which the orbitals are non-orthogonal. Each such VBO structure... 

Figure 1. Schematic valence bond orbital (a) and valence bond spin (b) structures of CH4.

In a time-dependent picture, one can imagine an electron being annihilated from a specific valence bond orbital at time t=0. This is obviously not a stationary state of the ion and hence one must follow the time dependent evolution of the system from this initial condition. This requires solving the time-dependent Schrodinger equation which may be written as the following set of coupled equations for the time dependent probabihty amplitudes, aj (t) ... 

Figure 3. Schematic valence bond orbital representation of the CH and CC bonds in acetylene.

As with the smaller compounds, reliable computational descriptions of methyl phenyl sulfoxide excited states are not available. Ground state computations are easily accessible for molecules of this size. At the RHF/6-31G(d,p) level, the HOMO is 7t with regard to the SO bond but delocalized throughout the whole n-system. The next two descending orbitals are localized on the phenyl and SO, respectively. (The sulfur lone pair is the HOMO-2 when the valence bond orbitals are approximated by the Edmiston-Ruedenberg method.) While the LUMO is extensively delocalized, the LUMO-fl is entirely localized on the phenyl ring. 

Figure 3.3 Natural and generalized valence bond orbitals of SF/OF(X n, a L ) at the AVTZ level, (a) Natural orbitals for SF and OF states (b) Generalized Valence Bond orbitals for SF and OF states.

Figure 3.4 Natural and generalized valence bond orbitals of Sp2(X A, b Aj) at the...

Figure 3.5 Generalized valence bond orbitals for SF(a E ) + F( P) separations at the AVTZ level.

Reliability of the pair-defect-sum approximation for the strength of valence-bond orbitals. Proc. Natl. Acad. Sci. 79 (1982) 1361—1365. (Linus Pauling, Zelek S. Herman, and Barclay J. Kamb). 

In the next few sections we ll examine the application of the valence bond-orbital hybridization model to alkenes and alkynes, then return to other aspects of alkanes in Section 2.11. We ll begin with ethylene. 

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