Valence bond orbital structures

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. 

On a more qualitative level, the bonding in the more stable isomer lb can be explained on the basis of the general molecular orbital scheme for bent (C2v) metallocenes containing 14 valence electrons, as shown in Fig. 5. The localization of three electron pairs in bonding orbitals (lal, 2 i, 2b2) is primarily responsible for the Si-Cp interaction the absence of a silicon orbital of a2 symmetry imposes the presence of a ligand-based non-bonding orbital. Structural adjustment from D5d (ferrocene type) to C2v... 

The complete active space valence bond (CASVB) method is an approach for interpreting complete active space self-consistent field (CASSCF) wave functions by means of valence bond resonance structures built on atom-like localized orbitals. The transformation from CASSCF to CASVB wave functions does not change the variational space, and thus it is done without loss of information on the total energy and wave function. In the present article, some applications of the CASVB method to chemical reactions are reviewed following a brief introduction to this method unimolecular dissociation reaction of formaldehyde, H2CO — H2+CO, and hydrogen exchange reactions, H2+X — H+HX (X=F, Cl, Br, and I). 

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.

Figure 9-11 Representations of the bonding in the benzene molecule, CgHg. (a) Lewis formulas of the two valence bond resonance structures, (b) The six p orbitals of the benzene ring, shown overlapping to form the (hypothetical) double bonds of the two resonance forms of valence bond theory, (c) In the MO description the six electrons in the pi-bonded region are dehcalized, meaning they occupy an extended pi-bonding region above and below the plane of the six C atoms.

Representation of the /i-orbital overlap in the valence bond resonance structures, In each resonance form, the p orbitals on two atoms would overlap to form then components of the hypothetical double bonds. Each 0 atom has two additional sp2 orbitals (not shown) in the plane of the nuclei. Each of these additional sp orbitals contains an oxygen unshared pair. 

A point to bear in mind is that there are different types of excited states, and each of them has different theoretical requirements. A valence state can be viewed as a promotion from one occupied molecular orbital to a virtual one. On the other hand, a Rydberg state, in a simple MO theory, is the result of exciting one electron from one occupied molecular orbital to an atomic-like orbital of higher quantum number. Valence excited states are more compact than the diffuse Rydberg states. A valence state can be denoted as covalent or zwitterionic according to the type of valence bond (VB) structures. Covalent and zwitterionic states are described by... 

In practice, each CSF is a Slater determinant of molecular orbitals, which are divided into three types inactive (doubly occupied), virtual (unoccupied), and active (variable occupancy). The active orbitals are used to build up the various CSFs, and so introduce flexibility into the wave function by including configurations that can describe different situations. Approximate electronic-state wave functions are then provided by the eigenfunctions of the electronic Flamiltonian in the CSF basis. This contrasts to standard FIF theory in which only a single determinant is used, without active orbitals. The use of CSFs, gives the MCSCF wave function a structure that can be interpreted using chemical pictures of electronic configurations [229]. An interpretation in terms of valence bond sti uctures has also been developed, which is very useful for description of a chemical process (see the appendix in [230] and references cited therein). 

We describe here a new structure representation which extends the valence bond concept by new bond types that account for multi-haptic and electron-deficient bonds. This representation is called Representation Architecture for Molecular Structures by Electron Systems (RAMSES) it tries to incorporate ideas from Molecular Orbital (MO) Theory [8T]. 

A is a parameter that can be varied to give the correct amount of ionic character. Another way to view the valence bond picture is that the incorporation of ionic character corrects the overemphasis that the valence bond treatment places on electron correlation. The molecular orbital wavefimction underestimates electron correlation and requires methods such as configuration interaction to correct for it. Although the presence of ionic structures in species such as H2 appears coimterintuitive to many chemists, such species are widely used to explain certain other phenomena such as the ortho/para or meta directing properties of substituted benzene compounds imder electrophilic attack. Moverover, it has been shown that the ionic structures correspond to the deformation of the atomic orbitals when daey are involved in chemical bonds. 

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