Molecular orbitals repulsion theory

Kao and Huang employed molecular mechanics and ab initio molecular orbital (MO) theory to determine the structure, energies, and conformations of the (Z)- (40, R = H) and ( )- (12, R1 - R4 = H) isomers. For the (Z)-isomer, an unsymmetrical conformation (67) is favored by at least 6 kcal over symmetrical chair, boat, and twist forms, which suffer from ethane-type and other H-H repulsions. In the case of ( )-isomer, the twist... 

In molecular orbital (MO) theory, which is the most common implementation of QM used by chemists, electrons are distributed around the atomic nuclei until they reach a so-called self-consistent field (SCF), that is, until the attractive and repulsive forces between all the particles (electrons and nuclei) are in a steady state, and the energy is at a minimum. An SCF calculation yields the electronic wave function 4C (the electronic motion being separable from nuclear motion thanks to the Born-Oppenheimer approximation). This is the type of wave function usually referred to in the literature and in the rest of this chapter. 

Last, you have learned to predict the three-dimensional structure of molecules using the valence shell electron pair repulsion (VSEPR) model and molecular orbital (MO) theory. An ability to predict three-dimensional structure is critical to understanding the properties and reactivity of molecules. 

Organic chemists led the way in picturing molecular bonding. They relied on such concepts as radicals (which kept their identity through various reactions) and atoms with a fixed valence or combining power. Once the electron was discovered in the early part of the twentieth century, Lewis was able to explain some aspects of bonding on the basis of his electron-dot formulas and the octet mle. The valence-shell electron-pair repulsion (VSEPR), valence-bond (VB), and molecular orbital (MO) theories followed in the 1930s. 

Other approximate, more empirical methods are the extended Huckel 31> and hybrid-based Hiickel 32. 3> approaches. In these methods the electron repulsion is not taken into account explicitly. These are extensions of the early Huckel molecular orbitals 4> which have successfully been used in the n electron system of planar molecules. On account of the simplest feature of calculation, the Hiickel method has made possible the first quantum mechanical interpretation of the classical electronic theory of organic chemistry and has given a reasonable explanation for the chemical reactivity of sizable conjugated molecules. 

All lone pair orbitals have a node between the two atoms and, hence, have a slightly antibonding character. This destabilizing effect of the lone pair localized molecular orbitals corresponds to the nonbonded repulsions between lone pair atomic orbitals in the valence bond theory. In the MO theory all bonding and antibonding resonance effects can be described as sums of contributions from orthogonal molecular orbitals. Hence, the nonbonded repulsions appear here as intra-orbital antibonding effects in contrast to the valence-bond description. 

Like atomic orbitals (AOs), molecular orbitals (MOs) are conveniently described by quantum mechanics theory. Nevertheless, the approach is more complex, because the interaction involves not simply one proton and one electron, as in the case of AOs, but several protons and electrons. For instance, in the simple case of two hydrogen atoms combined in a diatomic molecule, the bulk coulombic energy generated by the various interactions is given by four attractive effects (proton-electron) and two repulsive effects (proton-proton and electron-electron cf figure 1.20) ... 

The basis of the VSEPR theory is that the shape of a molecule (or the geometry around any particular atom connected to at least two other atoms) is assumed to be dependent upon the minimization of the repulsive forces operating between the pairs of sigma (a) valence electrons. This is an important restriction. Any pi (7t) or delta (8) pairs are discounted in arriving at a decision about the molecular shape. The terms sigma , pi and delta refer to the type of overlap undertaken by the contributory atomic orbitals in producing the molecular orbitals, and are referred to by their Greek-letter symbols in the remainder of the book. 

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