Molecular orbital theory sigma bonds

It is informative to compare methylene and nitrene in terms of simple molecular orbital theory and then to extend this comparison to their aromatic derivatives phenyl carbene and phenyl nitrene. Hoffman et al. [28] have described the molecular orbitals of CH2 in the following way. Methylene has two nonbonding molecular orbitals, one is an in-plane, a type, hybrid orbital, the other is an out-of-plane pure p type n orbital. Singlet methylene has a bond angle of 105° and the in-plane, sigma, orbital is doubly occupied. Triplet methylene has both a singly occupied n and a orbital and a bond angle of 135°. 

We can now state that each carbon-to-carbon linkage in benzene contains a sigma bond and a partial pi bond. The bond order between any two adjacent carbon atoms is therefore between 1 and 2. Thus molecular orbital theory offers an alternative to the resonance approach, which is based on valence bond theory. (The resonance structures of benzene are shown on p. 349.)... 

In this section, we focus on the mode by which orbitals overlap—end to end or side to side—to see the detailed makeup of covalent bonds. These two modes give rise to the two types of covalent bonds—sigma bonds and pi bonds. WeTl use valence bond theory to describe the two types here, but they are essential features of molecular orbital theory as well. 

An approximate treatment of tt electron systems was introduced in 1931 by Erich Huckel (Figure 15.17) and is called the Huckel approximation of tt orbitals. The first step in a Huckel approximation is to treat the sigma bonds separately from the pi bonds. Therefore, in a Huckel approximation of a molecule, only the tt bonds are considered. The usual assumption is that the <7 bonds are understood in terms of regular molecular orbital theory. The <7 bonds form the overall structure of the molecule, and the tt bonds spread out over, or span, the available carbon atoms. Such 77 bonds are formed from the side-on overlap of the carbon 2p orbitals. If we are assuming that the tt bonds are independent of the cr bonds, then we can assume that the 77 molecular orbitals are linear combinations of only the 2p orbitals of the various carbon atoms. [This is a natural consequence of our earlier linear combination of atomic orbitals—molecular orbitals (LCAO-MO) discussion.] Consider the molecule 1,3-butadiene (Figure 15.18). The tt orbitals are assumed to be combinations of the 2p atomic orbitals of the four carbon atoms involved in the conjugated double bonds ... 

A covalent bond is formed when an electron pair is shared between atoms. According to valence bond theory, electron sharing occurs by overlap of two atomic orbitals. According to molecular orbital (MO) theory, bonds result from the mathematical combination of atomic orbitals to give molecular orbitals, which belong to the entire molecule. Bonds that have a circular cross-section and are formed by head-on interaction are called sigma (cr) bonds bonds formed by sideways interaction ot p orbitals are called pi (77-) bonds. 

We start with some biographical notes on Erich Huckel, in the context of which we also mention the merits of Otto Schmidt, the inventor of the free-electron model. The basic assumptions behind the HMO (Huckel Molecular Orbital) model are discussed, and those aspects of this model are reviewed that make it still a powerful tool in Theoretical Chemistry. We ask whether HMO should be regarded as semiempirical or parameter-free. We present closed solutions for special classes of molecules, review the important concept of alternant hydrocarbons and point out how useful perturbation theory within the HMO model is. We then come to bond alternation and the question whether the pi or the sigma bonds are responsible for bond delocalization in benzene and related molecules. Mobius hydrocarbons and diamagnetic ring currents are other topics. We come to optimistic conclusions as to the further role of the HMO model, not as an approximation for the solution of the Schrodinger equation, but as a way towards the understanding of some aspects of the Chemical Bond. 

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