Molecular orbital model sigma

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. 

FIGURE 1.25 (a) A wedge-dashed wedge formula for the sigma bonds in ethene and a schematic depiction of the overlapping of adjacent p orbitals that form the tt bond, (b) A calculated structure for ethene. The blue and red colors indicate opposite phase signs in each lobe of the tt molecular orbital. A ball-and-stick model for the o- bonds in ethene can be seen through the mesh that indicates the ir bond. 

Antibonding molecular Dipole moment (/u), p. 420 orbital, p. 440 Homonuclear diatomic Bond order, p. 444 molecule, p. 445 Bonding molecular Hybrid orbital, p. 428 orbital, p. 440 Hybridization, p. 428 Delocalized molecular Molecular orbital, p. 440 orbital, p. 449 Nonpolar molecule, p. 421 Pi bond (77 bond), p. 437 Valence-shell electron-pair Pi molecular orbital, p. 443 repulsion (VSEPR) Polar molecule, p. 421 model, p. 410 Sigma bond (cr bond), p. 437 Sigma molecular orbital, p. 441 Valence shell, p. 410... 

In Chapter 3, Section 3.5, molecular orbitals described the bonding in alkanes using the hybridization model. Specifically, sp hybrid orbitals overlap to form a sigma-covalent bond (a o-bond). It is possible to have two covalent bonds between adjacent carbon atoms, a carbon-carbon double bond. One of the two bonds is the usual o-bond, but the other is called a 7i-bond. Hydrocarbons that contain one 7t-bond are called alkenes. In other words, an alkene will have a C=C unit. Each carbon atom of the C=C unit will have four bonds, but only three of the bonds are o-bonds, and the fourth bond is a 7i-bond. 

Each sp hybrid orbital is shaped like a p orbital, except that its two lobes are of unequal size (Fig. 19.1). In order to simplify the use of orbital pictures for molecules, the small lobes are omitted. The four sp hybrid AO s overlap head-to-head with die Is AO of each of the four H atoms to form four tr and four molecular orbitals. In general, bonds formed from hybrid AO s fabricated from s and p atomic orbitals will be sigma bonds. The 8 electrons needed for bonding (4 from C and 4 from the H atoms) fill the four cr MO s. Each a- MO encompasses only the C atom and the particular H atom—it is said to be a localized two-centered MO. A more sophisticated model involves delocalized mul-ticentered MO s, each of which encompasses the entire molecule. As we shall see later, for some purposes the delocalized description is needed but in general all tr and most tt bonds can be assumed to be localized two-centered molecular orbitals. 

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