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Introduction to Atomic and Molecular Orbitals

Covalent bonding's more detailed model requires a consideration of valence shell atomic orbitals. For the elements of second period like oxygen, carbon and nitrogen, these orbitals have been designated 2s, 2px, 2py & 2pz. Spatial distribution of electrons that is occupying each of these orbitals is displayed in the diagram. 

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The carbon's valence shell electron configuration is 2s2, 2px1, 2py1 & 2pz0. In the covalent bonding if this was a configuration that is used, then the carbon would only be able to form two bonds. In this case, valence shell would contain six electrons- two shy of an octet. Even Though, the tetrahedral structures of carbon and methane tetrachloride demonstrate that carbon can form four equivalent bonds, leading to desired octet. The Linus Pauling proposed an orbital hybridization model to describe this covalent bonding, in which all the valence shell electrons of carbon are reorganized.

Hybrid Orbitals

The 2s and three 2p orbitals are converted to four equivalent hybrid atomic orbitals to explain the structure of methane (CH4), each one having 25% s and 75% p character, and represented as sp3. These hybrid orbitals have a particular orientation and four are naturally oriented in a tetrahedral fashion. So, the four covalent bonds of methane consist of shared electron pairs with four hydrogen atoms in a tetrahedral configuration, by the theory of VSEPR this can be predicted.

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Molecular Orbitals
Like the valence electrons of atoms occupy atomic orbitals (AO), the shared electron pairs of covalently bonded atoms can be thought of as occupying molecular orbitals (MO). It is suitable to approximate molecular orbitals by mixing two or more atomic orbitals. Usually, that mixing of n atomic orbitals always generates n molecular orbitals. A simple example of MO formation is provided by Hydrogen molecule. In the picture, to give a sigma (σ) bonding (low energy) molecular orbital the two 1s atomic orbitals are combined and a second higher energy MO represented as an antibonding orbital. By two electrons of opposite spin the Bonding MO is occupied, result is being a covalent bond.

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The notation that is used for molecular orbitals parallels that used for atomic orbitals. So, s-orbitals contain a spherical symmetry surrounding a single nucleus, and σ-orbitals have a cylindrical symmetry and include two (or more) nuclei. In case of bonds between second period elements, to form molecular orbitals, p-orbitals or the hybrid atomic orbitals having p-orbital character are used. For an instance, the sigma molecular orbital that serves to bond two fluorine atoms together is generated by the overlap of p-orbitals (part A below) and two sp3 hybrid orbitals of carbon can be combine to give a similar sigma orbital, while by a pair of electrons these bonding orbitals are occupied, a covalent bond,  sigma bond results. Even Though, we have ignored the remaining p-orbitals, their inclusion in the molecular orbital treatment does not lead to any additional bonding, as may be displays by activating fluorine correlation picture below.

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One instance of the benefit offered from the molecular orbital approach to bonding is the oxygen molecule. Here, the picture correctly describes the paramagnetic character of this simple diatomic compound. Likewise, the diagram of the orbital correlation for methane provides one more example of the variation in electron density predicted by molecular orbital calculations from that of the localized bond model.

By the red and blue colored spheres or ellipses, P-orbitals in this model are represented, which stand for the different phases, described by the mathematical wave equations for this type of orbitals.

At last, in case of carbon atoms with only two bonding partners, for the sigma bonds only two hybrid orbitals are needed and these sp hybrid orbitals are directed 180º from each other. The Two p-orbitals not used on each sp hybridized atom and these overlap to give the two pi-bonds

Following formation of a sigma bond (a triple bond), such as shown in the diagram.

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