Hybrid Orbitals and the Structure of Methane

The concept of hybridization explains how carbon forms four equivalent tetrahedral bonds but not why it does so. The shape of the hybrid orbital suggests the answer. When an s orbital hybridizes with three p orbitals, the resultant sp hybrid orbitals are unsymmetrical about the nucleus. One of the two lobes is larger than the other and can therefore overlap more effectively with an orbital from another atom to form a bond. As a result, sp hybrid orbitals form stronger bonds than do unhybridized s or 

The asymmetry of sp orbitals arises because, as noted previously, the two lobes of a p orbital have different algebraic signs, + and -, in the wave function. Thus, when a p orbital hybridizes with an s orbital, the positive p lobe adds to the s orbital but the negative p lobe subtracts from the s orbital. The resultant hybrid orbital is therefore imsymmetrical about the nucleus and is strongly oriented in one direction. 

Pauling was a scientific giant, who made fundamental discoveries in fields ranging from chemical bonding to molecular biology to medicine. A lifelong pacifist, 

Pauling is the only solo winner of two Nobel Prizes in different fields the first in 1954 for chemistry and the second in 1963 for peace. 

ActiveFlgure1.il The structure of methane, showing its 109.5 bond angles. Sign in at www.thomsonedu.com to see a 

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Atomic Structure The Nucleus Atomic Structure Orbitals 4 Atomic Structure Electron Configurations 6 Development of Chemical Bonding Theory 7 The Nature of Chemical Bonds Valence Bond Theory sp Hybrid Orbitals and the Structure of Methane 12 sp Hybrid Orbitals and the Structure of Ethane 13 sp2 Hybrid Orbitals and the Structure of Ethylene 14 sp Hybrid Orbitals and the Structure of Acetylene 17 Hybridization of Nitrogen, Oxygen, Phosphorus, and Sulfur 18 The Nature of Chemical Bonds Molecular Orbital Theory 20 Drawing Chemical Structures 21 Summary 24... 

It is known that, in the MO framework, the nondynamical electron correlation is accounted for by means of a so-called CASSCF calculation, which is nothing else than a full Cl in a given space of orbitals and electrons, in which the orbitals and the coefficients of the configurations are optimized simultaneously. If the active space includes all the valence orbitals and electrons, then the totality of the nondynamical correlation of the valence electrons is accounted for. In the VB framework, an equivalent VB calculation, defined with pure AOs or purely localized hybrid atomic orbitals (HAOs), would involve all the covalent and ionic structures that may possibly be generated for the molecule at hand. Note that the resulting covalent—ionic VB wave function would have the same dimension as the valence—CASSCF one (e.g., 1764 VB structures for methane, and 1764 MO SCF configurations in the CASSCF framework). 

Let us start by using the hybrid orbital method to predict the structure of methane. Methane, CH4, is composed of a carbon atom and four hydrogen atoms. The carbon atom has an electron configuration of Is2 2s2 2p2. Each hydrogen atom has an electron configuration of Is1. Experiments showed that the geometry of the... 

The universally accepted argument that explains the structure of methane in terms of the well known scheme of sp orbital hybridization derives from several statements and postulates originally formulated by Linus Pauling [1], Some of these... 

Hybrid atomic orbitals that account for the structure of methane can be derived from carbon s second-shell s and p orbitals as follows (Fig. 1.13) ... 

In contrast to the four tetrahedrally oriented elliptic orbits of the Sommer-feld model, the new theory leads to only three, mutually orthogonal orbitals, at variance with the known structure of methane. A further new theory that developed to overcome this problem is known as the theory of orbital hybridization. In order to simulate the carbon atom s basicity of four an additional orbital is clearly required. The only possible candidate is the 2s orbital, but because it lies at a much lower energy and has no angular momentum to match, it cannot possibly mix with the eigenfunctions on an equal footing. The precise manoeuvre to overcome this dilemma is never fully disclosed and appears to rely on the process of chemical resonance, invented by Pauling to address this, and other, problems. With resonance, it is assumed that, linear combinations of an s and three p eigenfunctions produce a set of hybrid orbitals with the required tetrahedral properties. 

Ketene looks pretty unlikely It is CH2=C=0 with two tt bonds (C=C and C=0) to the same carbon atom. The orbitals for these jt bonds must be orthogonal because the central carbon atom is sp hybridized with two linear o bonds and two p orbitals at right angles both to the o bonds and to each other. Can such a molecule exist When acetone vapour is heated to very high temperatures (700-750 °C) methane is given off and ketene is supposed to be the other product. What is isolated is a ketene dimer (C4H4O2) and even the structure of this is in doubt as two reasonable structures can be written. 

The first three geometries involve the tetrahedral, trigonal, and digonal hybrids discussed above and the fourth involves the use of pure s and p orbitals as discussed on page 149. The last structure contains three equivalent bonds at mutual angles of 60 and a fourth bond at an angle of approximately 145 to the others. It is impossible to construct s-p hybrid orbitals with angles less than 90 , and so structure V is ruled out. In this sense it may be said that hybridization does not allow structure V, but it may not be said that it chooses one of the others. Carbon hybridizes sp, sp, and sp in various compounds, and the choice of sp in methane is a result of the fact that the tetrahedral structure is the most stable possible. 

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