Orbital hybridisation

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In chemistry, hybridisation is the concept the mixing of atomic orbitals to form new hybrid orbitals suitable for the qualitative description of atomic bonding properties. Hybridised orbitals are very useful in the explanation of the shape of molecular orbitals for molecules. It is an integral part of the valence shell electron-pair repulsion (VSEPR) theory.

Historical development

The hybridisation theory was theorised by chemist Linus Pauling [1] in order to explain the existence of molecules such as methane (CH₄). Historically, this concept was necessary in order to explain the bonding observed in very simple chemical systems. It was later found to be more widely applicable, and today it is considered an effective heuristic for understanding organic chemistry.

It is less (or not) applicable to other branches of chemistry for which the d orbitals are involved. Transition metal chemistry is one example. Although hybridisation schemes in transition metal chemistry can be used, they are not accurate and have little predictive power. The result of this was a development of entirely new branches of bonding theory, and these are an active area of theoretical chemical research today.

It is important to note that orbitals are a model representation of how an electron around an atom behaves. In the case of simple hybridisation, this approximation is based on the atomic orbitals of hydrogen. Hybridised orbitals are assumed to be mixtures of these atomic orbitals, superimposed on each other in various different proportions. Hydrogen orbitals are used as a basis for simple schemes of hybridisation because it is one of the few examples of orbitals for which an exact analytic solution to its Schrödinger equation is known. These orbitals are then assumed to be slightly, but not significantly distorted in heavier atoms, like carbon, nitrogen, and oxygen. Under these assumptions is the theory of hybridisation most applicable. It must be noted, that one does not need hybridisation to describe molecules, but for molecules made up from carbon, nitrogen and oxygen (and to a lesser extend, sulphur and phosphorus) the hybridisation theory/model makes the description much easier.

Hybridisation theory

The hybridisation theory finds its use mainly in organic chemistry, and mostly concerns C, N and O (and to a lesser extent P and S).

The problem with methane

Hybridisation describes the bonding atoms from an atom's point of view. That is, for a tetrahedrally coordinated carbon (e.g. methane, CH₄), the carbon should have 4 orbitals with the correct symmetry to bond to the 4 hydrogen atoms. The problem with the existence of methane is now this: Carbon's ground-state configuration is 1s² 2s² 2p_x¹ 2p_y¹ or perhaps more easily read:

(Note: The 1s orbital is lower in energy than the 2s orbital, and the 2s orbital is lower in energy than the 2p orbitals)

The valence bond theory would predict, based on the existence of two half-filled p-type orbitals (the designations p_x p_y or p_z are meaningless at this point, as they do not fill in any particular order), that C forms two covalent bonds. CH₂. However, methylene is a very reactive molecule (see also: carbene) and cannot exist outside of a molecular system. Therefore, this theory alone cannot explain the existence of CH₄.

Furthermore, ground state orbitals cannot be used for bonding in CH₄. While exciting a 2s electron into a 2p orbital would theoretically allow for four bonds, according to the valence bond theory which has been proved experimentally correct for systems like O₂ this would imply that the various bonds of CH₄ would have differing energies due to differing levels of orbital overlap. Once again, this has been experimentally disproved: any hydrogen can be removed from a carbon with equal ease.

To summarise, to explain the existence of CH₄ (and many other molecules) a method by which as many as 12 bonds (for transition metals) of equal strength (and therefore equal length) can be created was required.

Application of hybridisation theory

The first step in hybridisation is the excitation of one (or more) electrons (we will have a look on the carbon atom in methane, for simplicity of the discussion):

The proton that forms the nucleus of a hydrogen atom attracts one of the valence electrons on carbon. This causes an excitation, moving a 2s electron into a 2p orbital. This, however, increases the influence of the carbon nucleus on the valence electrons by increasing the effective core potential (the amount of charge the nucleus exerts on a given electron = Charge of Core - Charge of all electrons closer to the nucleus).

The combination of these forces creates new mathematical functions known as hybridised orbitals. In the case of carbon attempting to bond with four hydrogens, four orbitals are required. Therefore, the 2s orbital (core orbitals are almost never involved in bonding) mixes with the three 2p orbitals to form four sp³ hybrids (read as s-p-three). See graphical summary below.

becomes

In CH₄, four sp³ hybridised orbitals are overlapped by hydrogen's 1s orbital, yielding four sigma (σ) bonds. The four bonds are of the same length and strength, and there are four of them. This theory fits our requirements.

translates into

Other C-compounds and other molecules may be explained similarly, for example ethene (C₂H₄). Therefore, ethene has a double bond between the carbons. The Lewis structure looks like this:

Image:Ethene.png

Carbon will sp² hybridise, because hybrid orbitals will form only sigma bonds and one pi bond is required for the double bond between the carbons. The hydrogen-carbon bonds are all of equal strength and length, which agrees with experimental data.

The amount of p-character is not restricted to integer values, i.e. hybridisations like sp^2.5 are also readily described. In this case the geometries are somewhat distorted from the ideally hybridised picture. For example, as stated in Bent's rule, a bond tends to have higher p-character when directed toward a more electronegative substituent.

Another solution to the problem

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An alternative view is: View the carbon as the C^4- anion. In this case all the orbitals on the carbon are filled:

If we now recombine these orbitals with the empty s-orbitals of 4 hydrogens (4 protons, H⁺) and allow maximum separation between the 4 hydrogens (i.e. tetrahedral surrounding of the carbon), we see that at any orientation of the p-orbitals, a single hydrogen has an overlap of 25% with the s-orbital of the C, and a total of 75% of overlap with the 3 p-orbitals (see that the relative percentages are the same as the character of the respective orbital in an sp³-hybridisation model, 25% s- and 75% p-character).

Hybridisation and molecule shape

Using hybridisation, along with the VSEPR theory, helps to explain molecule shape:

• AX₂ (eg, BeCl₂): sp hybridisation; linear or diagonal shape
• AX₃ (eg, BCl₃): sp² hybridisation; trigonal planar shape
• AX₄ (eg, CCl₄): sp³ hybridisation; tetrahedral shape
• AX₅ (eg, PCl₅): sp³d hybridisation; trigonal bipyramidal shape
• AX₆ (eg, SF₆): sp³d² hybridisation; octahedral (or square bipyramidal) shape

This holds if there are no lone electron pairs on the central atom. If there are, they should be counted in the X_i number, but bond angles become smaller due to increased repulsion. For example, in water (H₂O), the oxygen atom has two bonds with H and two lone electron pairs (as can be seen with the valence bond theory as well from the electronic configuration of oxygen), which means there are four such 'elements' on O. The model molecule is, then, AX₄: sp³ hybridization is utilized, and the electron arrangement of H₂O is tetrahedral. This agrees with the shape, we know water has a non-linear, bent structure, with an angle of 104.5 degrees (the two lone-pairs are not visible).

References

[1] L. Pauling, J. Am. Chem. Soc. 53 (1931), 1367

• Clayden, Greeves, Warren, Wothers. Organic Chemistry. Oxford University Press (2001), ISBN 0198503466.

See also

• Linear combination of atomic orbitals molecular orbital method

External links

• Covalent Bonds and Molecular Structure
  
• Hybridisation flash movie