Orbital Hybridisation
In chemistry, hybridisation is the mixing of atomic orbitals to form new orbitals suitable for bonding.
Hybridisation is an integral part of the valence shell electron-pair repulsion (VSEPR) theory as well as a
quantum mechanical model for orbital electrons to describe groups 2,3,4 of the periodic families of
elements whose electron orbital clouds fuse into one hybrid orbital. Groups 1,5,6 and 7 in the period table
do not hybridise. The hybridisation theory was theorised by chemist Linus Pauling in order to explain the
existence of molecules such as methane (CH4). The problem with the existence of methane is this: It is
made up of a carbon atom bonded to four hydrogen atoms. Carbon's ground-state configuration is 1s² 2s²
2px¹ 2py¹ 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 px py or pz are meaningless at this point, as they do not fill in any particular order), that C
forms two covalent bonds. CH2, however, is known as a methylene group 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 is required.
The answer is the theory of hybridisation. At this time it is important to note that orbitals are, and always
will be, a model. They are not real. They are derived from specialised solutions of the Schrödinger
equation and therefore to hybridise, to mix an orbital, is simply to change the mathematical function
governing where that electron should be. It is not altering the structure of the atom in any way.
The first step in hybridisation is the excitation of one (or more) electrons. From this point of the
explanation on, it can be assumed that the subject of study is carbon in the context of methane, for
simplicity. 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 orbitals, 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). Carbon
will never form any less than four bonds unless it is given no other choice, which seldom occurs.
Therefore, ethene has two double bonds between the carbons. The Lewis structure looks like this:
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.
Molecule shape
Hybridisation helps to explain molecule shape.
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AX2 (eg, BeCl2): sp hybridisation; linear or digonal 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 Xi number. 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
hybridisation is utilised, and the electron arrangement of H2O is tetrahedral. The shape, however, is nonlinear bent, since lone electron pairs are not visible, and also because repulsions must be taken into
account. The HOH angle is round about 104.5 degrees.