THEORY OF HYBRIDIZATION
In chemistry, hybridisation (or hybridization) is the concept of mixing atomic orbitals into
new hybrid orbitals (with different energies, shapes, etc., than the component atomic orbitals)
suitable for the pairing of electrons to form chemical bonds in valence bond theory. Hybrid
orbitals are very useful in the explanation of molecular geometry and atomic bonding
properties. Although sometimes taught together with the valence shell electron-pair repulsion
(VSEPR) theory, valence bond and hybridisation are in fact not related to the VSEPR model
Historical development
Chemist Linus Pauling first developed the hybridisation theory in 1931 in order to explain the
structure of simple molecules such as methane (CH4) using atomic orbitals.[2] Pauling pointed
out that a carbon atom forms four bonds by using one s and three p orbitals, so that "it might
be inferred" that a carbon atom would form three bonds at right angles (using p orbitals) and
a fourth weaker bond using the s orbital in some arbitrary direction. In reality however,
methane has four bonds of equivalent strength separated by the tetrahedral bond angle of
109.5°. Pauling explained this by supposing that in the presence of four hydrogen atoms, the
s and p orbitals form four equivalent combinations or hybrid orbitals, each denoted by sp3 to
indicate its composition, which are directed along the four C-H bonds.[3] This concept was
developed for such simple chemical systems, but the approach was later applied more widely,
and today it is considered an effective heuristic for rationalising the structures of organic
compounds.
Orbitals are a model representation of the behaviour of electrons within molecules. In the
case of simple hybridisation, this approximation is based on atomic orbitals, similar to those
obtained for the hydrogen atom, the only neutral atom for which the Schrödinger equation
can be solved exactly. In heavier atoms, such as carbon, nitrogen, and oxygen, the atomic
orbitals used are the 2s and 2p orbitals, similar to excited state orbitals for hydrogen. Hybrid
orbitals are assumed to be mixtures of these atomic orbitals, superimposed on each other in
various proportions. It provides a quantum mechanical insight to Lewis structures.
Hybridisation theory finds its use mainly in organic chemistry.
spx and sdx terminology
This terminology describes the weight of the respective components of a hybrid orbital. For
example, in methane, the C hybrid orbital which forms each carbon–hydrogen bond consists
of 25% s character and 75% p character and is thus described as sp3 (read as s-p-three)
hybridised. Quantum mechanics describes this hybrid as an sp3 wavefunction of the form N(s
+ √3pσ), where N is a normalization constant (here 1/2) and pσ is a p orbital directed along
the C-H axis to form a sigma bond. The ratio of coefficients (denoted λ in general) is √3 in
this example. Since the electron density associated with an orbital is proportional to the
square of the wavefunction, the ratio of p-character to s-character is λ2 = 3. The p character or
the weight of the p component is N2λ2 = 3/4.
For atoms forming equivalent hybrids with no lone pairs, there is a correspondence to the
number and type of orbitals used. Thus sp3 hybrids in methane are formed from one s and
three p orbitals. However, in other cases, there may be no such correspondence. For example,
the two bond-forming hybrid orbitals of oxygen in water can be described as sp4, which
means that they have 20% s character and 80% p character, but does not imply that they are
formed from one s and four p orbitals. As a result, the amount of p-character is not restricted
to integer values; i.e., hybridisations like sp2.5 are also readily described. For more
information see variable hybridization.
An analogous notation is used to describe sdx hybrids. For example, the permanganate ion
(MnO4–) has sd3 hybridisation with orbitals that are 25% s and 75% d.
Types of hybridisation
sp3 hybrids
Four sp3 orbitals.
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.
Carbon's ground state configuration is 1s2 2s2 2px1 2py1 or more easily read:
C
↑↓ ↑↓ ↑
↑
1s 2s 2px 2py 2pz
The carbon atom can utilize its two singly occupied p-type orbitals (the designations px py or
pz are meaningless at this point, as they do not fill in any particular order), to form two
covalent bonds with two hydrogen atoms, yielding the "free radical" methylene CH2, the
simplest of the carbenes. The carbon atom can also bond to four hydrogen atoms by an
excitation of an electron from the doubly occupied 2s orbital to the empty 2p orbital, so that
there are four singly occupied orbitals.
C*
↑↓ ↑
↑
↑
↑
1s 2s 2px 2py 2pz
As the energy released by formation of two additional bonds more than compensates for the
excitation energy required, the formation of four C-H bonds is energetically favoured.
Quantum mechanically, the lowest energy is obtained if the four bonds are equivalent which
requires that they be formed from equivalent orbitals on the carbon. A set of four equivalent
orbitals can be obtained which are linear combinations of the valence-shell (core orbitals are
almost never involved in bonding) s and p wave functions[4] which are the four sp3 hybrids.
C*
↑↓ ↑
↑
↑
↑
1s sp3 sp3 sp3 sp3
In CH4, four sp3 hybrid orbitals are overlapped by hydrogen 1s orbitals, yielding four σ
(sigma) bonds (that is, four single covalent bonds) of equal length and strength.
translates into
sp2 hybrids
Three sp2 orbitals.
Ethene structure
Other carbon based compounds and other molecules may be explained in a similar way as
methane. For example, ethene (C2H4) has a double bond between the carbons.
For this molecule, carbon will sp2 hybridise, because one π (pi) bond is required for the
double bond between the carbons, and only three σ bonds are formed per carbon atom. In sp2
hybridisation the 2s orbital is mixed with only two of the three available 2p orbitals:
C*
↑↓ ↑
↑
↑
↑
1s sp2 sp2 sp2 2p
forming a total of three sp2 orbitals with one p orbital remaining. In ethylene (ethene) the two
carbon atoms form a σ bond by overlapping two sp2 orbitals and each carbon atom forms two
covalent bonds with hydrogen by s–sp2 overlap all with 120° angles. The π bond between the
carbon atoms perpendicular to the molecular plane is formed by 2p–2p overlap. The
hydrogen–carbon bonds are all of equal strength and length, which agrees with experimental
data.
sp hybrids
Two sp orbitals
The chemical bonding in compounds such as alkynes with triple bonds is explained by sp
hybridisation.
C*
↑↓ ↑
↑
↑
↑
1s sp sp 2p 2p
In this model, the 2s orbital mixes with only one of the three p orbitals resulting in two sp
orbitals and two remaining unchanged p orbitals. The chemical bonding in acetylene (ethyne)
(C2H2) consists of sp–sp overlap between the two carbon atoms forming a σ bond and two
additional π bonds formed by p–p overlap. Each carbon also bonds to hydrogen in a σ s–sp
overlap at 180° angles.
Hybridisation and molecule shape
Hybridisation helps to explain molecule shape since the angles between bonds are
(approximately) equal to the angles between hybrid orbitals, as explained above for the
tetrahedral geometry of methane. As another example, the three sp2 hybrid orbitals are at
angles of 120° to each other, so this hybridisation favours trigonal planar molecular geometry
with bond angles of 120°. Other examples are given in the table below.
Classification Main group
 Linear (180°)
 sp hybridisation
AX2
 E.g., CO2
AX3


Trigonal planar (120°)
sp2 hybridisation
Transition metal[5]
 Bent (90°)
 sd hybridisation
 E.g., VO2+


Trigonal pyramidal (90°)
sd2 hybridisation
AX4
AX5
AX6

E.g., BCl3

E.g., CrO3



Tetrahedral (109.5°)
sp3 hybridisation
E.g., CCl4



Tetrahedral (109.5°)
sd3 hybridisation
E.g., MnO4−



Square pyramidal (66°, 114°)[6][7]
sd4 hybridisation
E.g., Ta(CH3)5



Trigonal prismatic (63°, 117°)[6][7]
sd5 hybridisation
E.g., W(CH3)6
-
-
Main group compounds with lone pairs
For main group compounds with lone electron pairs, the s orbital lone pair can be hybridised
to a certain extent with the bond pairs.[8] This is analogous to s-p mixing in molecular orbital
theory, and maximizes energetic stability according to the Walsh diagram for the molecule.



Trigonal pyramidal (AX3E1)
o The s-orbital can be hybridised with the three p-orbital bonds to give bond
angles greater than 90°.
o Ex. NH3
Bent (AX2E1-2)
o The s-orbital lone pair can be hybridised with the two p-orbital bonds to give
bond angles greater than 90°. The out-of-plane p-orbital can either be a lone
pair or pi bond. If it is a lone pair, the in-plane and out-of-plane lone pairs are
inequivalent, contrary to the common picture depicted by VSEPR theory (see
below).
o Exs. SO2, H2O
Monocoordinate (AX1E1-3)
o The s-orbital lone pair can be hybridised with the p-orbital bond. The two outof-line p-orbitals can either be lone pairs or pi bonds. The p-orbital lone pairs
are not equivalent to the s-rich lone pair.
o Exs. CO, SO, HF
Hybridization theory vs. Molecular Orbital theory
Hybridisation theory is an integral part of organic chemistry and in general discussed together
with molecular orbital theory in advanced organic chemistry textbooks although for different
reasons. One textbook notes that for drawing reaction mechanisms sometimes a classical
bonding picture is needed with two atoms sharing two electrons It also comments that
predicting bond angles in methane with MO theory is not straightforward. Another textbook
treats hybridisation theory when explaining bonding in alkenes and a third uses MO theory to
explain bonding in hydrogen but hybridisation theory for methane.
Bonding orbitals formed from hybrid atomic orbitals may be considered as localized
molecular orbitals, which can be formed from the delocalized orbitals of molecular orbital
theory by an appropriate mathematical transformation. For molecules with a closed electron
shell in the ground state, this transformation of the orbitals leaves the total many-electron
wave function unchanged. The hybrid orbital description of the ground state is therefore
equivalent to the delocalized orbital description for explaining the ground state total energy
and electron density, as well as the molecular geometry which corresponds to the minimum
value of the total energy.
There is no such equivalence, however, for ionized or excited states with open electron shells.
Hybrid orbitals cannot therefore be used to interpret photoelectron spectra, which measure
the energies of ionized states, identified with delocalized orbital energies using Koopmans'
theorem. Nor can they be used to interpret UV-visible spectra which correspond to electronic
transitions between delocalized orbitals. From a pedagogical perspective, the hybridisation
approach tends to over-emphasize localisation of bonding electrons and does not effectively
embrace molecular symmetry as does MO theory.