University College of Pharmacy,

University of the Punjab, Lahore

“HYBRIDIZATION”
Definition:
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.

Importance:
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. Hybridization tells about:

 Structure of Molecule
 Bond of Molecule
 Bond Angle of Molecule
 Geometry of Molecule
 Shape of Molecule

Atomic Orbitals:
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.

Types of Hybridization:

 sp3 Hybridization:

(Four sp3 hybrid orbitals)

Muhammad Muneeb
D16M137
 University College of Pharmacy,
University of the Punjab, Lahore
Hybridization describes the bonding atoms from an atom's point of view. 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 2p2:
↑↓ ↑↓ ↑ ↑
C
1s 2s 2px 2py 2pz

The carbon atom can use its two singly occupied p-type orbitals, to form
two covalent bonds with two hydrogen atoms, yielding the singlet methylene CH2, the
simplest carbene. 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, producing four
singly occupied orbitals.
↑↓ ↑ ↑ ↑ ↑
C*
1s 2s 2p 2p 2p

The energy released by formation of two additional bonds more than compensates
for the excitation energy required, energetically favouring the formation of four C-H bonds.
Quantum mechanically, the lowest energy is obtained if the four bonds are
equivalent, which requires that they are formed from equivalent orbitals on the carbon. A
set of four equivalent orbitals can be obtained that are linear combinations of the valence-
shell (core orbitals are almost never involved in bonding) s and p wave functions, which are
the four sp3 hybrids.
↑↓ ↑ ↑ ↑ ↑
C*
3 3 3 3
1s sp sp sp sp

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.

Muhammad Muneeb
D16M137
 University College of Pharmacy,
University of the Punjab, Lahore

 sp2 Hybridization:

(Three sp2 orbitals) (Ethene Structure)

Other carbon based compounds and other molecules may be explained in a similar
way. For example, ethene (C2H4) has a double bond between the carbons.
For this molecule, carbon sp2 hybridizes, 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,
forming a total of three sp2 orbitals with one remaining p orbital.
In ethylene (ethene) the two carbon atoms form a σ bond by overlapping two
2
sp 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, in agreement with experimental data.
↑↓ ↑ ↑ ↑ ↑
C*
2 2 2
1s sp sp sp 2p

 sp Hybridization:

(Two sp orbitals)

The chemical bonding in compounds such as alkynes with triple bonds is explained
by sp hybridisation. In this model, the 2s orbital is mixed with only one of the three p
orbitals, resulting in two sp orbitals and two remaining 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.
↑↓ ↑ ↑ ↑ ↑
C*
1s sp sp 2p 2p

Muhammad Muneeb
D16M137
 University College of Pharmacy,
University of the Punjab, Lahore
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 Transition metal

 Linear (180°)  Bent (90°)

AX2  sp hybridisation  sp hybridisation
 E.g., CO2  E.g., VO2+
AX3  Trigonal planar (120°)  Trigonal pyramidal (90°)
 sp2 hybridisation  sd2 hybridisation
 E.g., BCl3  E.g., CrO3
AX4  Tetrahedral (109.5°)  Tetrahedral (109.5°)
 sp3 hybridisation  sd3 hybridisation
 E.g., CCl4  E.g., MnO4−
AX5  Square pyramidal (73°, 123°)
 sd4 hybridisation
 E.g., Ta(CH3)5[8]
AX6  Trigonal prismatic (63.5°, 116.5°)
 sd5 hybridisation
 E.g., W(CH3)6

Hybridisation of Hypervalent Molecules:

Hybridisation is often presented for main group AX5 and above, as well as for many
transition metal complexes, using the hybridisation scheme first proposed by Pauling.

Classification Main group Transition metal

 Linear (180°)
AX2  sp hybridisation
 E.g., Ag(NH3)2+
AX3  Trigonal planar (120°)
 sp2 hybridisation
 E.g., Cu(CN)32−
AX4  Tetrahedral (109.5°)

Muhammad Muneeb
D16M137
 University College of Pharmacy,
University of the Punjab, Lahore
 sp3 hybridisation
 E.g., Ni(CO)4
 Square planar (90°)
2
 dsp hybridisation
2−
 E.g., PtCl4
AX5  Trigonal bipyramidal (90°, 120°) Trigonal bipyramidal or
 sp3d hybridisation Square pyramidal
 E.g., PCl5
AX6  Octahedral (90°)  Octahedral (90°)
 sp3d2 hybridisation 2 3
 d sp hybridisation
 E.g., SF6  E.g., Mo(CO)6
AX7  Pentagonal bipyramidal (90°, 72°) Pentagonal bipyramidal,
 sp3d3 hybridisation Capped octahedral or
 E.g., IF7 Capped trigonal prismatic

In this notation, d orbitals of main group atoms are listed after the s and p orbitals
since they have the same principal quantum number (n), while d orbitals of transition
metals are listed first since the s and p orbitals have a higher n. Thus for AX 6 molecules,
sp3d2 hybridisation in the S atom involves 3s, 3p and 3d orbitals, while d 2sp3 for Mo involves
4d, 5s and 5p orbitals.
Isovalent Hybridization:
Although ideal hybrid orbitals can be useful, in reality most bonds require orbitals of
intermediate character. This requires an extension to include flexible weightings of atomic
orbitals of each type (s, p, d) and allows for a quantitative depiction of bond formation when
the molecular geometry deviates from ideal bond angles. The amount of p-character is not
restricted to integer values; i.e., hybridizations like sp2.5 are also readily described.
The hybridization of bond orbitals is determined by Bent's rule: "Atomic s character
concentrates in orbitals directed towards electropositive substituents".
Molecules with Lone Pairs:
For molecules with lone pairs, the bonding orbitals are isovalent hybrids. For
example, the two bond-forming hybrid orbitals of oxygen in water can be described as sp4 to
give the inter-orbital angle of 104.5°. This means that they have 20% s character and 80% p
character and does not imply that a hybrid orbital is formed from one s and four p orbitals
on oxygen since the 2p sub-shell of oxygen only contains three p orbitals. The shapes of
molecules with lone pairs are:
 Trigonal pyramidal
 Three isovalent hybrid bond orbitals
 E.g., NH3
 Bent
 Two isovalent hybrid bond orbitals
 E.g., SO2, H2O

Muhammad Muneeb
D16M137
 University College of Pharmacy,
University of the Punjab, Lahore
In such cases, there are two mathematically equivalent ways of representing lone
pairs. They can be represented by orbitals of sigma and pi symmetry similar to molecular
orbital theory or by equivalent orbitals similar to VSEPR theory.

Hypervalent Molecules:
For hypervalent molecules with lone pairs, the bonding scheme can be split into a
hypervalent component and a component consisting of isovalent bonding hybrids. The
hypervalent component consists of resonating bonds using p orbitals. The table below
shows how each shape is related to the two components and their respective descriptions.

Number of isovalent bonding hybrids (marked in red)

Two One –

Hypervalent Linear axis Seesaw (AX4E1) T-shaped (AX3E2) Linear (AX2E3) (180°)
component (one p (90°, 180°, >90°) (90°, 180°)
orbital)

Square Square Square

planar pyramidal (AX5E1) planar (AX4E2) (90°)
equator (90°, 90°)
(two p
orbitals)

Pentagonal Pentagonal Pentagonal

planar pyramidal (AX6E1) planar (AX5E2) (72°)
equator (90°, 72°)
(two p

Muhammad Muneeb
D16M137
 University College of Pharmacy,
University of the Punjab, Lahore
orbitals)

Hybridization Defects:
Hybridisation of s and p orbitals to form effective sp x hybrids requires that they have
comparable radial extent. While 2p orbitals are on average less than 10% larger than 2s, in
part attributable to the lack of a radial node in 2p orbitals, 3p orbitals which have one radial
node, exceed the 3s orbitals by 20–33%. The difference in extent of s and p orbitals
increases further down a group. The hybridisation of atoms in chemical bonds can be
analyzed by considering localized molecular orbitals, for example using natural localized
molecular orbitals in a natural bond orbital (NBO) scheme.
In methane, CH4, the calculated p/s ratio is approximately 3 consistent with "ideal"
3
sp hybridisation, whereas for silane, SiH4, the p/s ratio is closer to 2. A similar trend is seen
for the other 2p elements. Substitution of fluorine for hydrogen further decreases the p/s
ratio. The 2p elements exhibit near ideal hybridisation with orthogonal hybrid orbitals.
For heavier p block elements this assumption of orthogonality cannot be justified.
These deviations from the ideal hybridisation were termed hybridisation defects
by Kutzelnigg.
Hybridisation Theory v/s Molecular Orbital Theory:
Hybridisation theory is an integral part of organic chemistry and in general discussed
together with molecular orbital theory. For drawing reaction mechanisms sometimes a
classical bonding picture is needed with two atoms sharing two electrons. Predicting bond
angles in methane with MO theory is not straightforward. Hybridisation theory explains
bonding in alkenes and 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 ground state total energy and
electron density, as well as the molecular geometry that corresponds to the minimum total
energy value.

To Find Hybridization in Molecules:

Kinds:

Type of Hybridization Steric No. Geometry s-character

Muhammad Muneeb
D16M137
 University College of Pharmacy,
University of the Punjab, Lahore
sp 2 Linear 50%
sp2 3 Trigonal Planer 33%
sp3 4 Tetrahedral 25%
sp3d 5 Trigonal Bi-pyramidal 20%
sp3d2 6 Square bi-pyramidal 16%
sp3d3 7 Pentagonal bi-pyramidal 14%
Steric Number:

Steric Number = No. of Sigma Bonds + Lone Pair

For Example:

1. H2O (Water) 3. SO2 (Sulphur Di-oxide)

(Steric Number = 2 + 2 = 4) (Steric Number= 3+0=3)

2. CH4 (Methane): 3. Ammonia (NH3)

(Steric Number = 4 + 0=4) (Steric Number 3+1=4)

SO2 CH4 NH3 H2O

Steric No. 3 4 4 4
Hybridization sp2 sp3 sp3 sp3
Geometry Trigonal Tetrahedral Tetrahedral Tetrahedral
Shape Bent Tetrahedral Trigonal Bent
Valance Electrons:

Valance Electrons = Outermost Shell Electrons

1. If electrons are >2 or ≤8 then divide it with 2.

2. If electrons are >8 or ≤ 58 then divide it with 8.
3. If electrons are >56 then divide it with 18.

e.g.

 CH4:

Valance electrons of Carbon = 4

Valance electrons of Hydrogen = 1*4 = 4
Valance Electrons = 8
Now 8/2 = 4, then we can conclude that this molecule has 1s and 3p hybrid orbitals.

Muhammad Muneeb
D16M137
 University College of Pharmacy,
University of the Punjab, Lahore
 XeO3:

Valance electrons of Xenon = 8

Valance electrons of Oxygen = 6*3 = 18
Valance Electrons = 26
Now 26/8 = 3, then we can conclude that this molecule has 1s and 2p hybrid orbitals.

 PCl5:

Valance electrons of Phosphorus = 5

Valance electrons of Chlorine = 7*5 = 35
Valance Electrons = 40
Now 40/8 = 5, then we can conclude that this molecule has 1s, 3p and 1d hybrid orbitals.

How to Find Lone Pairs:

Lone Pairs = No. of Orbitals – Surrounding elements

 ICl2-:

So No. of Orbitals are 2+3 = 5 (i.e. sp3d hybridization)

According to formula of Lone Pair:
Lone Pair on I = 5 – 2 = 3

 XeOF2:

Valance Electrons = 8+6+14=28

So No. of Orbitals are 2+3 = 5 (i.e. sp3d hybridization)
According to formula of Lone Pair:
Lone Pair on Xe = 5 – 3 = 2

Muhammad Muneeb
D16M137
 University College of Pharmacy,
University of the Punjab, Lahore

General Overview of Hybridization According to Sigma and Pi Bonds:

All 𝜎 sp3
3 𝜎, 1 π sp2
2 𝜎, 2 π sp
Electronegativity: sp > sp2 > sp3
Priority Order while Placing the Positions: Lone Pair > Double Bond > Single Bond

Muhammad Muneeb
D16M137
 University College of Pharmacy,
University of the Punjab, Lahore
 sp3d geometry:

 SF4:

(Geometry: Trigonal bipyramidal, Shape: See-saw Shape)

 ClF3:

(Geometry: Trigonal bipyramidal, Shape: See-saw Shape)

 sp3d2 geometry:

Muhammad Muneeb
D16M137
 University College of Pharmacy,
University of the Punjab, Lahore
 XeO3F2:

(Geometry: Trigonal bi-pyramidal)

___________________________________________________________________________

Muhammad Muneeb
D16M137