Lecture 2
Chemical Bonds: Atomic Orbital
Theory and Molecular Orbital
Theory
Dr. A.K.M. Shafiqul Islam
10.07.09
1s and 2s Atomic Orbitals
• An orbital is a three-dimensional region around the
nucleus where there is a high probability of finding an
electron.
• The node is the region where the probability of finding an
electron falls to zero.
Nodal planes for p orbitals
• p Atomic orbitals have two lobes and are dumbbell-shaped.
• The two lobes are of opposite phase. + and – sign are not
opposite charge.
Degenerate 2p atomic orbitals
• The 2p orbitals lie along the x, y, and z axes.
Each p orbital contains up to 2 electrons.
Sigma bonds for a hydrogen molecule
• Sigma bonds can form where two s orbitals
overlap. The sigma bond is cylindrically
symmetrical.
Bond length for hydrogen atoms
• The change in potential energy that occurs as two 1s
atomic orbitals approach each other.
• The internuclear distance at minimum energy is the
length of the hydrogen-hydrogen covalent bond.
Atomic and molecular orbitals of H and H2
• Before covalent bond formation, each electron is in an atomic orbital.
• After covalent bond formation, both electrons are in the bonding molecular
orbital.
• The antibonding molecular orbital is empty.
p Orbital bonding (end-to-end)
• End-on overlap of two p orbitals to form a sigma
bonding molecular orbital and a sigma
antibonding molecular orbital.
p Orbital bonding (side-to-side)
• Side-to-side overlap of two parallel p orbitals to
form a pi bonding molecular orbital and a pi
antibonding molecular orbital.
MO diagram for MOs made from p atomic orbitals.
• p Atomic orbitals can overlap end-on to form sigma bonding
and antibonding molecular orbitals.
• The bonding combination has less energy than the
antibonding combination.
• p Atomic orbitals can also overlap side-to-side to form pi
bonding and antibonding molecular orbitals.
• The relative energies are bonding sigma < bonding pi <
antibonding pi < antibonding sigma.
Carbon-oxygen pi bond formation
• Side-to-side overlap of a p atomic orbital from carbon
with a p atomic orbital from oxygen results in pi bonding
and pi antibonding molecular orbitals
Models of methane
The ball-and-stick model, the space-filling model, and
the electrostatic potential map are shown for methane
Relative Energies of Atomic Orbitals
The Electronic Configurations of the
Smallest Atoms
sp3 Hybridization
• A carbon atom has a 2s electron promoted to a 2p orbital.
• Promotion of a 2s electron to a 2p orbital is needed so
that carbon has four unpaired electrons.
sp3 Hybridization.
• One s and three p orbitals are hybridized to form
an sp3-hybridized orbital
Formation of sp3 hybrid orbital
• The s orbital adds to one lobe of the p orbital
and subtracts from the other lobe of the p orbital.
Formation of four sp3 hybrid orbitals
• One s atomic orbital combines with three p
atomic orbitals to make four sp3 hybrid orbitals.
Structure of methane
(a) Four sp3 orbitals are directed toward the corners of a
tetrahedron causing each bond angle to be 109.5 degrees.
(b) An orbital picture of methane showing the overlap of each
sp3 orbital of the carbon with the s orbital of hydrogen.
Bonds in ethane
• The two carbon atoms in ethane are tetrahedral.
Each carbon uses four sp3 orbitals to form four
covalent bonds.
Bonding in ethane
• The carbon-carbon bond is formed by sp3-sp3
overlap, and each carbon-hydrogen bond is
formed by sp3-s overlap.
Structure of ethane
• The two carbons in ethane are tetrahedral. Each
carbon uses four sp3 atomic orbitals to form four
covalent bonds.
Orbital diagram for ethane
• End to end overlap of two sp3 hybrid orbitals on
the carbon atoms in ethane form sigma bonding
and antibonding molecular orbitals.
Ethene, ethylene
• Ethene contains a carbon-carbon double bond.
sp2 Hybridization
• A carbon atom has a 2s electron promoted to a 2p orbital.
• One s and two p orbitals are hybridized to form an sp2hybridized orbital.
sp2 Hybrid orbitals
•
•
The three sp2 hybrid orbitals lie in a plane.
The unhybridized p orbital is perpendicular to
the plane.
Structure of a double bond
(a) One C-C bond in ethene is a sigma bond formed by sp2-sp2 overlap,
and the C-H bonds are formed by sp2-s overlap.
(b) The second C-C bond is a pi bond formed by the side-to-side overlap of
a p orbital of one carbon with a p orbital of the other carbon.
(c) There is an accumulation of electron density above and below the
plane containing the two carbons and four hydrogens.
Lewis structure, ball-and-stick model, space-filling
model, and electrostatic potential map of ethene
• Ethene consists of a carbon-carbon double bond
and four carbon-hydrogen single (sigma) bonds
Ethyne, acetylene
• Ethyne contains a carbon-carbon triple bond and
two carbon-hydrogen single bonds.
sp Hybridization
• A carbon atom has a 2s electron promoted to a
2p orbital. One s orbital and one p orbital are
hybridized to form an sp-hybridized orbital.
sp-Hybridized carbon atom
• The two sp orbitals are oriented 180 degrees
away from each other, perpendicular to the two
unhybridized p orbitals.
Orbital structure of ethyne
(a) The C-C sigma bond in ethyne is formed by sp-sp overlap, and the
C-H bonds are formed by sp-s overlap. The carbon atoms and the
atoms bonded to them are in a straight line.
(b) The two carbon-carbon pi bonds are formed by the side-to-side
overlap of the p orbitals of one carbon with the p orbitals of the other
carbon.
(c) The triple bond has an electron-dense region above and below and
in front of and in back of the internuclear axis of the molecule.
Lewis structure, ball-and-stick model, space-filling
model, and electrostatic potential map of ethyne
• A carbon-carbon triple bond consists of three
pairs of electrons.
Orbital depiction, ball-and-stick models, and an
electrostatic potential map of the methyl cation
• The carbon only has six electrons around it in a
methyl cation
Orbital depiction, ball-and-stick models, and an
electrostatic potential map of the methyl radical
• The carbon in a methyl radical has seven
electrons
Orbital depiction, ball-and-stick models, and an
electrostatic potential map of the methyl anion
• The carbon in the methyl anion has eight
electrons.
sp3 Hybridization in water
• One s and three p orbitals are hybridized to form
an sp3-hybridized orbital.
Orbital depiction, ball-and-stick model, and an
electrostatic potential map of water
• The oxygen is sp3 hybridized
sp3 Hybridization in ammonia
• One s and three p orbitals are hybridized to form
an sp3-hybridized orbital.
Orbital depiction, ball-and-stick model, and
electrostatic potential map of ammonia
• The nitrogen in ammonia is sp3 hybridized