Lecture 2Chemical 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 sp2-

hybridized 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