Lecture 2 Chemical Bonds: Atomic Orbital Theory and Molecular Orbital Theory Dr. A.K.M. Shafiqul Islam

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 H 2 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

sp 3 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.

sp 3 Hybridization. One s and three p orbitals are hybridized to form an sp 3 -hybridized orbital

Formation of sp 3 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 sp 3 hybrid orbitals One s atomic orbital combines with three p atomic orbitals to make four sp 3 hybrid orbitals.

Structure of methane (a)Four sp 3 orbitals are directed toward the corners of a tetrahedron causing each bond angle to be degrees. (b)An orbital picture of methane showing the overlap of each sp 3 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 sp 3 orbitals to form four covalent bonds.

Bonding in ethane The carbon-carbon bond is formed by sp 3 -sp 3 overlap, and each carbon-hydrogen bond is formed by sp 3 -s overlap.

Structure of ethane The two carbons in ethane are tetrahedral. Each carbon uses four sp 3 atomic orbitals to form four covalent bonds.

Orbital diagram for ethane End to end overlap of two sp 3 hybrid orbitals on the carbon atoms in ethane form sigma bonding and antibonding molecular orbitals.

Ethene, ethylene Ethene contains a carbon-carbon double bond.

sp 2 Hybridization A carbon atom has a 2s electron promoted to a 2p orbital. One s and two p orbitals are hybridized to form an sp 2 - hybridized orbital.

sp 2 Hybrid orbitals The three sp 2 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 sp 2 -sp 2 overlap, and the C-H bonds are formed by sp 2 -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.

sp 3 Hybridization in water One s and three p orbitals are hybridized to form an sp 3 -hybridized orbital.

Orbital depiction, ball-and-stick model, and an electrostatic potential map of water The oxygen is sp 3 hybridized

sp 3 Hybridization in ammonia One s and three p orbitals are hybridized to form an sp 3 -hybridized orbital.

Orbital depiction, ball-and-stick model, and electrostatic potential map of ammonia The nitrogen in ammonia is sp 3 hybridized