Lecture 2 Chemical Bonds: Atomic Orbital Theory and Molecular Orbital Theory Dr. A.K.M. Shafiqul Islam 18.07.08

1s and 2s Atomic Orbitals Figure: 01-01-36UN Title: 1s and 2s Atomic orbitals. Caption: 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. 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 Figure: 01-01-38UN Title: Nodal planes for p orbitals. Caption: p Atomic orbitals have two lobes and are dumbbell-shaped. The two lobes are of opposite phase. 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 Figure: 01-01-39UN Title: Degenerate 2p atomic orbitals. Caption: The 2p orbitals lie along the x, y, and z axes. Each p orbital contains up to 2 electrons. 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 Figure: 01-01-40UN Title: Sigma bonds for a hydrogen molecule. Caption: Sigma bonds can form where two s orbitals overlap. The sigma bond is cylindrically symmetrical. Sigma bonds can form where two s orbitals overlap. The sigma bond is cylindrically symmetrical.

Bond length for hydrogen atoms Figure: 01-02 Title: Figure 1.2. Bond length for hydrogen atoms. Caption: 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. 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 Figure: 01-04 Title: Figure 1.4. Atomic and molecular orbitals of H and H2. Caption: 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. 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 Figure: 01-05 Title: Figure 1.5. p Orbital bonding (end-to-end). Caption: End-on overlap of two p orbitals to form a sigma bonding molecular orbital and a sigma antibonding molecular orbital. End-on overlap of two p orbitals to form a sigma bonding molecular orbital and a sigma antibonding molecular orbital.

Figure: 01-06 Title: Figure 1.6. p Orbital bonding (side-to-side). Caption: Side-to-side overlap of two parallel p orbitals to form a pi bonding molecular orbital and a pi antibonding molecular orbital. 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. Figure: 01-07 Title: Figure 1.7. MO diagram for MOs made from p atomic orbitals. Caption: 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.

Figure: 01-08 Title: Figure 1.8. Carbon-oxygen pi bond formation. Caption: 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.

Figure: 01-08-02UN Title: Models of methane. Caption: The ball-and-stick model, the space-filling model, and the electrostatic potential map are shown for methane.

The Electronic Configurations of the Smallest Atoms Figure: 01-T02 Title: Table 1.2. The Electronic Configurations of the Smallest Atoms. Caption: The electronic configuration is based upon the number of valence electrons. s can have a maximum of 2 electrons; p can have a maximum of 6 electrons. For the p orbitals, the px, py, and pz must have one electron each before another electron is placed in the shell.

sp3 Hybridization Figure: 01-08-03UN Title: sp3 Hybridization. Caption: 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. 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. Figure: 01-08-04UN Title: sp3 Hybridization. Caption: One s and three p orbitals are hybridized to form an sp3-hybridized orbital. One s and three p orbitals are hybridized to form an sp3-hybridized orbital

Formation of sp3 hybrid orbital Figure: 01-09 Title: Figure 1.9. Formation of sp3 hybrid orbital. Caption: The s orbital adds to one lobe of the p orbital and subtracts from the other lobe of the p 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 Figure: 01-10 Title: Figure 1.10. Formation of four sp3 hybrid orbitals. Caption: One s atomic orbital combines with three p atomic orbitals to make four sp3 hybrid orbitals. One s atomic orbital combines with three p atomic orbitals to make four sp3 hybrid orbitals.

Structure of methane Figure: 01-11 Title: Figure 1.11. Structure of methane. Caption: (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. Four sp3 orbitals are directed toward the corners of a tetrahedron causing each bond angle to be 109.5 degrees. An orbital picture of methane showing the overlap of each sp3 orbital of the carbon with the s orbital of hydrogen.

Bonds in ethane Figure: 01-11-01UN Title: Bonds in ethane. Caption: The two carbon atoms in ethane are tetrahedral. Each carbon uses four sp3 orbitals to form four covalent bonds. The two carbon atoms in ethane are tetrahedral. Each carbon uses four sp3 orbitals to form four covalent bonds.

Bonding in ethane Figure: 01-12 Title: Figure 1.12. Bonding in ethane. Caption: The carbon-carbon bond is formed by sp3-sp3overlap, and each carbon-hydrogen bond is formed by sp3-s overlap. The carbon-carbon bond is formed by sp3-sp3overlap, and each carbon-hydrogen bond is formed by sp3-s overlap.

Structure of ethane Figure: 01-12-01UN Title: Structure of ethane. Caption: The two carbons in ethane are tetrahedral. Each carbon uses four sp3 atomic orbitals to form four covalent bonds. The two carbons in ethane are tetrahedral. Each carbon uses four sp3 atomic orbitals to form four covalent bonds.

Orbital diagram for ethane Figure: 01-13 Title: Figure 1.13. Orbital diagram for ethane. Caption: End to end overlap of two sp3 hybrid orbitals on the carbon atoms in ethane form sigma bonding and antibonding molecular orbitals. 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. Figure: 01-13-01UN Title: Ethene, ethylene. Caption: Ethene contains a carbon-carbon double bond. Ethene contains a carbon-carbon double bond.

sp2 Hybridization Figure: 01-13-02UN Title: sp2 Hybridization. Caption: 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. 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. Figure: 01-14 Title: Figure 1.14. sp2 Hybrid orbitals. Caption: (a) The three sp2 hybrid orbitals lie in a plane. (b) The unhybridized p orbital is perpendicular to the plane. The three sp2 hybrid orbitals lie in a plane. The unhybridized p orbital is perpendicular to the plane.

Structure of a double bond Figure: 01-15 Title: Figure 1.15. Structure of a double bond. Caption: (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. 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. 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. 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 Figure: 01-15-01UN Title: Lewis structure, ball-and-stick model, space-filling model, and electrostatic potential map of ethene. Caption: Ethene consists of a carbon-carbon double bond and four carbon-hydrogen single (sigma) bonds. Ethene consists of a carbon-carbon double bond and four carbon-hydrogen single (sigma) bonds

Ethyne, acetylene Figure: 01-15-02UN Title: Ethyne, acetylene. Caption: Ethyne contains a carbon-carbon triple bond and two carbon-hydrogen single bonds. Ethyne contains a carbon-carbon triple bond and two carbon-hydrogen single bonds.

sp Hybridization Figure: 01-15-03UN Title: sp Hybridization. Caption: 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. 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 Figure: 01-16 Title: Figure 1.16. sp-Hybridized carbon atom. Caption: The two sp orbitals are oriented 180 degrees away from each other, perpendicular to the two unhybridized p orbitals. The two sp orbitals are oriented 180 degrees away from each other, perpendicular to the two unhybridized p orbitals.

Orbital structure of ethyne 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. 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. 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. Figure: 01-17 Title: Orbital structure of ethyne. Caption: (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.

A carbon-carbon triple bond consists of three pairs of electrons. Lewis structure, ball-and-stick model, space-filling model, and electrostatic potential map of ethyne Figure: 01-17-01UN Title: Lewis structure, ball-and-stick model, space-filling model, and electrostatic potential map of ethyne. Caption: A carbon-carbon triple bond consists of three pairs of electrons. A carbon-carbon triple bond consists of three pairs of electrons.

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 cation Figure: 01-17-05UN Title: Orbital depiction, ball-and-stick models, and an electrostatic potential map of the methyl cation. Caption: The carbon only has six electrons around it in a methyl cation. The carbon only has six electrons around it in a methyl cation

The carbon in a methyl radical has seven electrons Orbital depiction, ball-and-stick models, and an electrostatic potential map of the methyl radical Figure: 01-17-06UN Title: Orbital depiction, ball-and-stick models, and an electrostatic potential map of the methyl radical. Caption: The carbon in a methyl radical has seven electrons. The carbon in a methyl radical has seven electrons

The carbon in the methyl anion has eight electrons. Orbital depiction, ball-and-stick models, and an electrostatic potential map of the methyl anion Figure: 01-17-07UN Title: Orbital depiction, ball-and-stick models, and an electrostatic potential map of the methyl anion. Caption: The carbon in the methyl anion has eight electrons. The carbon in the methyl anion has eight electrons.

sp3 Hybridization in water Figure: 01-17-08UN Title: sp3 Hybridization in water. Caption: One s and three p orbitals are hybridized to form an sp3-hybridized orbital. One s and three p orbitals are hybridized to form an sp3-hybridized orbital.

The oxygen is sp3 hybridized Orbital depiction, ball-and-stick model, and an electrostatic potential map of water Figure: 01-17-09UN Title: Orbital depiction, ball-and-stick model, and an electrostatic potential map of water. Caption: The oxygen is sp3 hybridized. The oxygen is sp3 hybridized

sp3 Hybridization in ammonia Figure: 01-17-10UN Title: sp3 Hybridization in ammonia. Caption: One s and three p orbitals are hybridized to form an sp3-hybridized orbital. One s and three p orbitals are hybridized to form an sp3-hybridized orbital.

The nitrogen in ammonia is sp3 hybridized Orbital depiction, ball-and-stick model, and electrostatic potential map of ammonia Figure: 01-17-11 Title: Orbital depiction, ball-and-stick model, and electrostatic potential map of ammonia. Caption: The nitrogen in ammonia is sp3 hybridized. The nitrogen in ammonia is sp3 hybridized