1. CHAPTER 2: VALENCE BOND THEORY CHEM210/Chapter 2/2014/01 HOMONUCLEAR DIATOMIC MOLECULES: VALENCE BOND (VB) THEORY The word homonuclear is used in two ways: A homonuclear covalent bond is formed between atoms of the same element, e.g. the H – H bond in H 2, the O = O bond in O 2 and the O – O bond in H 2 O 2. A homonuclear molecule contains one type of element, e.g. H 2, N 2 and F 2 and larger molecules such as O 3, P 4, S 8 and C 60.

2. CHEM210/Chapter 2/2014/02 Before discussing covalent bonding, we consider the following: For an atom X, the value of the single bond covalent radius, r cov, is half the internuclear separation in a homonuclear X – X bond. The van der Waals radius, r v, of an atom X is half of the distance of closest approach of two non-bonded atoms of X In covalent bonding, as two nuclei approach each other their atomic orbitals overlap. As the amount of overlap increases, the energy of the interaction decreases. At some distance the minimum energy is reached. The minimum energy corresponds to the bonding distance (or bond length). As the two atoms get closer, their nuclei begin to repel and the energy increases. At the bonding distance, the attractive forces between nuclei and electrons just balance the repulsive forces (nucleus-nucleus, electron-electron).

3. CHEM210/Chapter 2/2014/03

4. CHEM210/Chapter 2/2014/04 A covalent bond forms when the orbitals of two atoms overlap and the overlap region, which is between the nuclei, is occupied by a pair of electrons. A set of overlapping orbitals has a maximum of two electrons that must have opposite spins. The greater the orbital overlap, the stronger (more stable) the bond. The valence atomic orbitals in a molecule are different from those in isolated atoms. There is a hybridization of atomic orbitals to form molecular orbitals.

5. CHEM210/Chapter 2/2014/05

6. CHEM210/Chapter 2/2014/06 HYBRIDIZATION The number of hybrid orbitals obtained equals the number of atomic orbitals mixed. The type of hybrid orbitals obtained varies with the types of atomic orbitals mixed. sp hybrid orbital The sp hybrid orbitals in gaseous BeCl 2. atomic orbitals hybrid orbitals

7. CHEM210/Chapter 2/2014/07 orbital box diagrams with orbital contours

8. CHEM210/Chapter 2/2014/08 sp 2 hybrid orbitals All molecules with trigonal planar electron pair geometries have sp 2 orbitals on the central atom. When we mix n atomic orbitals we must get n hybrid orbitals. sp 2 hybrid orbitals are formed with one s and two p orbitals, therefore, there is one unhybridized p orbital remaining. The large lobes of sp 2 hybrids lie in a trigonal plane. The sp 2 hybrid orbitals in BF 3.

9. CHEM210/Chapter 2/2014/09 sp 3 hybrid orbitals sp 3 hybrid orbitals are formed from one s and three p orbitals, therefore, there are four large lobes. Each lobe points towards the vertex of a tetrahedron. The angle between the large lobes is 109.5  The sp 3 hybrid orbitals in CH 4.

10. CHEM210/Chapter 2/2014/10 The sp 3 hybrid orbitals in NH 3.

11. CHEM210/Chapter 2/2014/11 The sp 3 hybrid orbitals in H 2 O.

12. CHEM210/Chapter 2/2014/12 Geometrical arrangements characteristic of hybrid orbital sets Atomic orbital set Hybrid orbital set GeometryExamples s, pTwo spBeF 2, HgCl 2 s, p, pThree sp 2 BF 3, SO 3 s, p, p, pFour sp 3 CH 4, NH 3, H 2 O, NH 4 +

13. CHEM210/Chapter 2/2014/13 Composition and orientation of orbitals

14. CHEM210/Chapter 2/2014/14 MULTIPLE BONDS Have  and  -bonds. In  -bonds, the electron density lies on the axis between the nuclei. All single bonds are  -bonds.  -Bonds: electron density lies above and below the plane of the nuclei. A double bond consists of one  -bond and one  - bond. A triple bond has one  -bond and two  - bonds. Often, the p-orbitals involved in  -bonding come from unhybridized orbitals.

15. CHEM210/Chapter 2/2014/15 Ethane, C 2 H 6 both Cs are sp 3 hybridized s-sp 3 overlaps to σ bonds sp 3 -sp 3 overlap to form a σ bond relatively even distribution of electron density over all σ bonds

16. CHEM210/Chapter 2/2014/16 Ethylene, C 2 H 4 One  - and one  -bond with both C atoms being sp 2 hybridized. Both C atoms with trigonal planar electron pair and molecular geometries.

17. CHEM210/Chapter 2/2014/17 electron density overlap in one position - σ p overlap - π

18. CHEM210/Chapter 2/2014/18 Acetylene, C 2 H 2 In acetylene: the electron pair geometry of each C is linear,therefore, the C atoms are sp hybridized. the sp hybrid orbitals form the C-C and C-H  -bonds. there are two unhybridized p-orbitals. both unhybridized p-orbitals form the two  -bonds, one  -bond is above and below the plane of the nuclei and the other  -bond is in front and behind the plane of the nuclei. When triple bonds form (e.g. N 2 ), one  bond is always above and below and the other is in front and behind the plane of the nuclei. Electron density and bond order.

19. CHEM210/Chapter 2/2014/19 EXAMPLE Describe the types of bonds and orbitals in acetone, (CH 3 ) 2 CO SOLUTION Use the Lewis structures to ascertain the arrangement of groups and shape at each central atom. Postulate the hybrid orbitals taking note of the multiple bonds and their orbital overlaps. σ bonds π bonds

20. CHEM210/Chapter 2/2014/20 Delocalized π bonding So far all the bonds we have encountered are localized between two nuclei. In the case of benzene: there are 6 C-C  bonds, 6 C-H  bonds. each C atom is sp 2 hybridized. there are 6 unhybridized p orbitals on each C atom.

21. CHEM210/Chapter 2/2014/21 In benzene there are two options for the 3  bonds: localized between C atoms or delocalized over the entire ring (i.e. the  electrons are shared by all 6 C atoms). Experimentally, all C-C bonds are the same length in benzene, therefore, all C- C bonds are of the same type (recall single bonds are longer than double bonds).

22. CHEM210/Chapter 2/2014/22 Restricted rotation of π-bonded molecules in C 2 H 2 Cl 2 cis- trans-

23. CHEM210/Chapter 2/2014/23 General conclusions on multiple bonds Every two atoms share at least 2 electrons. Two electrons between atoms on the same axis as the nuclei are  bonds.  bonds are always localized. If two atoms share more than one pair of electrons, the second and third pair form  bonds. When resonance structures are possible, delocalization is also possible.