Lecture 11 Bonding Theories Text: Chapter 3, Sections 4 and following Covalent Bonding and Orbital Overlap valence-bond theory orbital overlap H H H Cl Cl Cl 1s 3p 3p 3p Sigma bonds form the skeleton of the molecule. For diatomic molecules, one atomic orbital from each atom combine to form a -bond between the atoms. Chapter 9 Molecular Geometry 1 Pi bonds form the extra double or triple bonds in a bond region. Hybrid Orbitals (Used for molecules with 3 or more atoms) The mathematical combinations of wave functions on the same atom to form a new set of equivalent wave functions are called hybrid atomic functions. On an atom, there is one hybrid orbital per Electron Domain. They point in the same directions as the lone pairs and bond regions. Chapter 9 Molecular Geometry 2 Chapter 9 Molecular Geometry 3 1s 2s 2p 1s sp 2p 1s 2s 2p 1s sp2 2p 1s 2s 2p 1s sp3 Geometry Bond Angles Hybridization Linear 180° 2 sp orbitals Trigonal 120° 3 sp2 orbitals Tetrahedral 109.5° 4 sp3 orbitals Trigonal bipyramidal 2 x 90°, 3 x 120° 5 sp3d orbitals Octahedral 90° 6 sp3d2 orbitals Chapter 9 Molecular Geometry 4 Multiple Bonds internuclear axis sigma () bonds electron density along internuclear axis. pi (p) bonds overlap of two p orbitals oriented perpendicularly to the internuclear axis. Overlap is above and below internuclear axis, no probability of finding electron on the internuclear axis. H C C H H H = H H H C C All single bonds are sigma bonds. All multiple bonds contain one sigma bond. Delocalized bonding Chapter 9 Molecular Geometry 5 H Molecular Orbitals A molecular orbital is a mathematical function that describes the wave-like behavior of an electron in a molecule. Whenever two atomic orbitals overlap, two molecular orbitals form. Chapter 9 Molecular Geometry 6 y = exp(-x) y = exp(-abs(x)) y = exp(-|x-1|) y = exp(-|x+1|) Chapter 9 Molecular Geometry 7 y = exp(-|x-1|) + exp(-|x+1|) y = exp(-|x-1|) - exp(-|x+1|) Chapter 9 Molecular Geometry 8 energy-level diagram (molecular orbital diagram) bonding molecular orbital () antibonding molecular orbital (*) Procedure for Using Molecular Orbital Energy Diagrams 1) Sum up electrons from two atoms and possible charge 2) Fill in the boxes on appropriate MO diagram according to Hund’s rule. Chapter 9 Molecular Geometry 9 Bond Order = 1 2 Bond Order = # bonding electrons - # antibonding electrons 1 single bond 2 double bond 3 triple bond Bond orders can be 1/2, 3/2, 5/2 with radicals Chapter 9 Molecular Geometry 10 Second-Row Diatomic Molecules 1. The number of molecular orbitals formed equals the number of atomic orbitals combined. 2. Atomic orbitals combine most efficiently with other atomic orbitals of similar energy. 3. As the overlap increases the bonding MO lowers in energy. 4. Each molecular orbital can accommodate, at most, two electrons, with their spins paired (Pauli exclusion principle). 5. When MOs have the same energy, one electron enters each orbital (with the same spin) before spin pairing occurs (Hund’s rule). Molecular Orbitals from 2p Atomic Orbitals paramagnetism – some electrons unpaired diamagnetism – all electrons paired NO, NO+, NO– Chapter 9 Molecular Geometry 11 Chapter 9 Molecular Geometry 12