• 11.5 Molecular Orbital Theory. – Bonding and antibonding molecular orbitals, properties of

molecular orbitals, bond order, molecular orbital diagrams, diatomics of the first period elements, molecular orbitals of the second period elements, a special look at O2, heteronuclear diatomic molecules.

• 11.6 Delocalized Electrons: Bonding in the Benzene Molecule

– Delocalized pi bonding and resonance, delocalized molecular orbitals, other structures with delocalized molecular orbitals, non-bonding molecular orbitals.

June 10, 2009 – Class 37 and 38 Overview

• Lewis structures, VSEPR theory and valence bond method are normally satisfactory for describing covalent bonding and molecular structures.

Molecular Orbital Theory

They do not answer the questions:

Why is O2 paramagnetic?Why is H2

+ a stable species?What is the explanation for electronic (UV-vis) spectra?

These answers require another method to describe chemical bonding.

• Molecular Orbital Theory: describes the covalent bonds in a molecule by replacing atomic orbitals of the component atoms by molecular orbitals belonging to the molecule as a whole. A set or rules is used to assign electrons to these molecular orbitals, thereby yielding the electronic structure of the molecule.

– Molecular orbitals are mathematical functions.– Molecular orbitals may each, only accommodate two

electrons, with opposite spins.

Molecular Orbital Theory

• Even for a seemingly simple molecule like H2, to solve the Schrodinger equation we must make assumptions.

– Atomic orbitals are isolated on atoms.– Molecular orbitals span two or more atoms.– Linear combination of atomic orbitals.

Molecular Orbital Theory

Ψ1 = φ1 + φ2

Two 1s wave functions combine by constructive interference.

Ψ2 = φ1 - φ2

Two 1s wave functions combine by deconstructive interference.

Bonding molecular orbital: describes regions of high electron probability or charge density in the internuclear region between two bonded atoms.

Antibonding molecular orbital (*): describes regions in a molecule in which there is a low electron probability or charge density between two bonded atoms.

Molecular Orbital Theory

Molecular Orbital Theory – H2

For antibonding orbitals:

Electron density is high in parts of the molecule outside the internuclear region.

Nuclei are therefore not shielded from each other and strong repulsions occur.

Population of these orbitals leads to bond weakening.

Molecular Orbital Theory – H2

For bonding orbitals:

Electron density is high in the internuclear region.

Nuclei are therefore shielded from each other and repulsions are minimized.

Population of these orbitals leads to strong bonds.

Molecular Orbital Theory – H2

• Properties of molecular orbitals– The number of molecular orbitals (MOs) formed is equal to the

number of atomic orbitals combined.

– Of the two MOs formed when two atomic orbitals are combined, one is a bonding MO (lower energy) and one is an antibonding MO (higher energy).

– In the ground state, electrons enter the lowest energy MO available.

– Pauli Exclusion Principle is obeyed: a maximum of two electrons may be contained in a single MO.

– Hund’s rule is obeyed: in the ground state, electrons enter degnerate orbitals singly before pairing up.

Molecular Orbital Theory

• Molecular orbital diagrams show the energy levels of the isolated atoms to the left and right of the MOs for a molecule.

Molecular Orbital Theory

Molecular orbital diagrams for diatomics of the first period elements

• A stable molecular species is one that has more electrons in bonding MOs than in antibonding MOs.

• Previously, we had stated that for a single bond, the bond order (B.O.) = 1, for a double bond B.O. = 2, etc…we may now formally define this in terms of MOs.

• Bond order: one-half the difference between the numbers of electrons in bonding and in antibonding molecular orbitals in a covalent bond.

Molecular Orbital Theory

Bond Order = # e- in bonding MOs - # e- in antibonding MOs

2

Problem: Calculate the bond order for the diatomic molecules of the first-period elements and state whether these should be stable species.

Molecular Orbital Theory

• First period elements use only 1s orbitals for formation of molecular orbitals.

• Second period elements have 2s and 2p orbitals available.

• p orbital overlap:– End-on overlap is best – sigma bond (σ).– Side-on overlap is good – pi bond (π).

Molecular orbitals of the second period elements

Molecular orbitals of the second period elements

(a) The addition of two 2p orbitals, in phase, along the internuclear axis to form a 2p MO.

Electron density is located between the nuclei leading to bond formation.

(b) The addition of two 2p orbitals, out of phase, forming a 2p MO.

This orbital has a nodal plane perpendicular to the internuclear axis (as do all antibonding orbitals!)

Molecular orbitals of the second period elements

(c) The addition of two 2p orbitals, in phase, perpendicular to the internuclear axis to form a 2p MO.

Electron density is located between the nuclei contributing to multiple bond formation.

(d) The addition of two 2p orbitals, out of phase, forming a 2p MO.

This orbital also has a nodal plane perpendicular to the internuclear axis (as do all antibonding orbitals!)

Molecular orbitals of the second period elements

Molecular orbitals of the second period elementsFor diatomics of the second period elements with Z = 7 or less, the energy difference between the s and p orbitals is small, and both produce regions of electron density between the nuclei (through 2s and 2p MOs). This leads to mixing of the 2s and 2p MOs.

This leads to the following molecular orbital energy level scheme.

Molecular orbitals of the second period elements

Molecular orbitals of the second period elementsFor diatomics of the second period elements with Z = 8 or greater, the energy difference between the s and p orbitals is large, and little s and p orbital mixing takes place.

This leads to the following molecular orbital energy level scheme.

Molecular orbitals of the second period elements

• A special look at O2

– Experimentally, O2 is paramagnetic.

– The experimentally determined bond length of O2 is consistent with double bond character.

– Molecular orbital theory explains both observations! (FINALLY!)

Molecular Orbital Theory

Problem: Write a molecular orbital diagram and determine the bond order for:

(a) Ne2+

(b) C22-

Problem: Using energy level diagrams for the MO’s of N2, N2

+, O2 and O2+, explain the following data, which

shows that removing an electron from N2 weakens the bond and lengthens it but removing an electron from O2 strengthens the bond and shortens it.

Molecular Orbital Theory

Molecular Orbital Theory - Heteronuclear diatomic molecules

For heterodiatomics, the energy of the bonding orbital is closer to that of the more electronegative atom and energy of the antibonding orbital is closer to that of the less electronegative atom.

The atoms involved must not be too far apart so that the order of the energy levels is not too different than that of the homodiatomics.

When deciding what MO energy level diagram to use, if either of the atoms is O or F, use the splitting pattern for Z ≥ 8.

Problem: Write a molecular orbital diagram and determine the bond order for:

(a) CN-

(b) BN

Molecular Orbital Theory

Delocalized Electrons: Bonding in the Benzene Molecule

(a) Lewis structure for C6H6 showing alternate carbon-to-carbon single and double bonds.

(b) Kekule structures for benzene

(c) A space filling model

Delocalized Electrons: Bonding in the Benzene MoleculeValence Bond Method

(a) Carbon atoms use sp2 and p orbitals. Each carbon atom forms three bonds, two with neighboring C atoms in the hexagonal ring and a third with an H atom.

(b) The overlap in sidewise fashion of 2p orbitals produces three bonds.

(c) Because the three bonds are delocalized around the benzene ring, the molecule is often represented through a hexagon with an inscribed circle.

Delocalized Electrons: Bonding in the Benzene MoleculeMolecular Orbital Theory

• Delocalized molecular orbital: describes a region of high electron probability or charge density that extends over three or more atoms.

Molecular orbital representation of bonding in benzene.

A computer-generated model of the benzene molecule.

The planar bond framework is clearly visible.

The p orbitals above and below the C and H plane are highlighted

Delocalized Electrons: Bonding in the Benzene MoleculeMolecular Orbital Theory

MO for bonding in benzene.

Each C in C6H6 has one p electron available for -bonding, consistent with the number of e- present in the bonding orbitals.

Other structures with delocalized molecular orbitals

sp2 hybridize orbitals on each oxygen, leaving 3 p orbitals.

14 of the 18 electrons occupy these orbitals.

The three p orbitals form 3 molecular orbitals and there are four electrons to occupy these orbitals.

Other structures with delocalized molecular orbitalsThe molecule has one σ bond between each pair of O atoms and a bond delocalized over two pairs of O atoms for a bond order of 1.5.

Non-bonding MOs have the same energy as the atomic orbitals from which they came, but neither add nor detract from bond formation