Molecular orbital theoryMolecular orbital theory

Overcoming the shortcomings of Overcoming the shortcomings of the valence bondthe valence bond

Learning objectivesLearning objectives

Describe basic principles of MO theoryDescribe basic principles of MO theory Write MO diagrams for some simple Write MO diagrams for some simple

diatomic moleculesdiatomic molecules Explain optical and magnetic properties of Explain optical and magnetic properties of

OO22 using MO theory using MO theory

Shortcomings of valence bondShortcomings of valence bond

The orbitals still maintain atomic identityThe orbitals still maintain atomic identity Bonds are limited to two atomsBonds are limited to two atoms Cannot accommodate the concept of Cannot accommodate the concept of

delocalized electrons – bonds covering delocalized electrons – bonds covering more than two atomsmore than two atoms

Problems with magnetic and spectroscopic Problems with magnetic and spectroscopic propertiesproperties

Molecular orbital theory: Molecular orbital theory: wavefunctions revisitedwavefunctions revisited

The wave function The wave function describes the path of the describes the path of the electron – electron – ΨΨA A (has no real (has no real physical meaning)physical meaning)

Wave functions have Wave functions have phase – indicated by “+” phase – indicated by “+” and “-”and “-”

Approach of atoms causes Approach of atoms causes overlap of orbitals overlap of orbitals + adds to + (constructive + adds to + (constructive

interference); + subtracts interference); + subtracts from – (destructive from – (destructive interference) interference)

Wavefunctions and electron densityWavefunctions and electron density

ΨΨ describes the electron path describes the electron path ΨΨ22 describes the electron density describes the electron density Molecular wavefunction Molecular wavefunction ΨΨAA + + ΨΨBB

Joint density is (Joint density is (ΨΨAA + + ΨΨBB))22 = = ΨΨAA22 + + ΨΨBB

22 + +

22ΨΨAAΨΨBB

In molecular orbital the density is greater In molecular orbital the density is greater between the nuclei by an amount 2between the nuclei by an amount 2ΨΨAAΨΨBB

Molecular orbital theory: bonding Molecular orbital theory: bonding and antibondingand antibonding

Bonding orbital: additive Bonding orbital: additive combination of atomic combination of atomic orbitalsorbitals

Antibonding orbital: Antibonding orbital: subtractive combination of subtractive combination of atomic orbitalsatomic orbitals

In antibonding orbital there In antibonding orbital there is no density between the is no density between the atomsatoms

The antibonding orbitals The antibonding orbitals are at higher energyare at higher energy

MO energy level diagrams: MO energy level diagrams: HH22 exists but He exists but He22 does not does not

In HIn H22 two electrons are two electrons are

paired in the bonding paired in the bonding σσ MO, MO, and the antibonding and the antibonding σσ* MO * MO is vacant. is vacant. Total number of bonds = 1Total number of bonds = 1 Configuration (Configuration (σσ1s1s))22

In HeIn He22 four electrons are four electrons are

paired, two in the bonding paired, two in the bonding and two in the antibonding and two in the antibonding σσ** Total number of bonds = 0Total number of bonds = 0 Configuration (Configuration (σσ1s1s))22((σσ**1s1s))22

Bond orderBond order

Bond order = ½(no. bonding electrons – no. Bond order = ½(no. bonding electrons – no. antibonding electrons)antibonding electrons)

Bond order 1 = single bondBond order 1 = single bond Bond order 2 = double bondBond order 2 = double bond Bond order 3 = triple bondBond order 3 = triple bond

Second row elementsSecond row elements

LiLi22 contains 6 electrons contains 6 electrons Bonding Bonding σσ orbitals orbitals

between 1s and 2sbetween 1s and 2s Antibonding Antibonding σσ* orbitals * orbitals

between 1s and 2sbetween 1s and 2s Occupied: Occupied: σσ1s1s,,σσ2s2s, and , and

σσ**1s1s

Bond order = 2 – 1 = 1Bond order = 2 – 1 = 1 Does BeDoes Be22 exist? exist?

Formation of Formation of ππ orbitals in MO orbitals in MO

Defining the Defining the internuclear axis as internuclear axis as zz Overlap of the pOverlap of the pzz

orbitals produces orbitals produces σσ bondbond

Overlap of pOverlap of pxx and pand pyy

orbitals produces orbitals produces ππ bondsbonds

General energy level diagram for General energy level diagram for second-row homonuclear diatomicssecond-row homonuclear diatomics

Assumes no interaction Assumes no interaction between the 2s and 2p orbitalsbetween the 2s and 2p orbitals

2s orbitals are lower in energy 2s orbitals are lower in energy than the 2p orbitals. The than the 2p orbitals. The σσ2s2s and and σσ**2s2s orbitals are lower than orbitals are lower than the the σσ2p2p orbital orbital

Overlap of the 2pOverlap of the 2pzz is greater is greater than that of the 2pthan that of the 2pxx or 2p or 2pyy so so σσ2p2p is lower than the is lower than the ππ2p2p orbital orbital

The The ππ2p2p and and ππ**2p2p are degenerate are degenerate (2 orbitals with the same (2 orbitals with the same energy)energy)

2s - 2p interactions affect energy 2s - 2p interactions affect energy levelslevels

The 2s and 2p orbitals The 2s and 2p orbitals do interactdo interact

σσ2s2s and and σσ2p2p orbitals orbitals move further apart in move further apart in energyenergy

Strength of interaction Strength of interaction changes with atomic changes with atomic numbernumber Case A: Case A: σσ2p2p < < ππ2p2p

Case B: Case B: σσ2p2p > > ππ2p2p

Filling the orbitals: the second row Filling the orbitals: the second row diatomicsdiatomics

BB22, C, C22, and N, and N22 are case B are case B

OO22, F, F22 and Ne and Ne22 are case A are case A

Note bond order from MO theory matches what we Note bond order from MO theory matches what we obtain from Lewis dot diagramsobtain from Lewis dot diagrams

MO theory and magnetismMO theory and magnetism

ParamagnetismParamagnetism: substance is attracted by a magnetic field: substance is attracted by a magnetic field Diamagnetism: Diamagnetism: substance is repelled by a magnetic fieldsubstance is repelled by a magnetic field

Paramagnetic effect is much greater than diamagnetic effectParamagnetic effect is much greater than diamagnetic effect Diamagnetic substances have no unpaired electronsDiamagnetic substances have no unpaired electrons Paramagnetic substances have unpaired electronsParamagnetic substances have unpaired electrons

Magnetic properties of OMagnetic properties of O22 expose expose

limitations of Lewislimitations of Lewis MO theory gives two degenerate MO theory gives two degenerate ππ and and ππ** orbitals orbitals In OIn O22, Hund’s rule states that these are singly , Hund’s rule states that these are singly

occupiedoccupied OO22 is paramagnetic is paramagnetic

O O

Correlate magnetic properties with Correlate magnetic properties with MO diagramMO diagram

Heteronuclear molecules and NOHeteronuclear molecules and NO

NO contains 11 electrons implies high reactivityNO contains 11 electrons implies high reactivity Two possible Lewis structuresTwo possible Lewis structures

Lewis structure favours unpaired electron on NLewis structure favours unpaired electron on N Experimental bond order appears greater than 2Experimental bond order appears greater than 2

+1

-1

N O00

N O

MO description of NOMO description of NO

AOs of more electronegative AOs of more electronegative atom are lower in energyatom are lower in energy The bonding orbitals have more The bonding orbitals have more

of the more electronegative of the more electronegative atom characteratom character

The antibonding orbitals have The antibonding orbitals have more of the less electronegative more of the less electronegative atom characteratom character

MO diagram shows bond order MO diagram shows bond order 2.5 consistent with experiment2.5 consistent with experiment

Unpaired electron is in Unpaired electron is in ππ* orbital * orbital which is more N-like (consistent which is more N-like (consistent with Lewis dot structurewith Lewis dot structure