Molecular orbital theory Overcoming the shortcomings of the valence bond

Learning objectives  Describe basic principles of MO theory  Write MO diagrams for some simple diatomic molecules  Explain optical and magnetic properties of O 2 using MO theory

Shortcomings of valence bond  The orbitals still maintain atomic identity  Bonds are limited to two atoms  Cannot accommodate the concept of delocalized electrons – bonds covering more than two atoms  Problems with magnetic and spectroscopic properties

Molecular orbital theory: wavefunctions revisited  The wave function describes the path of the electron – Ψ A (has no real physical meaning)  Wave functions have phase – indicated by “+” and “-”  Approach of atoms causes overlap of orbitals  + adds to + (constructive interference); + subtracts from – (destructive interference)

Wavefunctions and electron density  Ψ describes the electron path  Ψ 2 describes the electron density  Molecular wavefunction Ψ A + Ψ B  Joint density is (Ψ A + Ψ B ) 2 = Ψ A 2 + Ψ B 2 + 2Ψ A Ψ B  In molecular orbital the density is greater between the nuclei by an amount 2Ψ A Ψ B

Molecular orbital theory: bonding and antibonding  Bonding orbital: additive combination of atomic orbitals  Antibonding orbital: subtractive combination of atomic orbitals  In antibonding orbital there is no density between the atoms  The antibonding orbitals are at higher energy

MO energy level diagrams: H 2 exists but He 2 does not  In H 2 two electrons are paired in the bonding σ MO, and the antibonding σ* MO is vacant.  Total number of bonds = 1  Configuration (σ 1s ) 2  In He 2 four electrons are paired, two in the bonding and two in the antibonding σ*  Total number of bonds = 0  Configuration (σ 1s ) 2 (σ* 1s ) 2

Bond order Bond order = ½(no. bonding electrons – no. antibonding electrons)  Bond order 1 = single bond  Bond order 2 = double bond  Bond order 3 = triple bond

Second row elements  Li 2 contains 6 electrons  Bonding σ orbitals between 1s and 2s  Antibonding σ* orbitals between 1s and 2s  Occupied: σ 1s,σ 2s, and σ* 1s  Bond order = 2 – 1 = 1  Does Be 2 exist?

Formation of π orbitals in MO  Defining the internuclear axis as z  Overlap of the p z orbitals produces σ bond  Overlap of p x and p y orbitals produces π bonds

General energy level diagram for second-row homonuclear diatomics  Assumes no interaction between the 2s and 2p orbitals  2s orbitals are lower in energy than the 2p orbitals. The σ 2s and σ* 2s orbitals are lower than the σ 2p orbital  Overlap of the 2p z is greater than that of the 2p x or 2p y so σ 2p is lower than the π 2p orbital  The π 2p and π* 2p are degenerate (2 orbitals with the same energy)

2s - 2p interactions affect energy levels  The 2s and 2p orbitals do interact  σ 2s and σ 2p orbitals move further apart in energy  Strength of interaction changes with atomic number  Case A: σ 2p < π 2p  Case B: σ 2p > π 2p

Filling the orbitals: the second row diatomics  B 2, C 2, and N 2 are case B  O 2, F 2 and Ne 2 are case A  Note bond order from MO theory matches what we obtain from Lewis dot diagrams

MO theory and magnetism  Paramagnetism: substance is attracted by a magnetic field  Diamagnetism: substance is repelled by a magnetic field  Paramagnetic effect is much greater than diamagnetic effect  Diamagnetic substances have no unpaired electrons  Paramagnetic substances have unpaired electrons

Magnetic properties of O 2 expose limitations of Lewis  MO theory gives two degenerate π and π * orbitals  In O 2, Hund’s rule states that these are singly occupied  O 2 is paramagnetic

Correlate magnetic properties with MO diagram

Heteronuclear molecules and NO  NO contains 11 electrons implies high reactivity  Two possible Lewis structures  Lewis structure favours unpaired electron on N  Experimental bond order appears greater than NO 00 NO

MO description of NO  AOs of more electronegative atom are lower in energy  The bonding orbitals have more of the more electronegative atom character  The antibonding orbitals have more of the less electronegative atom character  MO diagram shows bond order 2.5 consistent with experiment  Unpaired electron is in π* orbital which is more N-like (consistent with Lewis dot structure