Molecular orbital theory Overcoming the shortcomings of the valence bond

Learning objectives  Describe basic principles of MO theory  Describe differences between Valence Bond and MO theories  Write MO diagrams for some simple diatomic molecules  Explain optical and magnetic properties of O2 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 – ΨA (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  Ψ2 describes the electron density

 Orbital ΨA and ΨB overlap to form bond  Molecular wavefunction (ΨA + ΨB)  Joint density is (ΨA + ΨB)2 = ΨA2 + ΨB2 + 2ΨAΨB  In molecular orbital the density is greater between the nuclei by an amount 2ΨAΨB

Molecular orbital theory: bonding and antibonding  Bonding orbital: additive combination of atomic orbitals σ  Antibonding orbital: subtractive combination of atomic orbitals σ*

Linear combination of atomic orbitals  Valence Bond theory  Hybrid orbitals made using weighted average of different ao’s on the same atom  Hybrid orbital confined to that atom

 Molecular Orbital theory (LCAO)  Weighted average of different ao’s on all atoms of molecule  Resulting mo involves all atoms of molecule

Formation of molecular orbitals  Bonding orbital  More electron density between nuclei  More electrostatic attraction  Bonding MO at lower energy

 Antibonding orbital  No density between atoms  Lower electrostatic attraction  Antibonding MO at higher energy

Bond order BO  1 { bonding elecs -  antibonding elecs} 2  Bond order 1 = single bond (1/2 x 2)  Bond order 2 = double bond (1/2 x 4)  Bond order 3 = triple bond (1/2 x 6)

Summary of important concepts in MO  MO’s are formed by linear combination of AO’s  Two AO’s combine to give two MO’s: one is higher in energy, one is lower  Orbital filling follows aufbau principle: lowest energy orbitals first  Maximum occupancy of MO is two (spin-paired)  Hund’s rule: degenerate orbitals are singly occupied before pairing  Bond order is one half times (number of electrons in bonding MO’s minus number of electrons in anti-bonding MO’s)

On the existence of molecules: MO energy level diagrams  H2 (2 electrons) in bonding σ MO; antibonding σ* MO is vacant.  Total number of bonds = (+1 – 0) = 1  Configuration (σ1s)2

 He2 (4 electrons): two in bonding σ, two in antibonding σ*  Total number of bonds = (+ 1 – 1) = 0  Configuration (σ1s)2(σ*1s)2

Second row elements  Li2 contains 6 electrons  Bonding σ orbitals between 1s and 2s  Antibonding σ* orbitals between 1s and 2s  Occupied: σ1s,σ2s, and σ*1s  Bond order = 2 – 1 = 1  Does Be2 exist?

Formation of π orbitals in MO  Defining the internuclear axis as z  Overlap of the pz orbitals produces σ bond  Overlap of px and py orbitals produces π bonds

General energy level diagram for second-row homonuclear diatomics  Assumes no interaction between the 2s and 2p orbitals  2s orbitals lower in energy than 2p orbitals  σ2s and σ*2s orbitals lower than σ2p orbital

 Overlap of the 2pz is greater than that of the 2px or 2py so σ2p is lower than the π2p orbital  The π2p and π*2p are degenerate (2 orbitals with the same energy)

Consequences of interaction between 2s and 2p

 The 2s and 2p orbitals do interact  σ2s and σ2p orbitals move further apart in energy  Strength of interaction changes with atomic number  Case A NO interaction: σ2p < π2p  Case B STRONG interaction: σ2p > π2p

Second row diatomics: interaction decreases across period  B2, C2, and N2 are case B (strong interaction)  O2, F2 and Ne2 are case A (weak interaction)  Bond order from MO theory matches bond order from Lewis dot diagrams perfectly

Magnetism and electrons  Paramagnetism: attracted by a magnetic field  Diamagnetism: repelled by a magnetic field  Paramagnetic effect is much greater than diamagnetic effect

 Electrons have magnetic moments  Diamagnetic substances have no unpaired electrons  Paramagnetic substances have unpaired electrons

Magnetism of O2 and the limitations of Lewis     

O2 is paramagnetic (YouTube) O2 must contain unpaired electrons Lewis dot diagram shows simple lone pairs Lewis predicts diamagnetism Another shortcoming of Lewis dot structures Lewis dot structure

O

O

   

MO theory to the rescue *

MO theory gives two degenerate π and π orbitals Hund’s rule states that these are singly occupied O2 is paramagnetic If the σ* was below the π* what is the situation?

Correlate magnetic properties with MO diagram

Heteronuclear molecules and NO  NO contains 11 electrons implies high 0 0 reactivity -1 +1

N

O N

O

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

MO description of NO  AOs of more electronegative atom lower in energy (O more electronegative than N)  Bonding orbitals have more of more electronegative atom character (O)  Antibonding orbitals have more of less electronegative atom character (N)

 MO diagram shows bond order 2.5 consistent with experiment  Unpaired electron in π* orbital is more N-like (consistent with Lewis dot structure)

0

0

N

O