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Molecular orbital theory

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.

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Molecular orbital theory

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  1. Molecular orbital theory Overcoming the shortcomings of the valence bond

  2. Learning objectives • Describe basic principles of MO theory • Write MO diagrams for some simple diatomic molecules • Explain optical and magnetic properties of O2 using MO theory

  3. 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

  4. 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)

  5. Wavefunctions and electron density • Ψ describes the electron path • Ψ2 describes the electron density • 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

  6. 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

  7. MO energy level diagrams: H2 exists but He2 does not • In H2 two electrons are paired in the bonding σ MO, and the antibonding σ* MO is vacant. • Total number of bonds = 1 • Configuration (σ1s)2 • In He2 four electrons are paired, two in the bonding and two in the antibonding σ* • Total number of bonds = 0 • Configuration (σ1s)2(σ*1s)2

  8. 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

  9. Second row elements • Li2 contains 6 electrons • Bonding σorbitals 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?

  10. Formation of π orbitals in MO • Defining the internuclear axis as z • Overlap of the pz orbitals produces σ bond • Overlap of pxand py orbitals produces π bonds

  11. 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 σ2s and σ*2s orbitals are lower than the σ2p orbital • Overlap of the 2pz is greater than that of the 2px or 2py so σ2p is lower than the π2p orbital • The π2pand π*2p are degenerate (2 orbitals with the same energy)

  12. 2s - 2p interactions affect energy levels • 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: σ2p < π2p • Case B: σ2p > π2p

  13. Filling the orbitals: the second row diatomics • B2, C2, and N2 are case B • O2, F2 and Ne2 are case A • Note bond order from MO theory matches what we obtain from Lewis dot diagrams

  14. 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

  15. Magnetic properties of O2 expose limitations of Lewis • MO theory gives two degenerate π andπ* orbitals • In O2, Hund’s rule states that these are singly occupied • O2 is paramagnetic

  16. Correlate magnetic properties with MO diagram

  17. -1 0 0 +1 N O N O 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 2

  18. 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

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