Molecular orbital theory. Overcoming the shortcomings of the valence bond

Transcription

1 Molecular orbital theory Overcoming the shortcomings of the valence bond

2 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 O 2 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 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)

5 Wavefunctions and electron density Ψ describes the electron path Ψ 2 describes the electron density Orbital Ψ A and Ψ B overlap to form bond 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

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

7 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

8 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

9 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)

10 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)

11 On the existence of molecules: MO energy level diagrams H 2 (2 electrons) in bonding σ MO; antibonding σ* MO is vacant. Total number of bonds = (+1 0) = 1 Configuration (σ 1s ) 2 He 2 (4 electrons): two in bonding σ, two in antibonding σ* Total number of bonds = (+ 1 1) = 0 Configuration (σ 1s ) 2 (σ* 1s ) 2

12 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?

13 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

14 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 σ 2s and σ* 2s orbitals lower than 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)

15 Consequences of interaction between 2s and 2p 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 NO interaction: σ 2p < π 2p Case B STRONG interaction: σ 2p > π 2p

16 Second row diatomics: interaction decreases across period B 2, C 2, and N 2 are case B (strong interaction) O 2, F 2 and Ne 2 are case A (weak interaction) Bond order from MO theory matches bond order from Lewis dot diagrams perfectly

17 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

18 Magnetism of O 2 and the limitations of Lewis O 2 is paramagnetic (YouTube) O 2 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

19 MO theory to the rescue MO theory gives two degenerate π and π * orbitals Hund s rule states that these are singly occupied O 2 is paramagnetic If the σ* was below the π* what is the situation?

20 Correlate magnetic properties with MO diagram

21 Heteronuclear molecules and NO NO contains 11 electrons implies high reactivity N O Lewis structure favours unpaired electron on N Experimental bond order appears greater than 2 N O

22 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 N 0 O