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MOLECULAR STRUCTUREMOLECULAR STRUCTURE
CHAPTER 14CHAPTER 14
Heteronuclear DiatomicsHeteronuclear Diatomics
• Almost all have polar bonds
• MO of the form: Ψ = cAA + cBB with cA ≠ cB
• where cA and cB are weighted coefficients
• Proportion of AOA = │cA│2 and of AOB = │cB│2
• For pure covalent bond │cA│2 = │cB│2
• For pure ionic bond in A+B− cA = 0 and cB = 1
• e.g., for HF Ψ = cHΨH + cFΨF
H F
electron richelectron richregionregionelectron poorelectron poor
regionregion
FH
e- riche- poor
+ -
Fig 11.36 AOs of H and F atoms with their MOs
Ψ = cHΨH ± cFΨF
1σ
2σ*
Heteronuclear DiatomicsHeteronuclear Diatomics
• Electronegativity - the ability of an atom in amolecule to attract electrons towards itself
Covalent
share e-
Polar Covalent
partial transfer of e-
Ionic
transfer e-
Increasing difference in electronegativity
Classification of bonds by difference in electronegativity
Difference Bond Type
0 Covalent
2 Ionic
0 < and <2 Polar Covalent
The Variation PrincipleThe Variation Principle
• A systematic method for determining thecoefficients in the LCAOs used to build the MOs
e.g., Ψ = cAA + cBB with cA ≠ cB
• Principle is basis for all modern MO calculations
• If an arbitrary wavefunction is used to calculatethe energy, the value calculated can never beless than the true energy
• Coefficients in trial function are varied until lowestenergy is achieved (HΨtrial = EtrialΨtrial)
Example of application of variation principle
Assume Ψtrial = cAA + cBB real but not normalized
d
dHE
*
*
The energy is the expectation value of the energyoperator:
Results are the secular equations
(αA-E)cA + (β-ES)cB = 0
(βA-ES)cA + (αA-E)cB = 0
Solved with the secular determinant
αA-E β-ES
β-ES αA-E= 0
Coulombintegral
Resonance integral
Example of application of variation principle
in HW Ex 11.9(b)
with trial function2ar
trial Ae
1st derivative = slope of line tangent to curve
0da
dEtrial
Fig 11.37 The molecular orbital energy leveldiagram for NO
Ground state configuration:
(1σ)2 (2σ)2 (3σ*)2 (1π)4 (2π*)1
3σ* and 1π primarily of Ocharacter
HOMO
LUMO
N=O••
••
••
•
Molecular orbitals for Polyatomics
• As with diatomics, we construct LCAO-MOs
i
iic
• All diatomics are linear, but polyatomics havea number of different geometries
• To determine molecular geometry, calculate Efor possible nuclear positions
• Lowest E indicates correct conformation
The Hϋckel Approximation
• For conjugated systems
• π orbitals treated separately from rigid molecular
frame formed from σ orbitals
• All C atoms treated identically so all Coulomb
integrals α are set equal
e.g., for H2C=CH2 take σ bonds as fixed
and find energy of π and π*
The Hϋckel Approximation
• Express π orbitals as LCAOs of C2p obitals
• Solve secular determinant
Ψ = cAA + cBB
αA-E β-ES
β-ES αA-E= 0
• Roots of equation: E± = α ± β
Fig 11.38 Hϋckel MO energy levels of ethene
HOMO
LUMO
Frontier orbitals
Fig 11.39 Hϋckel MO energy levels of butadiene
Fig 11.40 The σ framework of benzene formedfrom overlap of Csp2 hybrids
120°
Fig 11.41 Hϋckel MO energy levels of benzene
Bonding character
Antibonding character
Mixture of bonding, nonbonding,and antibondingcharacter
α+2β
α-2β
α+β
α-β
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