MOLECULAR STRUCTURE CHAPTER 14 Experiments show O 2 is paramagnetic

Heteronuclear Diatomics Almost all have polar bonds MO of the form: Ψ = c A A + c B B with c A ≠ c B where c A and c B are weighted coefficients Proportion of AO A = │ c A │ 2 and of AO B = │ c B │ 2 For pure covalent bond │ c A │ 2 = │ c B │ 2 For pure ionic bond in A + B − c A = 0 and c B = 1 e.g., for HF Ψ = c H Ψ H + c F Ψ F

H F electron rich region electron poor region F H e - riche - poor ++ --

Fig AOs of H and F atoms with their MOs Ψ = c H Ψ H ± c F Ψ F 1σ1σ 2σ*2σ*

Heteronuclear Diatomics Electronegativity - the ability of an atom in a molecule 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 DifferenceBond Type 0Covalent  2 Ionic 0 < and <2 Polar Covalent

The Variation Principle A systematic method for determining the coefficients in the LCAOs used to build the MOs e.g., Ψ = c A A + c B B with c A ≠ c B Principle is basis for all modern MO calculations If an arbitrary wavefunction is used to calculate the energy, the value calculated can never be less than the true energy Coefficients in trial function are varied until lowest energy is achieved (HΨ trial = E trial Ψ trial )

Example of application of variation principle Assume Ψ trial = c A A + c B B real but not normalized The energy is the expectation value of the energy operator: Results are the secular equations ( α A -E)c A + (β-ES)c B = 0 (β A -ES)c A + ( α A -E)c B = 0 Solved with the secular determinant α A -E β-ES α A -E = 0 Coulomb integral Resonance integral

Example of application of variation principle in HW Ex 11.9(b) with trial function 1st derivative = slope of line tangent to curve

Fig The molecular orbital energy level diagram for NO Ground state configuration: (1σ) 2 (2σ) 2 (3σ*) 2 (1π) 4 (2π*) 1 3σ* and 1π primarily of O character HOMO LUMO N=O

Molecular orbitals for Polyatomics As with diatomics, we construct LCAO-MOs All diatomics are linear, but polyatomics have a number of different geometries To determine molecular geometry, calculate E for 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 H 2 C=CH 2 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 = c A A + c B B α A -E β-ES α A -E = 0 Roots of equation: E ± = α ± β

Fig Hϋckel MO energy levels of ethene HOMO LUMO Frontier orbitals

Fig Hϋckel MO energy levels of butadiene

Fig The σ framework of benzene formed from overlap of Csp 2 hybrids 120°

Fig Hϋckel MO energy levels of benzene Bonding character Antibonding character Mixture of bonding, nonbonding, and antibonding character α+2β α-2β α+βα+β α-βα-β