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CHEM 121 Studioby Learn4Less · UBC CHEM 121

CHEM 121 glossary

HOMO–LUMO gap

The energy difference ΔE\Delta E between the HOMO and the LUMO: the smallest energy the molecule can absorb to promote an electron, which sets its longest-wavelength absorption, λ=hc/ΔE\lambda = hc/\Delta E. For a polyene in the box model, ΔE=(N+1)h2/(8meL2)\Delta E = (N+1)h^2/(8m_eL^2), so longer conjugation gives a smaller gap and a longer λ\lambda.

π molecular orbitals of 1,3-butadieneFour π MOs of butadiene with energies proportional to n squared (particle in a box). The four π electrons fill the two lowest MOs; the highest filled is the HOMO (n = 2), the lowest empty is the LUMO (n = 3). Absorbing a photon whose energy equals the gap promotes an electron from HOMO to LUMO.n = 1E₁HOMO n = 24E₁LUMO n = 39E₁n = 416E₁hν = ΔE

A photon with hν=ΔEh\nu = \Delta E lifts an electron from the HOMO to the LUMO.

Example

1,3-Butadiene: LL = 0.560 nm and NN = 4, so ΔE=5h2/(8meL2)=9.61×10−19\Delta E = 5h^2/(8m_eL^2) = 9.61 \times 10^{-19} J and λ=hc/ΔE\lambda = hc/\Delta E = 207 nm (measured 217 nm). That is in the UV, so butadiene is colourless.

See alsoHOMO (highest occupied molecular orbital)LUMO (lowest unoccupied molecular orbital)λmax (wavelength of maximum absorption)Conjugation