PIB and Highly Conjugated Molecules (14.7)
• Conjugated molecules have alternating carbon-carbon single and double
bonds
– π-electrons can move freely along all carbon atoms in the conjugated portion of the
molecule
– The 1D PIB model can be crudely applied to the energy states of a polyene (e.g., βcarotene)
• Energy levels (and wavefunctions) can be predicted given some
information
– Energy depends on quantum number, mass of particle (electron), and length of the box
– Number of nodes in the wavefunction can be predicted based on the quantum number
Electronic Spectroscopy of Highly Conjugated Molecules (14.7)
• Highly conjugated molecules often have color associated with them
– Absorb certain colors of visible light, so we see complimentary colors reflected back to
us
– Light is absorbed by an electron that is promoted from one state to a higher energy
state
– If PIB model holds, we can calculate the energy of the photon absorbed if we know two
things: length of the box and the energy levels the electron starts in and ends in
• Length of the box can be approximated by summing up the carbon-carbon
bond lengths in the conjugated part of the molecule
– Box is capped by double bonds, with single and double bonds alternating in the interior
– For β-carotene, we have 10 C-C single bonds (0.154 nm each) and 11 C-C double bonds
(0.133 nm each)
• Energy levels are determined by number of double bonds in the system
– Electron is promoted from last occupied π-bond (HOMO) to an unoccupied π-bond
(LUMO)
– For β-carotene: HOMO (n = 11) and LUMO (n = 12)
Electronic Spectroscopy of Highly Conjugated Molecules (Con’t)
• Energy of the photon absorbed can be predicted from formula for PIB
energy levels
– Knowing the quantum numbers involved simplifies the formula (watch units!)
h 

hc

 E n 1  E n
E n 1  E n  2 n  1
h
2
8 ma
2

• We can also predict what happens when we change some of the
conditions of the problem
– When conjugation is increased, the length of the box is increased (how does this affect
energy of the electronic transition?)
– If conjugation increases, what else changes?