5.61 Fall 2017 Lecture#34 page 1 Lecture#34 ELECTRONIC...

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5.61 Fall 2017 Lecture #34 page 1 updated 12/1/17 6:23 AM ! Lecture #34: ELECTRONIC SPECTROSCOPY AND PHO- TOCHEMISTRY The ability of light to induce electronic transitions is one of the most fascinating aspects of chemistry. It is responsible for the colors of the various dyes and pigments we manu- facture and forms the basis for photosynthesis, where photons are converted into chemi- cal energy. This all arises because electrons are the “glue” that holds molecules together, and it makes electronic spectroscopy perhaps the most natural form of spectroscopy for chemistry. The selection rules for purely electronic spectroscopy are fairly easy to write down. The transition between i and f is forbidden if the transition dipole between the states is zero: ! μ i f = Ψ el f * ˆ μ Ψ el i d τ el = e Ψ el f * ˆ r Ψ el i d τ el where we have noted that the dipole moment operator takes on a simple form for electrons. Unfortunately, the electronic wavefunctions of real molecules are so complicated that we typically cannot say anything about whether a given transition is allowed or not. There are only two cases where we get selection rules. The first case is if the molecule has some symmetry. For example, if the molecule has a mirror plane, we will be able to characterize the electronic eigenfunctions as being odd or even with respect to reflection. Then we will find that transitions between two even (or two odd) functions will be forbidden because r is odd, (even) × (odd) × (even)=odd and the integral of an odd function gives zero. In general, we see that allowed elec- tronic transitions must involve a change in symmetry . For large molecules, or even small molecules in asymmetric environments, it is rare that we have a perfect symmetry. However, for an approximate symmetry we expect the functions to be nearly symmetric, so that transitions that don’t involve a change in (approximate) parity will be only weakly allowed. The second thing we note is that the dipole moment is a one electron operator . That is to say, it counts up contributions one electron at a time. This stands in contrast to an opera- tor like the Coulomb interaction, which counts up energy contribution between pairs of electrons repelling one another – the Coulomb repulsion is a two electron operator while the dipole is a one electron operator . As a result, the brightest transitions (i.e. the ones with large transition dipoles) tend to be dominated by the motion of one elec- tron at a time. Thus, a ( σ 2 π 2 ) ( σ 2 ππ *) transition would typically be allowed be- cause we are just moving one electron (from π to π *). Meanwhile, a ( σ 2 π 2 ) ( σ 2 π * 2 ) transition would typically be forbidden because we have to move two electrons from π to π * to make it work. In practice the one-electron selection rule is only approximate because real electronic states never differ by a purely one electron or two electron substi- tution. As we saw in discussing electron correlation, the wavefunctions will be mixtures of many different substituted states. However, in practice, the
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