14 - Page 99 MIT Department of Chemistry 5.74, Spring 2004:...

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MIT Department of Chemistry Page 99 5.74, Spring 2004: Introductory Quantum Mechanics II Instructor: Prof. Andrei Tokmakoff Förster Energy Transfer Nonradiative transfer of electronic excitation from a donor molecule to an acceptor molecule: * * D + A D + A The transfer arises from dipole-dipole coupling, but does not involve a light field. In general, there are four states to worry about: |⟩ D* A* V A D 0d D Q D A Q A Let’s just consider the case where we have already excited the donor electronic transition, and the acceptor is in the ground state. We will state that the system can only exist either with the donor excited and acceptor in the ground state, or vice-versa. If the system is weakly coupled through a dipole-dipole interaction, we can write: HH 0 + V = D A H * * A D H * * = D A + A H 0 D A
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Page 100 2 m 2 H D = p + ω 2 ( Q d D ) + E D 2 m 2 2 H A = p + ω 2 ( Q d A ) + E A E D m 2 m E A d D Q d A V |⟩ D* A* Q DA represents the electronic and nuclear states for both donor and acceptor molecules, * (Here * which could be more properly written Dn An A ). D * The interaction between donor and acceptor takes the form of a dipole-dipole interaction: 3 ( µ⋅ r ˆ )( −µ A ⋅µ A D r ˆ ) D V = 3 r where r is the distance between donor and acceptor molecules, and the dipole operators are A * A * µ= A + A * A µ AA * µ A A D * D * D + D * D µ DD * µ D D For the dipole moment, we can factor out the orientational contribution as a unit vector, i.e., µ A = u ˆ A A where A is the dipole operator. This allows us to write: D A A D * * A D D A * * V
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This note was uploaded on 11/28/2011 for the course CHEM 5.74 taught by Professor Robertfield during the Spring '04 term at MIT.

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14 - Page 99 MIT Department of Chemistry 5.74, Spring 2004:...

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