13 - MIT Department of Chemistry 5.74, Spring 2004:...

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p. 88 NUCLEAR MOTION COUPLED TO ELECTRONIC TRANSITION * Vibronic structure is absorption spectra; wavepacket dynamics; coupling of electronic states to intramolecular vibrations or solvent; coupling of electronic excitation/excitons in solids/semiconductors to phonons. Also, extensions to Förster and Marcus Theories. Two-Electronic Level System: Displaced harmonic oscillators T 0 q +, We will calculate the electronic absorption spectrum using T.C.F. H H 0 . Vt 0 TOT ge Hg e He . H g TOT TQ . W g Q . E g H e TOT +,. W e Q E e Our Model : Nuclear kinetic energy p 2 /2 m W g Q / W e Q : Potential energy 1 2 m Z 0 2 Q 2 1 2 m 0 2 Q 0 d 2 E e 0 E g : Electronic energy gap * See Mukamel, p. 217, also p. 189. Q 0d E e E g E e g MIT Department of Chemistry 5.74, Spring 2004: Introductory Quantum Mechanics II Instructor: Prof. Andrei Tokmakoff
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p. 89 +, 2 2 2 1 0 2 2 22 1 0 2 2 2 . Z0. . . Z . TOT ee e e TOT g gg p Hm Q d E H E m p Q = H E m 1) Born-Oppenheimer Approximation g gn \ 2) Condon Approximation No Q dependence to P# 0 No vibrational excitation accompanying electronic excitation Vt 0 ¢ Et g P ge e . e eg g Now let’s calculate an absorption lineshape. Write dipole correlation function: 00 II nII n tp n t n PP ¦ iH t / iH t / g, 0 P P == since at low T all population in 0 By substituting our Hamiltonian 0 H and dipole operator P we find: + , 2 eg g e iE E t/ iH t / iH t / eg Ct e 0 PP P = = = Note we can write our correlation function as 2 () mn it g t nm n n p V e 0 ¦ Z where g(t) is our lineshape function. Lets concentrate on F(t) = exp ( 0 g ( t )), sometimes known as the dephasing function: electronic state vibrational state e 0 i eg t Ft
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p. 90 +, 00 g e iH t / iH t / Ft ee 0 = = From problem set 1: displacement operator !! e i D p Qe 0 i p Q . = @ H e e idp / = H g e 0 idp / = gg iH t / iH t / idp / idp / eee e 0 0 p == (+++) + + +* + , 0 idp t / idp / 0 since pt U g p 0 U g Now, using !!
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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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13 - MIT Department of Chemistry 5.74, Spring 2004:...

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