pset04 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY 5.73 Quantum...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY 5.73 Quantum Mechanics I Fall, 2002 Professor Robert W. Field Problem Set #4 DUE : At the start of Lecture on Friday, October 4. Reading : CTDL, pages 94-144. Problems : 1. RKR and Franck-Condon. Use Robert LeRoy's programs! http://theochem.uwaterloo.edu/~leroy/ For CO, consider the A 1 and X 1 + electronic states. The molecular constants (in cm −1 units) are: X 1 + A 1 Y 00 0.190 –0.554 Y 10 2169.814 1518.24 Y 20 –13.288 –19.40 Y 30 0.01051 0.766 Y 01 1.931281 1.6115 Y 11 –0.017504 –0.02325 Y 21 5.487 × 10 −7 0.00159 μ = 6.85620871 amu D 0 0 (X) = 89462cm −1 T e = 65075.77cm −1 D 0 0 (A) = (89462–64748)cm −1 =24714 cm –1 R e (X) = 0.1128323nm R e (A) = 0.12353nm
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Chemistry 5.73 Page 2 Problem Set #4 A. Determine the RKR V( x ) potential energy curves for the CO X 1 + and A 1 electronic states. Use the following G( v ) and B( v ) functions GY Y Y Y BY Y Y ( ) (/ ) ) ) () ( /) ( vv v v v =+ + + + + + + + + 00 10 20 2 30 3 01 11 21 2 12 as input to RKR. Ask RKR to calculate turning points for –1/2 v < 15 in steps of 0.25. B. Calculate overlap integrals, v |v ′′⟩ , and Franck Condon factors for all transitions between v = 0 of the X-state to 0 v 15 of the A-state. The Franck-Condon factor is q ′′ =′′ | 2 where q is the F-C factor, v and v are respectively the vibrational quantum numbers for the upper ( A ) and lower ( X ) electronic states. C. Sketch what the A–X absorption spectrum would look like. Consider that initially only v = 0 is populated and represent each vibrational band as a vertical line, at the frequency of the v ′ ← v = 0 transition, with height equal to the F-C factor. [This cartoon of the spectrum ignores the rotational structure of each vibrational band.] D. Now create a wavepacket in the A 1 state by using a 1fs laser pulse, centered at ~72,000 cm –1 , to in effect transfer the v
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pset04 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY 5.73 Quantum...

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