MIT5_74s09_lec17

MIT5_74s09_lec17 - MIT OpenCourseWare http:/ocw.mit.edu...

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MIT OpenCourseWare http://ocw.mit.edu 5.74 Introductory Quantum Mechanics II Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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Andrei Tokmakoff, MIT Department of Chemistry, 6/15/2009 p. 11-54 11.6. TWO-DIMENSIONAL CORRELATION SPECTROSCOPY Our examination of pump-probe experiments indicates that the third-order response reports on the correlation between different spectral features. Let’s look at this in more detail using a system with two excited states as an example, for which the absorption spectrum shows two spectral features at ω ba and ca . Imagine a double resonance (pump-probe) experiment in which we choose a tunable excitation frequency pump , and for each pump frequency we measure changes in the absorption spectrum as a function of probe . Generally speaking, we expect resonant excitation to induce a change of absorbance. The question is: what do we observe if we pump at ba and probe at ca ? If nothing happens, then we can conclude that microscopically, there is no interaction between the degrees of freedom that give rise to the ba and ca transitions. However, a change of absorbance at ca indicates that in some manner the excitation of ba is correlated with ca . Microscopically, there is a coupling or chemical conversion that allows deposited energy to flow between the coordinates. Alternatively, we can say that the observed transitions occur between eigenstates whose character and energy encode molecular interactions between the coupled degrees of freedom (here β and χ) :
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Andrei Tokmakoff, MIT Department of Chemistry, 6/15/2009 p. 11-55 Now imagine that you perform this double resonance experiment measuring the change in absorption for all possible values of ω pump and probe , and plot these as a two-dimensional contour plot: 1 This is a two-dimensional spectrum that reports on the correlation of spectral features observed in the absorption spectrum. Diagonal peaks reflect the case where the same resonance is pumped and probed. Cross peaks indicate a cross-correlation that arises from pumping one feature and observing a change in the other. The principles of correlation spectroscopy in this form were initially developed in the area of magnetic resonance, but are finding increasing use in the areas of optical and infrared spectroscopy. Double resonance analogies such as these illustrate the power of a two-dimensional spectrum to visualize the molecular interactions in a complex system with many degrees of freedom. Similarly, we can see how a 2D spectrum can separate components of a mixture through the presence or absence of cross peaks.
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Andrei Tokmakoff, MIT Department of Chemistry, 6/15/2009 p. 11-56 Also, it becomes clear how an inhomogeneous lineshape can be decomposed into the distribution of configurations, and the underlying dynamics within the ensemble. Take an inhomogeneous lineshape with width Δ and mean frequency ω ab , which is composed of a distribution of homogeneous transitions of width Γ . We will now subject the system to the same
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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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MIT5_74s09_lec17 - MIT OpenCourseWare http:/ocw.mit.edu...

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