Abstract
We propose a general framework for calculating and interpreting multidimensional electronic spectroscopy signals in terms of the wave-packet-shaping, amplitude-transferring effects of femtosecond laser pulses on time-dependent molecular states. The chapter sets up basic expressions for two-dimensional wave-packet interferometry (WPI) experiments on an electronic energy-transfer (EET) system as a quantum yield-weighted sum of contributing overlaps between multi-pulse wave packets. Further, we identify the ranges of interpulse delay within which each overlap is not excluded by its order of pulse action from contributing to the WPI signal. Example calculations are carried out for the case of a spatially oriented, weakly-coupled EET dimer. Semiclassical analyses of the necessary conditions for phase-space coincidence between the bra and ket, the dynamical consequences of a site-energy difference between the two chromophores, and the sensitivity of contributions accessing or originating from doubly electronically excited states of the dimer to the possible presence of an exciton shift all provide physical interpretations of individual wave-packet overlaps.
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Notes
- 1.
The monomers may be the same or different. Our model neglects states such as \( | \bar{e}^{\prime }g \rangle \) or \( | \bar{e}^{\prime }e^{\prime \prime } \rangle \) in which one or both of the molecules occupy higher-lying electronic excited states.
- 2.
We do not include an average over any possible orientational distribution of the dimer at a given location, regarding this as being implicitly included in the spatial distribution of population.
- 3.
Note that any polarization dependence of a 2D-WPI signal enters through the \( F_{I}^{( \xi \bar{\xi } )}\).
- 4.
The net signal from an isotropic sample of dimers with a certain internal geometry would be a weighted sum of signals from a handful of representative space-fixed orientations.
- 5.
Specifically, these assumptions mean that \( t_{CB} \) is positive and greater than the pulse duration. In addition, since \( t_{BA} \) and \( t_{DC} \) are defined to be positive, they also mean that pulse-overlap effects will be ignored when either is very short.
- 6.
2D interferograms from \( \langle \uparrow _{A} \! | \! \uparrow _{B} \uparrow _{C} \downarrow _{D} \rangle \) alone in model dimers akin to that considered here, under the same polarization conditions—but with arbitrarily abrupt laser pulses—were the subject of earlier work by Cina et al. [6].
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Acknowledgements
This work was supported by a grant from the US National Science Foundation. JAC thanks Professor Cathy Wong, University of Oregon, for helpful conversations.
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Cina, J.A., Kiessling, A.J. (2019). Nuclear Wave-Packet Dynamics in Two-Dimensional Interferograms of Excitation-Transfer Systems. In: Cho, M. (eds) Coherent Multidimensional Spectroscopy. Springer Series in Optical Sciences, vol 226. Springer, Singapore. https://doi.org/10.1007/978-981-13-9753-0_3
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