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note
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Compare our results with Figures 3 and 4 of ref 1 and Figures 5 and 6 of ref 2.
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See also Figures 5 and 6 of Zhu, F.; Galli, C.; Hochstrasser, R. M. J. Chem. Phys. 1993, 98, 1042.
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11444269039
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note
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In the equal-energy case the two site energies are the same on average, so the donor and acceptor designations are arbitrary. We refer to donor-excited and acceptor-excited states to identify an initially excited state and one excited via energy transfer, but alt our calculations treat both chromophores on the same footing.
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19
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0001109194
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Continuous-wave spectra of this dimer model have been well documented: Fulton, R. L.; Gouterman, M. J. Chem. Phys. 1964, 41, 2280.
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11444250389
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11444257391
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note
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The sign in eq 11 is chosen so that increased stimulated emission leads to a positive change in 5.
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27
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11444258030
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note
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We neglect the effects of pulse overlap, which should be insignificant for the short pulses of differing center frequency that we employ.
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28
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0002373685
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Ungar, L. W.; Cina, J. A. Ady. Chem. Phys. 1997, 100, 171, Appendix A. The equivalence between stimulated and spontaneous emission is approximate, as it neglects the frequency dependence of the density of states of the radiation field in the latter process.
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11444270749
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note
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2 Γ, where Γ is the angle between the polarizations of the two pulses. The absence of a cosΓsinΓ cross-term can be checked for the stimulated emission component by explicitly averaging eq 11.
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32
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0003502032
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Mukamel, S.1
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33
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11444268112
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note
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b, ≤ 9.
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35
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11444249355
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note
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2} Where e = 1 or l′
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36
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11444267865
-
-
note
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The surface-crossing description of energy and vibrational-coherence transfer given here can be re-framed in terms more closely aligned with the spectral-overlap picture of Förster theory, and conversely. A coherently vibrating donor molecule exhibits an oscillatory time-dependent emission spectrum. At the inner turning point of such a short-pulse-excited vibration, the peak emission frequency matches the peak absorption of an equal-site-energy acceptor molecule in its electronic ground state, facilitating the reabsorption of donor-emitted light by the acceptor and launching a Franck-Condon-excited wave packet in the acceptor whose phase of motion matches that of the donor. Similar time-dependent spectral descriptions can be given for various differences in site energy between donor and acceptor, and the relative phases of vibrational motion in the two molecules predicted accordingly. See the comments below on ref 52, which generalizes Förster theory along lines similar to these.
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37
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0001775120
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The initial anisotropy value 0.4 was first observed in picosecond experiments on fluorescein dyes: Fleming, G. R.; Robinson, G. W. Chem. Phys. 1976, 17, 91.
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0003069276
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y bands of cadmium tetraphenylporphyrin (assigned to vibrational coherence in stimulated emission and excited-state absorption); see Figure 2 of Galli, C.; Wynne, K.; LeCours, S. M.; Therien, M. J.; Hochstrasser, R. M. Chem. Phys. Lett. 1993, 206 493.
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11444257540
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note
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vib on a reduced sample of 110 realizations under the same conditions as Figure 3 exhibits undamped vibration-period oscillations in both components of the polarized emission and a long-time anisotropy in the same range.
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41
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11444266544
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note
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Pump-probe calculations have been reported for dimers with separate intramolecular vibrations and unequal site energies. These were compared with experiments from the LHC-II antenna of green plants, the B820 subunit of LH1, and the pigment-protein complexes of cyanobacteria. See ref 20 and Section 9.2 of ref 21.
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43
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0001531951
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b) = (d/2, d/2) (see Figure 8); the distance from the Franck-Condon point is decreased to d/√2 and the absorption bandwidth to the adiabatic levels thereby narrowed by 1/√2 relative to the site-state absorption of the weak-coupling case.
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11444256831
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note
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The theories of refs 43 and 44 are based on separating vibrations that do or do not couple crude (i.e., nuclear coordinate independent) electronic eigenstates, rather than the nuclear-coordinate-dependent adiabatic electronic states used here. While the roles of these groups of coordinates resemble those of our q and Q, respectively, the identification is therefore not exact
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47
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11444269630
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note
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vib in the numerical calculation.
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11444258029
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note
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FC is larger than 2J.
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55
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11444251476
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note
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II and S∥. plotted in Figure 11, and the individual terms cannot be separated.
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56
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0038617364
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0000141639
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Vibrational quantum beats were not observed, however, in femtosecond pump-probe polarization experiments on the B850 band of the peripheral light-harvesting complex LH2, despite its structural similarity to LH1: Nagarajan, V.; Johnson, E. T.; Williams, J. C.; Parson, W. W. J. Phys. Chem. B 1999, 103, 2297.
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11444270068
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note
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br.
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67
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11444254541
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note
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Jean and Fleming noted a related broadening of the vibrational power spectrum in their calculations on strongly coupled one-dimensional curve-crossing system. See Figures 6 and 8 of ref 47.
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68
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11444266111
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See the residual power spectra in Figure 8 of ref 2 and also Figures 5 and 6 of ref 4.
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See the residual power spectra in Figure 8 of ref 2 and also Figures 5 and 6 of ref 4.
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11444262718
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note
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Because the probe is here assumed to be shorter than both electronic and vibrational time-scales, we replace the resonance curves in Figure 8 with their anti-diagonal tangent lines.
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