Viewpoint Cite This: J. Phys. Chem. Lett. 2018, 9, 1568−1572
pubs.acs.org/JPCL
Coherence from Light Harvesting to Chemistry
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properties of the ensemble to be revealed that, in turn, tell us about the underlying Hamiltonian that is relevant to the natural function under any excitation conditions. Specifically, the twodimensional electronic spectroscopy experiments reveal that the donor emission spectrum is correlated with the acceptor absorption spectrum; these quantities are not independent, as assumed in Förster theory. Therefore, it has been discovered that a more sophisticated treatment of the spectral overlap is neededone that accounts for the way electronic coupling correlates the donor and acceptor spectra. Although the physical concept is obscured in the theories that have been developed to resolve this issue, they are essentially accounting for correlations that introduce (weak) adiabaticity into the theory for energy transfer. Therefore, the function of this coherence does not hinge on a delicate superposition of states that is fragile to dephasing. Instead it represents a chunk, possibly significant in breadth, of phase space characterizing the trajectories via which donor states evolve to acceptor states. Hence, it is indeed relevant for light harvesting function. Nonadiabatic (e.g., Förster theory) versus adiabatic pictures of activated reactions are represented by free energy curves like those shown in Figure 1a,b, respectively. The difference between these curves is that the region around the transition state (barrier) in Figure 1b comprises an ensemble exciton state with partially or fully delocalized excitation. This is the origin of the spectral correlations. These curves are abbreviated “energy landscapes.” Specifically, if the probability that the system has a value X, conveniently defined as the transition energy X = hν, for electronic state α is P(X)α, then the free energy distribution is Fα(X) = −kBT[P(X)α], where kB is the Boltzmann constant and T is temperature.16 This makes clear that the free energy curves show electronic energy differences weighted by how frequently these energies are found around the equilibrium. In isolated molecules, the energy gap fluctuations hνa(t), hνb(t) that underlie the energy landscape of molecules a and b produce spectral line broadening, but in electronically coupled molecules the situation is more complicated because the fluctuations affect delocalization and localization of excitation.17 In the Förster limit the spectral overlap is associated with the spectrum of points, like Xj, where the trajectories cross. In the intermediate coupling case the trajectoriesnow of the eigenstates α and βnever cross because when the site energies hνa and hνb are degenerate the electronic coupling splits the eigenstates, according to the molecular exciton model.18−20 Because the system is slaved to the bath, the fluctuations along a trajectory switch exciton delocalization on and off. There are consequently regions of electronic delocalization along the trajectory, when |hνa − hνb| is less than the electronic coupling, that lower the barrier for the adiabatic crossing from the left free energy well to right. The weak coupling (Förster theory) and intermediate electronic coupling regimes are compared in more detail in Figure 1c,d, where the transition energies of donor and
oherence refers to order, sequence, and correlation. It is abundant in the macroscopic world, from the collective swimming of fish in a school to the rhythm of a heart to stripes on a zebra. Coherence is also notable on the molecular scale; for instance, it is well-known to be found in the ultrafast collective motions of molecules in liquids. A dramatic picture of coherence and its implications is indicated by comparing correlation-free soundwhite noiseto the sophisticated orchestration of sound in music. Clearly coherence underpins function. It is tantalizing to speculate about whether coherence can be found in chemistry; if so, can it be harnessed to yield new kinds of function or ways of expediting reactions?1 Wave coherence is specifically relevant to chemistry and properties on the molecular scale. It refers to waves held instep; that is, their phases line up in time or space. These waves can be associated with molecular structuree.g., molecular orbitals or periodic wave functions that define solid-state matterand can prove decisive in the properties and function of semiconductors and metals. The waves, however, can also refer to quantum mechanical amplitudes that are added to calculate probabilities. Examples include scattering problems or interference phenomena in superexchange-mediated electron transfer. The argument against a role for coherence in complex systems is that the lock-step alignment of “waves” is rapidly lost in systems characterized by disordered energy landscapes through “dephasing.” Indeed, spectral line widths imply the dephasing time scale to be
