# Biological Systems

In photosynthesis of higher plants, light is converted into chemical energy. The absorbed photon energy is transferred by charge migration to the so-called reaction center, where it is converted into an electrochemical gradient. The efficiency of this process is remarkably high: At low light intensities, 9 out of 10 photons create a charge separated state.1 A thorough understanding of this process can lead to a technological utilization of photosynthesis, as a promising and ecologically viable alternative to fossil fuels. This hope has motivated numerous studies, with the aim of finding and characterizing a bio-inspired, artificial light harvesting systems.

The initial step of the photosynthetic process is the absorption of a photon by a pigment in an antenna complex. Such pigments can be different variants of bacteriochlorophylls (BChl) and carotenoids, supported by and arranged in close proximity to one another by a protein matrix. Because of the short inter-pigment distance of down to 10 Ångstroms, an absorption process leads to an excited state shared by several different molecules. This delocalized, time dependent state is referred to as an exciton. **Creation, migration and annihilation of such excitons is at the heart of the functionality of photosynthetic pigment-protein complexes (PPCs).**

Excitonic absorption spectra can be spectrally broad and congested, meaning that several spectral features (sites) may overlap. Upon excitation with an ultrashort and therefore ultrabroadband pulse, all these spectral features are excited simultaneously. This could lead to a loss of spectroscopic information, as the dynamical behaviors of different sites might differ but are averaged out in the excitation process. The last decade has shown that **two-dimensional electronic spectroscopy** (2D-ES) solves this problem most elegantly. In its single-quantum variant (1Q-2D), it measures the full and complex signal of interest, namely the 3^{rd} order perturbation signal of the sample in its time dependence. With respect to photosynthesis, Fleming and co-workers used 1Q-2D to elucidate the energy flow in PPCs and to investigate the role of coherent electronic motion in several systems.^{2} In 2D-ES, the excitation process is shared by two distinct pulses with a temporal delay *t _{1}* between them. The experimental

*time*resolution is still defined by the duration of the two excitation pulses. The

*frequency*resolution however is not limited by the inverse of the time resolution anymore; if

*t*is scanned in small intervals, the subsequent Fourier-transformation

_{1}*t*→

_{1}*ω*leads to a signal with a well-resolved excitation frequency axis

_{1}*ω*.

_{1}The combination of high spectral and temporal resolution, the capacity of extracting correlation functions and the reduced spectral congestion are the key advantages of 1Q-2D over the far more common pump-probe. Nevertheless, 1Q-2D still interrogates the same contributions to the 3^{rd} order optical polarization as pump-probe. To further refine the understanding of exciton dynamics, to yield a richer, more profound data source for kinetic model building, it is therefore desirable to employ methods probing different, more specific excitation pathways. **Double quantum two-dimensional electronic spectroscopy** (2Q-2D) is such a method.^{3} In comparison to 1Q-2D, its double quantum variant 2Q-2D **greatly reduces the number of signal contributions** – it is defined by two instead of eight unique pathways.^{3}

**Exciton creation, migration and annihilation determine the function of** **natural- and artificial light harvesting systems**. The resulting excitonic bands are often congested and hard to analyse by the means of ultrafast spectroscopy. Via its excitation-frequency resolved signals, single quantum two-dimensional electronic spectroscopy (**1Q-2D**) has proven to be a viable solution to this problem. However, 1Q-2D still interrogates a multitude of excitation pathways. Not all of them are of interest when examining the function of light harvesting complexes. Its double-quantum variant (**2Q-2D**) greatly reduces the number of signal contributions and provides a clear view on a system’s energy level structure and dynamics. **The combination of 1Q- and 2Q-2D defines both the energy landscape and the dynamic processes on them**.

Left: the initially excited energy levels of b-carotene, according to conventional 3^{rd} order spectroscopic methods like transient absorption or 1Q-2D. States are determined solely by their transition energies and dipole moments. In comparison, the combination of 1Q- and 2Q-2D spectroscopy as shown on the right defines the system in transition energies and dipole moments, curve displacements, reorganization energies and even correlated spectral motion on the involved potential energy surfaces.

[1] Renger, T.; May, V.; Kuhn, O. *Phys Rep* **2001**, *343*, 138.

[2] Schlau-Cohen, G. S.; Ishizaki, A.; Fleming, G. R. *Chem Phys* **2011**, *386*, 1.

[3] Christensson, N.; Milota, F.; Nemeth, A.; Pugliesi, I.; Riedle, E.; Sperling, J.; Pullerits, T.; Kauffmann, H.; Hauer, J. *J Phys Chem Lett* **2010**, *1*, 3366.