Electronic Coherence Dephasing in Excitonic Molecular Complexes: Role of Markov and Secular Approximations Jan Olšina and Tomáš Mančal Institute of Physics of Charles University, Faculty of Mathematics and Physics, Charles University in Prague, Ke Karlovu 5, CZ-121 16 Prague 2, Czech Republic ∗ We compare four different types of equations of motion for reduced density matrix of a system of molecular excitons interacting with thermodynamic bath. All four equations are of second order in the linear system-bath interaction Hamiltonian, with different approximations applied in their derivation. In particular we compare time-nonlocal equations obtained from so-called Nakajima- Zwanzig identity and the time-local equations resulting from the partial ordering prescription of the cummulant expansion. In each of these equations we alternatively apply secular approximation to decouple population and coherence dynamics from each other. We focus on the dynamics of intra- band electronic coherences of the excitonic system which can be traced by coherent two-dimensional spectroscopy. We discuss the applicability of the four relaxation theories to simulations of popula- tion and coherence dynamics, and identify features of the two-dimensional coherent spectrum that allow us to distinguish time-nonlocal effects. in terms of a model describing the relevant DOF of the system (electronic states of photosynthetic molecules), and a thermodynamics bath (the protein environment). Parameters for such models can be supplied by experi- ment [4], QC studies [5, 6], MD modeling [7], or are a result of suitable simplified models [3]. Recent advances in non-linear spectroscopy have opened a wide new experimental window into the details of ultrafast photo-induced dynamics of molecular sys- tems. Experimental realization of two-dimensional (2D) coherent spectroscopy in the visible and near IR regions [8–11] has enabled to overcome some of the frequency- vs. time-resolution competition problem otherwise faced by ultrafast spectroscopy, and yielded thus unprecedented experimental details of the time evolution of molecular excitations. Most importantly, it was predicted that the presence of certain oscillatory features in 2D spectra is a manifestation of coherences between molecular excited states [12, 13]. It was also concluded that these oscil- lations should be present in the 2D spectrum of photo- synthetic Fenna-Matthews-Olson (FMO) chromophore- protein complex [12]. Experimental results not only con- firmed this prediction [14], but yielded also surprising results such as unexpectedly long life time of these co- herences, as compared to the predictions of standard de- phasing rate theory. Furthermore, while possible coher- ence transfer was ignored by the relaxation theory used in Ref. [12], the experiment provided some evidence for its role in excitation energy transfer. It was speculated that photosynthetic systems might use the coherent mode of energy transfer to more efficiently channel excitation en- ergy by scanning their energetic landscape in a process similar to quantum computing [14]. More experiments have recently reported coherent dynamics in photosyn- thetic systems [15] and conjugated polymers [16], and the field of energy transfer in photosynthesis has seen an increased interest from theoretical researchers from pre- viously unrelated fields [17–20]. Theoretical basis for the description of the decoher- Modeling molecular properties related to their non- equilibrium dynamics requires various theoretical ap- proaches depending on the particular microscopic pro- cesses related to the observed molecular features. Since the dawn of quantum mechanics, properties of molecules and solids have been studied theoretically in ever greater detail. This has led in recent years to a state in which dynamics of complex systems with multitude of degrees of freedom (DOF) is accessible to quantitative theoret- ical study [1]. Many properties of molecular systems are directly related to the equilibrium or time depen- dent conformations of nuclear DOF for which electronic states play the role of a background contributing to the nuclear potential energy surfaces. Problems like these are the realm of molecular dynamics (MD) in its clas- sical, quantum or mixed versions and quantum chem- istry (QC), where impressive qualitative and quantita- tive results have been achieved in recent years. For cer- tain types of dynamical problems, however, less expen- sive model approaches are the preferred choice due to the scale of studied system or due to the physical nature of studied processes. A good example of such a problem is ultrafast photo-induced excited state dynamics of small molecular systems and their aggregates [2]. Here, most of the relevant experimental information is only avail- able through ultrafast non-linear spectroscopy, and thus the theory has to span the whole distance between the microscopic dynamics of the molecular system, and the macroscopic description of experimental signals [3]. Typ- ical field in which such an approach has yielded deep un- derstanding of the relevant physico-chemical processes is the study of primary processes in photosynthesis. The re- lated quantum mechanical problem is usually formulated I. INTRODUCTION arXiv:1001.1657v1 [physics.chem-ph] 11 Jan 2010 ∗ Electronic address: tomas.mancal@mff.cuni.cz