Vibrational vs. electronic coherences in 2D spectrum of molecular systems

Abstract

Two-dimensional spectroscopy has recently revealed the oscillatory behavior of the excitation dynamics of molecular systems. However, in the majority of cases there is considerable debate over what is actually being observed: excitonic or vibrational wavepacket motion or evidence of quantum transport. In this letter we present a method for distinguishing between vibrational and excitonic wavepacket motion, based on the phase and amplitude relationships of oscillations of distinct peaks as revealed through a fundamental analysis of the two-dimensional spectra of two representative systems.Two-dimensional photon-echo (2DPE) spectroscopy is a powerful tool capable of resolving quantum correlations on the femtosecond timescale 1-3 . They appear as beats of specific peaks in the 2DPE spectrum for a number of molecular systems 3,4 . However, the underlying processes are often ambiguous. At first, the beats were attributed to the wave-like quantum transport with quantum coherences being responsible for an ultra-efficient excitation transfer 3-6 . The same process was associated with the opposite phase beats in the spectral regions which are symmetric with respect to the diagonal line 7 .In molecules and their aggregates, electronic transitions are coupled to various intra-and intermolecular vibrational modes. Vibrational energies of these are of the order of 100 -3000 cm −1 , while the magnitudes of the resonant couplings, J, in excitonic aggregates (e.g. in photosynthetic pigment-protein complexes or in J-aggregates) are in the same range. Thus, vibronic and excitonic systems show considerable spectroscopic similarities, and presence of electronic and/or vibrational beats in the 2DPE spectrum is expected. Indeed, similar spectral beats originating entirely from a high-energy vibrational wavepacket motion have been observed 8,9 . The possibility of distinguishing the electronic and vibrational origin of the beats from a 2DPE spectrum has been emphasized in a recent letter 10 . However, the reported conclusions have not been supported by theoretical arguments, and thus are questionable. Therefore, the highly relevant question of how vibrations interfere with electronic coherences in 2DPE spectrum is still an open one. A theoretical study of the origin of spectral beats, their phase relationships in the rephasing and non-rephasing components of the 2DPE spectrum is presented in this article.We address this problem by considering two generic model systems which exhibit distinct internal coherent dynamics. The simplest model of an isolated molecular electronic excitation is the vibronic system represented a) Electronic mail: darius.abramavicius@ff.vu.lt|e 2 . . . 1234 |g |e 1 |e 2 2 3 | f -ω 0 a b FIG. 1. Energy level structure of the displaced oscillator (a) and electronic dimer (b) and corresponding linear absorption spectra.by two electronic states, |g and |e , which are coupled to a one-dimensional nuclear coordinate q. We denote the model by a displaced oscillator (DO) system (Fig. 1a). Taking =1, the vibronic potentia...

Laser-Limited Signatures of Quantum Coherence

“…The importance of such a comparative study of measured results and the expected response based on calculations becomes immediately evident: even in a strongly coupled system where 2D spectral features are well-resolved, a multitude of dynamic contributions overlap in a nontrivial way. In particular, oscillatory signals associated with ground state vibrational wavepackets are strongly present at excitonic crosspeak locations, as was already emphasized by earlier studies [16,[23][24][25][26]. Using numerical predictions, we nevertheless managed to accurately extract the coherence between the two most radiant states of the homodimer system through excited state absorption features.…”

“…However, even for such simple molecules, vibronic coupling automatically gives rise to additional oscillating coherences of ground state vibrational wavepackets that might overlap with excited state features [16,23,24]. Studies aimed at disentangling vibrational and excitonic coherences in such cases have focused on limiting examples of purely vibrational and electronic excitations, and have not led to a consensus method for their distinction in measurements, without loss of generality [25,26].…”

Optimizing sparse sampling for 2D electronic spectroscopy

“…24 A 2D Fourier transform with respect to these two delay times yields a 2D spectrum for a given population time T. Especially for gaseous samples, coherences are long-lived 25 and hence require large time delays for the two indirect dimensions. Furthermore, it may also be useful to perform an additional Fourier transform with respect to the population time T and generate a quasi-3D spectrum in order to distinguish the origin of coherences 26,27 or different channels in molecular reactions. 15,28 Fully coherent fifth-order 3D spectroscopy methods have also been demonstrated.…”

Resolving Vibrational from Electronic Coherences in Two-Dimensional Electronic Spectroscopy: The Role of the Laser Spectrum

“…However, electronic transitions are commonly coupled to molecular vibrational modes, and vibrational coherences both in the ground and excited states can be prepared by broadband pulses, in the same way that a coherent superposition of different excitonic or electronic states may be prepared [17]. Recent theoretical and experimental research has explored the different coherence signatures arising in 2D-ES, but for the most part possible effects from the laser spectrum have been neglected [18][19][20][21][22][23][24].…”

“…2(a) there are 16 such pathways (Figs. S3-S7 display all [26]) and they generate oscillatory features in the data as a function of T. It is known that the phase of the oscillation due to each single pathway is a function of ðν 1 ;ν 3 Þ, and that interference between neighboring contributions can generate confounding features, so isolation of as few pathways as possible is helpful for proper interpretation of the data [18,38]. To that end, we note that eight of the coherence pathways are rephasing, while the other eight are nonrephasing.…”