Testing for memory-free spectroscopic coordinates by 3D IR exchange spectroscopy

Abstract

Using 3D infrared (IR) exchange spectroscopy, the ultrafast hydrogenbond forming and breaking (i.e., complexation) kinetics of phenol to benzene in a benzene/CCl 4 mixture is investigated. By introducing a third time point at which the hydrogen-bonding state of phenol is measured (in comparison with 2D IR exchange spectroscopy), the spectroscopic method can serve as a critical test of whether the spectroscopic coordinate used to observe the exchange process is a memory-free, or Markovian, coordinate. For the system under investigation, the 3D IR results suggest that this is not the case. This conclusion is reconfirmed by accompanying molecular dynamics simulations, which furthermore reveal that the non-Markovian kinetics is caused by the heterogeneous structure of the mixed solvent.3D IR spectroscopy | solvent dynamics | ultrafast dynamics W henever one writes a chemical reaction equation, such as in the simplest case of an equilibrium between two states of a molecular systemwith the corresponding Master equation for its kineticsone implicitly assumes Markovianity. That is, it is assumed that the probability to react per time unit, e.g., from C to F, scales linearly with concentration [C] with proportionality constant k CF , but does not depend on the history of how C has been formed. When the reaction is slow in comparison with the relaxation of its environment, then this assumption is well justified. One can however think of many situations where this is not the case. For example, proteins are heterogeneous on very long timescales due to their structural complexity, so enzymatic reaction catalyzed by them might not fulfill that condition (1). Other examples are found in glass-forming liquids close to the glass transition, when their relaxation covers many orders of magnitude in time (2). When the speed of a reaction approaches the ultrafast picosecond regime, which is the topic of the present paper, then even the solvation time of normal liquids far away from any glass transition may become time-limiting. For example, it has been shown that the distance between a Na + and a Cl − ion is not a good reaction coordinate to describe ion pair dissociation in aqueous solution (3), in the sense that the distance for which the free energy peaks does not correspond with the transition state of the reaction. Hidden coordinates exist, which must be solvent coordinates because there are no other degrees of freedom. Unless these solvent coordinates have not fully relaxed and lost their memory about a reaction event, the probability for a back reaction must depend on the history. Markovianity is related to a separation of timescales between the speed of a chemical reaction of a molecular system versus that of the relaxation of its solvent. Often, a separation of timescales goes hand-in-hand with a separation of solute and solvent, but such a system-bath approach fails for ultrafast reactions.It is important to recognize that the question of Markovianity is not an intrinsic property of a chemical process, but rather is relate...

Migration of small ligands in globins: Xe diffusion in truncated hemoglobin N

“…The observation of memory effects raises the question whether, and if so, on what time scale ligand migration is a Markovian process. Based on time scale considerations [ 46 , 47 ] a process is expected to be Markovian when one of its major sub-processes occurs on a considerably longer time scale with respect to other major sub-processes. For ligand migration, this would translate in transition times and intra-pocket relaxation occurring on different time scales.…”

“…While the assumption of Markovianity is commonly employed when describing chemical and biological processes, it has been known from several cases that it is not always valid [ 46 , 48 ]. Characteristic examples of processes exhibiting non-Markovian behaviour are enzymatic reactions [ 49 , 50 ] or the glass transition in polymers [ 51 ].…”

Direct observation of multistep energy transfer in LHCII with fifth-order 3D electronic spectroscopy

“…Fifth-order 3D optical spectroscopy is an extension of third-order 2D optical spectroscopy 13 14 15 16 17 18 . Applications include the probing of higher states of vibrational systems in order to better characterize the anharmonicity 14 19 , the testing of non-Markovian processes 20 and the characterizing of electron transfer systems 21 .…”

Revealing a full quantum ladder by nonlinear spectroscopy

“…In this paper, the direction towards higherorder nonlinear interactions is considered. The fifthorder coherent spectroscopy has been considered in the IR and the visible region and the complex information on the correlations in quantum systems has been represented in 3DIR [57], 3DES [58][59][60] or 3D fluorescence [61]. By spreading frequencies into the third spectral dimension high-frequency vibronic modes [58], double-exciton resonances [27][28][29] or specific exciton relaxation pathways [59,60] have been revealed.…”