Relation between Dephasing Time and Energy Gap Fluctuations in Biomolecular Systems

Abstract

Excitation energy and charge transfer are fundamental processes in biological systems. Because of their quantum nature, the effect of dephasing on these processes is of interest especially when trying to understand their efficiency. Moreover, recent experiments have shown quantum coherences in such systems. As a first step toward a better understanding, we studied the relationship between dephasing time and energy gap fluctuations of the individual molecular subunits. A larger set of molecular simulations has been investigated to shed light on this dependence. This set includes bacterio-chlorophylls in Fenna-Matthews-Olson complexes, the PE545 aggregate, the LH2 complexes, DNA, photolyase, and cryptochromes. For the individual molecular subunits of these aggregates it has been confirmed quantitatively that an inverse proportionality exists between dephasing time and average gap energy fluctuation. However, for entire complexes including the respective intermolecular couplings, such a relation still needs to be verified.

Quantum effects in ultrafast electron transfers within cryptochromes

“…Values of similar order were reported recently by Mallus et al using semiempirical quantum chemistry methodologies 98. The curves decay to zero within a few hundreds of femtoseconds.…”

Relation between Vibrational Dephasing Time and Energy Gap Fluctuations

“…Thus, this fit yields a basically exponential behavior, which is actually consistent with the form of the dephasing functions (examples shown in Figure ). In total and as in the case of the dephasing times for the individual pigments discussed in ref , one gets a clearly inverse proportional relation between the dephasing time and average gap fluctuation, but the respective proportionality factor can possibly differ between systems for excitonic states.…”

“…Interestingly, some earlier studies assumed a proportionality between correlation and dephasing times, whereas others explicitly showed an independence between the two time scales . In our previous study on individual pigments, we found that in general a dependence exits between correlation and dephasing times . Moreover, the latter two studies found a clear dependence between the dephasing times and the corresponding average energy gap fluctuations.…”

“…Moreover, the excitonic couplings have either been determined using the point-dipole approximation for the PE545 aggregate or the transition charges from the electrostatic potentials (TrEsp) method for the three other systems. In our previous study for the dephasing time of individual pigments, different approaches for the site energy and coupling calculations were used and the main findings were robust with respect to these variations …”

“…This function is of crucial importance for the present study because it is used to define the dephasing time. It is related to the line shape I (ω), which can be given as Using analytic approximation of the correlation function given in eq and assuming that one of the two correlation times is very short, whereas the other one is large, one obtains On the basis of the dephasing function, the dephasing time is defined as As already shown in ref , the relation between the dephasing time and energy gap fluctuation can be given in an analytical form with erfc­( x ) denoting the complementary error function and Two limiting cases can be given for the dephasing time expression. For vanishing α 1 , that is, in the so-called Gaussian limit, the dephasing time can be written as The constant, B , has a value of B = √2ℏ according to Kubo’s theory, although alternative values have been discussed as well. , In the opposite exponential limit, that is, with vanishing α 2 , one gets As will be seen below, for the case of excitonic energies, this exponential limit is of prime interest together with its dependence on the correlation time τ c,1 .…”