Detailed balance, internal consistency, and energy conservation in fragment orbital- based surface hopping

We have recently introduced an efficient semi-empirical non-adiabatic molecular dynamics method for the simulation of charge transfer/transport in molecules and molecular materials, denoted fragment orbital-based surface hopping (FOB-SH) [J. Spencer et al., J. Chem. Phys. 145, 064102 (2016)]. In this method, the charge carrier wavefunction is expanded in a set of charge localized, diabatic electronic states and propagated in the time-dependent potential due to classical nuclear motion. Here we derive and implement an exact expression for the non-adiabatic coupling vectors between the adiabatic electronic states in terms of nuclear gradients of the diabatic electronic states. With the non-adiabatic coupling vectors (NACVs) available, we investigate how different flavours of fewest switches surface hopping affect detailed balance, internal consistency, and total energy conservation for electron hole transfer in a molecular dimer with two electronic states. We find that FOB-SH satisfies detailed balance across a wide range of diabatic electronic coupling strengths provided that the velocities are adjusted along the direction of the NACV to satisfy total energy conservation upon a surface hop. This criterion produces the right fraction of energy-forbidden (frustrated) hops, which is essential for correct population of excited states, especially when diabatic couplings are on the order of the thermal energy or larger, as in organic semiconductors and DNA. Furthermore, we find that FOB-SH is internally consistent, that is, the electronic surface population matches the average quantum amplitudes, but only in the limit of small diabatic couplings. For large diabatic couplings, inconsistencies are observed as the decrease in excited state population due to frustrated hops is not matched by a corresponding decrease in quantum amplitudes. The derivation provided here for the NACV should be generally applicable to any electronic structure approach where the electronic Hamiltonian is constructed in a diabatic electronic state basis

Molecular hydrodynamics from memory kernels

The memory kernel for a tagged particle in a fluid, computed from molecular dynamics simulations, decays algebraically as t−3/2. We show how the hydrodynamic Basset-Boussinesq force naturally emerges from this long-time tail and generalize the concept of hydrodynamic added mass. This mass term is negative in the present case of a molecular solute, which is at odds with incompressible hydrodynamics predictions. Lastly, we discuss the various contributions to the friction, the associated time scales, and the crossover between the molecular and hydrodynamic regimes upon increasing the solute radius

Confronting surface hopping molecular dynamics with Marcus theory for a molecular donor-acceptor system

We investigate the performance of fewest switches surface hopping (SH) in describing electron transfer (ET) for a molecular donor–acceptor system. Computer simulations are carried out for a wide range of reorganisation energy (λ), electronic coupling strength (Hab) and driving force using our recently developed fragment orbital-based SH approach augmented with a simple decoherence correction. This methodology allows us to compute SH ET rates over more than four orders of magnitude, from the sub-picosecond to the nanosecond time regime. We find good agreement with semi-classical ET theory in the non-adiabatic ET regime. The correct scaling of the SH ET rate with electronic coupling strength is obtained and the Marcus inverted regime is reproduced, in line with previously reported results for a spin-boson model. Yet, we find that the SH ET rate falls below the semi-classical ET rate in the adiabatic regime, where the free energy barrier is in the order of kBT in our simulations. We explain this by first signatures of non-exponential population decay of the initial charge state. For even larger electronic couplings (Hab = λ/2), the free energy barrier vanishes and ET rates are no longer defined. At this point we observe a crossover from ET on the vibronic time scale to charge relaxation on the femtosecond time scale that is well described by thermally averaged Rabi oscillations. The extension of the analysis from the non-adiabatic limit to large electronic couplings and small or even vanishing activation barriers is relevant for our understanding of charge transport in organic semiconductors

KNOWING, CHARACTERIZING AND ASSESSING SYSTEMS OF ORGANIC CROP ROTATIONS

The choice of crop rotations in organic stockless cropping systems is the first leverage used to manage technical issues (to maintain soil fertility, to control pest and weeds) and economic issues (to insure income). The RotAB project (French Casdar funding 2008-2010) implemented complementary approaches to better knowing, characterizing and assessing arable crop rotations. Their conception depends on numerous factors such as the types of soil and climate (on which depend the types of crops, yield potential, possibility of mechanical weed control…) or the economic context (existence of outlets and continuity of markets). If nitrogen supply and weed control are the most important agronomic issues of organic farmers in stockless cropping systems, phosphorus availability appears to be the next important issue for soil fertility and system sustainability

Quantum localization and delocalization of charge carriers in organic semiconducting crystals

Charge carrier transport in organic semiconductors is at the heart of many revolutionary technologies ranging from organic transistors, light-emitting diodes, flexible displays and photovoltaic cells. Yet, the nature of charge carriers and their transport mechanism in these materials is still unclear. Here we show that by solving the time-dependent electronic Schrödinger equation coupled to nuclear motion for eight organic molecular crystals, the excess charge carrier forms a polaron delocalized over up to 10–20 molecules in the most conductive crystals. The polaron propagates through the crystal by diffusive jumps over several lattice spacings at a time during which it expands more than twice its size. Computed values for polaron size and charge mobility are in excellent agreement with experimental estimates and correlate very well with the recently proposed transient localization theor

Ultrafast Light-Driven Electron Transfer in a Ru(II)tris(bipyridine)-Labelled Multiheme Cytochrome

Multiheme cytochromes attract much attention for their electron transport properties. These proteins conduct electrons across bacterial cell walls, along extracellular filaments, and when purified can serve as bionanoelectronic junctions. Thus, it is important and necessary to identify and understand the factors governing electron transfer in this family of proteins. To this end we have used ultra-fast transient absorbance spectroscopy, to define heme-heme electron transfer dynamics in the representative multiheme cytochrome STC from Shewanella oneidensis in aqueous solution. STC was photo-sensitized by site-selective labelling with a Ru(II)(bipyridine)3 dye and the dynamics of light-driven electron transfer described by a kinetic model corroborated by molecular dynamics simulation and density functional theory calculations. With the dye attached adjacent to STC Heme IV, a rate constant of 87 x 106 s-1 was resolved for Heme IV → Heme III electron transfer. With the dye attached adjacent to STC Heme I, at the opposite terminus of the tetraheme chain, a rate constant of 125 x 106 s-1 was defined for Heme I → Heme II electron transfer. These rates are an order of magnitude faster than previously computed values for unlabeled STC. The Heme III/IV and I/II pairs exemplify the T-shaped heme packing arrangement, prevalent in multiheme cytochromes, whereby the adjacent porphyrin rings lie at 90o with edge-edge (Fe-Fe) distances of ≈6 (11) Å. The results are significant in demonstrating the opportunities for pump-probe spectroscopies to resolve inter-heme electron transfer in Ru-labeled multiheme cytochromes

Système de mesure du Doppler différentiel sur raies fluctuantes

In order to use differential Doppler (D.D) in target motion analysis, we present a measurement system providing accurate D.D estimation when the primary frequency lines are linearly modulated. Such low frequency variation, generally due to source motion, is frequently perturbating classical high resolution measurement techniques on real signals (Time delay-Doppler ambiguity, acceleration,..). The proposed system provides a non biaised estimation and avoids any perturbation induced by this phenomena. The algorithm, based on a maximum likehood estimator associated to a phase tracking loop, reaches theoretically the Cramer-Rao bound. Futhermore simulation results demonstrate the good practical behaviour of this system