Structural and Vibrational Properties of Carboxylates Intercalated into Layered Double Hydroxides: A Joint Computational and Experimental Study.

Layered double hydroxides (LDHs) are fascinating clay-like materials that display versatile properties, making them an extremely fertile playground for diverse applications, ranging from bio-compatible materials to the pharmaceutical industry to catalysis and photocatalysis. When intercalating organic and bio-organic species between the inorganic layers, such materials are named hybrid LDHs. The structure-property relation in these systems is particularly relevant, since most of the properties of the materials may be fine-tuned if a comprehensive understanding of the microscopic structure in the interlamellar space is achieved, especially with respect to the reorganization under water uptake (swelling). In this work, we combined experiments and simulations to rationalize the behavior of LDHs intercalating three carboxylates, the general structure of which can be given as [Mg4Al2(OH)12]A2-·XH2O (with A2- = succinate, aspartate, or glutamate and X representing increasing water content). Following this strategy, we were able to provide an interpretation of the different shapes observed for the experimental water adsorption isotherms and for the evolution of the infrared carboxylate band of the anions. Apart from small differences, due to the different reorganization of the conformational space under confinement, the behavior of the two amino acids is very similar. However, such behavior is quite different in the case of succinate. We were able to describe the different response of the anions, which has a significant impact on the isotherm and on the size of the interlamellar region, in terms of a different interaction mechanism with the inorganic layer.

Hydration effects on the vibrational properties of carboxylates: From continuum models to QM/MM simulations.

The presence of carboxyl groups in a molecule delivers an affinity to metal cations and a sensitivity to the chemical environment, especially for an environment that can give rise to intermolecular hydrogen bonds. Carboxylate groups can also induce intramolecular interactions, such as the formation of hydrogen bonds with donor groups, leading to an impact on the conformational space of biomolecules. In the latter case, the protonation state of the amino groups plays an important role. In order to provide an accurate description of the modifications induced in a carboxylated molecule by the formation of hydrogen bonds, one needs a compromise between a quantum chemical description of the system and the necessity to take into account explicit solvent molecules. In this work, we propose a bottom-up approach to study the conformational space and the carboxylate stretching band of (bio)organic anions. Starting from the anions in a continuum solvent, we then move to calculations using a microsolvation approach including one explicit water molecule per polar group, immersed in a continuum. Finally, we run QM/MM molecular dynamics simulations to analyze the solvation properties and to explore the anions conformational space. The results thus obtained are in good agreement with the description given by the microsolvation approach and they bring a more detailed description of the solvation shell and of the intermolecular hydrogen bonds.

Exciton transport in molecular organic semiconductors boosted by transient quantum delocalization.

Designing molecular materials with very large exciton diffusion lengths would remove some of the intrinsic limitations of present-day organic optoelectronic devices. Yet, the nature of excitons in these materials is still not sufficiently well understood. Here we present Frenkel exciton surface hopping, an efficient method to propagate excitons through truly nano-scale materials by solving the time-dependent Schrödinger equation coupled to nuclear motion. We find a clear correlation between diffusion constant and quantum delocalization of the exciton. In materials featuring some of the highest diffusion lengths to date, e.g. the non-fullerene acceptor Y6, the exciton propagates via a transient delocalization mechanism, reminiscent to what was recently proposed for charge transport. Yet, the extent of delocalization is rather modest, even in Y6, and found to be limited by the relatively large exciton reorganization energy. On this basis we chart out a path for rationally improving exciton transport in organic optoelectronic materials.

NMR Relaxation Rates of Quadrupolar Aqueous Ions from Classical Molecular Dynamics Using Force-Field Specific Sternheimer Factors.

The nuclear magnetic resonance (NMR) relaxation of quadrupolar nuclei is governed by the electric field gradient (EFG) fluctuations at their position. In classical molecular dynamics (MD), the electron cloud contribution to the EFG can be included via the Sternheimer approximation, in which the full EFG at the nucleus that can be computed using quantum density functional theory (DFT) is considered to be proportional to that arising from the external, classical charge distribution. In this work, we systematically assess the quality of the Sternheimer approximation as well as the impact of the classical force field (FF) on the NMR relaxation rates of aqueous quadrupolar ions at infinite dilution. In particular, we compare the rates obtained using an ab initio parametrized polarizable FF, a recently developed empirical FF with scaled ionic charges and a simple empirical nonpolarizable FF with formal ionic charges. Surprisingly, all three FFs considered yield good values for the rates of smaller and less polarizable solutes (Li+, Na+, K+, Cl-), provided that a model-specific Sternheimer parametrization is employed. Yet, the polarizable and scaled charge FFs yield better estimates for divalent and more polarizable species (Mg2+, Ca2+, Cs+). We find that a linear relationship between the quantum and classical EFGs holds well in all of the cases considered; however, such an approximation often leads to quite large errors in the resulting EFG variance, which is directly proportional to the computed rate. We attempted to reduce the errors by including first order nonlinear corrections to the EFG, yet no clear improvement for the resulting variance has been found. The latter result indicates that more refined methods for determining the EFG at the ion position, in particular those that take into account the instantaneous atomic environment around an ion, might be necessary to systematically improve the NMR relaxation rate estimates in classical MD.

How to calculate charge mobility in molecular materials from surface hopping non-adiabatic molecular dynamics - beyond the hopping/band paradigm.

Charge transport in high mobility organic semiconductors is in an intermediate regime between small polaron hopping and band transport limits. We have recently shown that surface hopping non-adiabatic molecular dynamics is a powerful method for prediction of charge transport mechanisms in organic materials and for near-quantitative prediction of charge mobilities at room temperature where the effects of nuclear zero-point motion and tunneling are still relatively small [S. Giannini et al., Nat. Commun., 2019, 10, 3843]. Here we assess and critically discuss the extensions to Tully's original method that have led to this success: (i) correction for missing electronic decoherence, (ii) detection of trivial crossings and (iii) removal of decoherence correction-induced spurious charge transfer. If any one of these corrections is not included, the charge mobility diverges with system size, each for different physical reasons. Yet if they are included, convergence with system size, detailed balance and good internal consistency are achieved.

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

Multiheme cytochromes attract much attention for their electron transport properties. These proteins conduct electrons across bacterial cell walls and 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 ultrafast transient absorbance spectroscopy, to define heme-heme electron transfer dynamics in the representative multiheme cytochrome STC from Shewanella oneidensis in aqueous solution. STC was photosensitized by site-selective labeling 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 × 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 × 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 90° with edge-edge (Fe-Fe) distances of ∼6 (11) Å. The results are significant in demonstrating the opportunities for pump-probe spectroscopies to resolve interheme electron transfer in Ru-labeled multiheme cytochromes.

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 theory.

Crossover from Hopping to Band-Like Charge Transport in an Organic Semiconductor Model: Atomistic Nonadiabatic Molecular Dynamics Simulation.

The mechanism of charge transport (CT) in a 1D atomistic model of an organic semiconductor is investigated using surface hopping nonadiabatic molecular dynamics. The simulations benefit from a newly implemented state tracking algorithm that accounts for trivial surface crossings and from a projection algorithm that removes decoherence correction-induced artificial long-range charge transfer. The CT mechanism changes from slow hopping of a fully localized charge to fast diffusion of a polaron delocalized over several molecules as electronic coupling between the molecules exceeds the critical threshold V ≥ λ/2 (λ is the reorganization energy). With increasing temperature, the polaron becomes more localized and the mobility exhibits a "band-like" power law decay due to increased site energy and electronic coupling fluctuations (local and nonlocal electron-phonon coupling). Thus, reducing both types of electron-phonon coupling while retaining high mean electronic couplings should be part of the strategy toward discovery of new organics with high room-temperature mobilities.

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.

Cysteine Linkages Accelerate Electron Flow through Tetra-Heme Protein STC.

Multi-heme proteins have attracted much attention recently due to their prominent role in mediating extracellular electron transport (ET), but one of their key fundamental properties, the rate constants for ET between the constituent heme groups, have so far evaded experimental determination. Here we report the set of heme-heme theoretical ET rate constants that define electron flow in the tetra-heme protein STC by combining a novel projector-operator diabatization approach for electronic coupling calculation with molecular dynamics simulation of ET free energies. On the basis of our calculations, we find that the protein limited electron flux through STC in the thermodynamic downhill direction (heme 1→4) is ∼3 × 106 s-1. We find that cysteine linkages inserting in the space between the two terminal heme pairs 1-2 and 3-4 significantly enhance the overall electron flow, by a factor of about 37, due to weak mixing of the sulfur 3p orbital with the Fe-heme d orbitals. While the packing density model, and to a higher degree, the pathway model of biological ET partly capture the predicted rate enhancements, our study highlights the importance of the atomistic and chemical nature of the tunneling medium at short biological tunneling distances. Cysteine linkages are likely to enhance electron flow also in the larger deca-heme proteins MtrC and MtrF, where heme-heme motifs with sub-optimal edge-to-edge distances are used to shuttle electrons in multiple directions.

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.

Collective water dynamics in the first solvation shell drive the NMR relaxation of aqueous quadrupolar cations.

Using molecular simulations, we analyze the microscopic processes driving the Nuclear Magnetic Resonance (NMR) relaxation of quadrupolar cations in water. The fluctuations of the Electric Field Gradient (EFG) experienced by alkaline and magnesium cations, which determine the NMR relaxation time, are mainly due to the dynamics of water molecules in their solvation shell. The dynamics of the ion plays a less important role, with the exception of the short-time dynamics in the lighter Li+ case, for which rattling in the solvent cage results in oscillations of the EFG autocorrelation function (ACF). Several microscopic mechanisms that may a priori contribute to the decay of the EFG-ACF occur in fact over too long time scales: entrance/exit of individual water molecules into/from the solvation shell, rotation of a molecule around the ion, or reorientation of the molecule. In contrast, the fluctuations of the ion-water distance are clearly correlated to that of the EFG. Nevertheless, it is not sufficient to consider a single molecule due to the cancellations arising from the symmetry of the solvation shell. The decay of the EFG-ACF, hence NMR relaxation, is in fact governed by the collective symmetry-breaking fluctuations of water in the first solvation shell.

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.

On the microscopic fluctuations driving the NMR relaxation of quadrupolar ions in water.

Nuclear Magnetic Resonance (NMR) relaxation is sensitive to the local structure and dynamics around the probed nuclei. The Electric Field Gradient (EFG) is the key microscopic quantity to understand the NMR relaxation of quadrupolar ions, such as (7)Li(+), (23)Na(+), (25)Mg(2+), (35)Cl(-), (39)K(+), or (133)Cs(+). Using molecular dynamics simulations, we investigate the statistical and dynamical properties of the EFG experienced by alkaline, alkaline Earth, and chloride ions at infinite dilution in water. Specifically, we analyze the effect of the ionic charge and size on the distribution of the EFG tensor and on the multi-step decay of its auto-correlation function. The main contribution to the NMR relaxation time arises from the slowest mode, with a characteristic time on the picosecond time scale. The first solvation shell of the ion plays a dominant role in the fluctuations of the EFG, all the more that the ion radius is small and its charge is large. We propose an analysis based on a simplified charge distribution around the ion, which demonstrates that the auto-correlation of the EFG, hence the NMR relaxation time, reflects primarily the collective translational motion of water molecules in the first solvation shell of the cations. Our findings provide a microscopic route to the quantitative interpretation of NMR relaxation measurements and open the way to the design of improved analytical theories for NMR relaxation for small ionic solutes, which should focus on water density fluctuations around the ion.

Accurate quadrupolar NMR relaxation rates of aqueous cations from classical molecular dynamics.

Nuclear magnetic resonance (NMR) relaxation rates encode information about the collective and local dynamics around nuclei. Provided a suitable microscopic model is available, this allows investigating, e.g., the solvation shell dynamics around aqueous ions. Previous attempts with molecular dynamics simulations faced the double challenge of calculating accurately the microscopic properties governing the relaxation process, such as the electric field gradient (EFG) at the nucleus, and of sampling the trajectories over sufficiently long times. Here we show how to compute the NMR relaxation rate from classical molecular dynamics simulations. We use a recently derived force field parametrized on ab initio calculations and show that the EFG predicted by this force field can be used to accurately estimate the one computed by DFT using the PAW method where the electronic structure is described explicitly. The predicted relaxation rates for aqueous alkaline and alkaline Earth cations are in good agreement with experimental data. Our approach opens the way to the quantitative interpretation of these rates with molecular simulation.

Two algorithms to compute projected correlation functions in molecular dynamics simulations.

An explicit derivation of the Mori-Zwanzig orthogonal dynamics of observables is presented and leads to two practical algorithms to compute exactly projected observables (e.g., random noise) and projected correlation function (e.g., memory kernel) from a molecular dynamics trajectory. The algorithms are then applied to study the diffusive dynamics of a tagged particle in a Lennard-Jones fluid, the properties of the associated random noise, and a decomposition of the corresponding memory kernel.