Simulation of solution phase electron transfer in a compact donor-acceptor dyad

Simulating Electron Transfer Reactions in Solution: Radical-Polar Crossover

Single-electron transfer (SET) promotes a wide variety of interesting chemical transformations, but modeling of SET requires a careful treatment of electronic and solvent effects to give meaningful insight. Therefore, a combined constrained density functional theory and molecular mechanics (CDFT/MM) tool is introduced specifically for SET-initiated reactions. Mechanisms for two radical-polar crossover reactions involving the organic electron donors tetrakis(dimethylamino)ethylene (TDAE) and tetrathiafulvalene (TTF) were studied with the new tool. An unexpected tertiary radical intermediate within the TDAE system was identified, relationships between kinetics and substitution in the TTF system were explained, and the impact of the solvent environments on the TDAE and TTF reactions were examined. The results highlight the need for including solvent dynamics when quantifying SET kinetics and thermodynamics, as a free energy difference of >20 kcal/mol was observed. Overall, the new method informs mechanistic analysis of SET-initiated reactions and therefore is envisioned to be useful for studying reactions in the condensed phase.

Molecular Dynamics Simulations of Bimolecular Electron Transfer: the Distance-Dependent Electronic Coupling

Understanding the distance dependence of the parameters underpinning Marcus theory is imperative when interpreting the results of experiments on electron transfer (ET). Unfortunately, most of these parameters are difficult or impossible to access directly with experiments, necessitating the use of computer simulations to model them. In this work, we use molecular dynamics simulations in conjunction with constrained density functional theory calculations to study the distance dependence of the electronic coupling matrix element, |H_RP|, for bimolecular ET. Contrary to what is typically assumed for such intermolecular reactions, we find that the magnitude of |H_RP| does not decay exponentially with the center-of-mass separation of the reactants, r_COM. The addition of other simple measures of donor/acceptor (D/A) orientation did not improve the correlation of |H_RP| with r_COM. Using the minimum distance separation, r_min, of the reactants as the structural descriptor allowed the system to be partitioned into high-coupling/close-contact and low-coupling/non-contact regimes, but large fluctuations of |H_RP| were still found for the close-contact reactant pairs. Despite the persistent large fluctuations of |H_RP|, its mean value was found to decay piecewise exponentially with increasing r_min, which was attributed to significant changes in the average D/A pair structure. The results herein advise one to use caution when interpreting the experimental results derived from spherical reactant models of bimolecular ET.

Theoretical-computational modeling of charge transfer and intersystem crossing reactions in complex chemical systems

In this paper we present a theoretical-computational methodology specifically aimed at describing processes involving internal conversion or intersystem crossing, from atomistic (semiclassical) simulations and, hence, very suitable for treating complex atomic-molecular systems. The core of the presented approach is the evaluation of the diabatic perturbed energy surfaces of a portion of the whole system, treated at the quantum level and therefore preventively selected, in semi-classical interaction with the atomic-molecular environment. Subsequently, the estimation of the coupling between the diabatic surfaces and the inclusion of the obtained observables within a properly designed kinetic model allows the reconstruction of the whole phenomenology directly comparable to the experimental (typically kinetic) data. Application to two systems has demonstrated that the proposed approach can represent a valuable tool, somewhat complementary to other methods based on explicit quantum-dynamical approaches, for the theoretical-computational investigations of large and complex atomic-molecular systems.

An Ab Initio Exciton Model Including Charge-Transfer Excited States

The Frenkel exciton model is a useful tool for theoretical studies of multichromophore systems. We recently showed that the exciton model could be used to coarse-grain electronic structure in multichromophoric systems, focusing on singly excited exciton states [ Acc. Chem. Res. 2014 , 47 , 2857 - 2866 ]. However, our previous implementation excluded charge-transfer excited states, which can play an important role in light-harvesting systems and near-infrared optoelectronic materials. Recent studies have also emphasized the significance of charge-transfer in singlet fission, which mediates the coupling between the locally excited states and the multiexcitonic states. In this work, we report on an ab initio exciton model that incorporates charge-transfer excited states and demonstrate that the model provides correct charge-transfer excitation energies and asymptotic behavior. Comparison with TDDFT and EOM-CC2 calculations shows that our exciton model is robust with respect to system size, screening parameter, and different density functionals. Inclusion of charge-transfer excited states makes the exciton model more useful for studies of singly excited states and provides a starting point for future construction of a model that also includes double-exciton states.

Efficient Constrained Density Functional Theory Implementation for Simulation of Condensed Phase Electron Transfer Reactions

Constrained density functional theory (CDFT) is a versatile tool for probing the kinetics of electron transfer (ET) reactions. In this work, we present a well-scaling parallel CDFT implementation relying on a mixed basis set of Gaussian functions and plane waves, which has been specifically tailored to investigate condensed phase ET reactions using an explicit, quantum chemical representation of the solvent. The accuracy of our implementation is validated against previous theoretical results for predicting electronic couplings and charge transfer energies. Subsequently, we demonstrate the efficiency of our method by studying the intramolecular ET reaction of an organic mixed-valence compound in water using a CDFT based molecular dynamics simulation.

Quantum-Classical Path Integral Simulation of Ferrocene-Ferrocenium Charge Transfer in Liquid Hexane

We employ the quantum-classical path integral methodology to simulate the outer sphere charge-transfer process of the ferrocene-ferrocenium pair in liquid hexane with unprecedented accuracy. Comparison of the simulation results to those obtained by mapping the solvent on an effective harmonic bath demonstrates the accuracy of linear response theory in this system.

A molecularly based theory for electron transfer reorganization energy

Using field-theoretic techniques, we develop a molecularly based dipolar self-consistent-field theory (DSCFT) for charge solvation in pure solvents under equilibrium and nonequilibrium conditions and apply it to the reorganization energy of electron transfer reactions. The DSCFT uses a set of molecular parameters, such as the solvent molecule's permanent dipole moment and polarizability, thus avoiding approximations that are inherent in treating the solvent as a linear dielectric medium. A simple, analytical expression for the free energy is obtained in terms of the equilibrium and nonequilibrium electrostatic potential profiles and electric susceptibilities, which are obtained by solving a set of self-consistent equations. With no adjustable parameters, the DSCFT predicts activation energies and reorganization energies in good agreement with previous experiments and calculations for the electron transfer between metallic ions. Because the DSCFT is able to describe the properties of the solvent in the immediate vicinity of the charges, it is unnecessary to distinguish between the inner-sphere and outer-sphere solvent molecules in the calculation of the reorganization energy as in previous work. Furthermore, examining the nonequilibrium free energy surfaces of electron transfer, we find that the nonequilibrium free energy is well approximated by a double parabola for self-exchange reactions, but the curvature of the nonequilibrium free energy surface depends on the charges of the electron-transferring species, contrary to the prediction by the linear dielectric theory.

A hybrid approach to simulation of electron transfer in complex molecular systems

Electron transfer (ET) reactions in biomolecular systems represent an important class of processes at the interface of physics, chemistry and biology. The theoretical description of these reactions constitutes a huge challenge because extensive systems require a quantum-mechanical treatment and a broad range of time scales are involved. Thus, only small model systems may be investigated with the modern density functional theory techniques combined with non-adiabatic dynamics algorithms. On the other hand, model calculations based on Marcus's seminal theory describe the ET involving several assumptions that may not always be met. We review a multi-scale method that combines a non-adiabatic propagation scheme and a linear scaling quantum-chemical method with a molecular mechanics force field in such a way that an unbiased description of the dynamics of excess electron is achieved and the number of degrees of freedom is reduced effectively at the same time. ET reactions taking nanoseconds in systems with hundreds of quantum atoms can be simulated, bridging the gap between non-adiabatic ab initio simulations and model approaches such as the Marcus theory. A major recent application is hole transfer in DNA, which represents an archetypal ET reaction in a polarizable medium. Ongoing work focuses on hole transfer in proteins, peptides and organic semi-conductors.

Efficient algorithms for the simulation of non-adiabatic electron transfer in complex molecular systems: application to DNA

In this work, a fragment-orbital density functional theory-based method is combined with two different non-adiabatic schemes for the propagation of the electronic degrees of freedom. This allows us to perform unbiased simulations of electron transfer processes in complex media, and the computational scheme is applied to the transfer of a hole in solvated DNA. It turns out that the mean-field approach, where the wave function of the hole is driven into a superposition of adiabatic states, leads to over-delocalization of the hole charge. This problem is avoided using a surface hopping scheme, resulting in a smaller rate of hole transfer. The method is highly efficient due to the on-the-fly computation of the coarse-grained DFT Hamiltonian for the nucleobases, which is coupled to the environment using a QM/MM approach. The computational efficiency and partial parallel character of the methodology make it possible to simulate electron transfer in systems of relevant biochemical size on a nanosecond time scale. Since standard non-polarizable force fields are applied in the molecular-mechanics part of the calculation, a simple scaling scheme was introduced into the electrostatic potential in order to simulate the effect of electronic polarization. It is shown that electronic polarization has an important effect on the features of charge transfer. The methodology is applied to two kinds of DNA sequences, illustrating the features of transfer along a flat energy landscape as well as over an energy barrier. The performance and relative merit of the mean-field scheme and the surface hopping for this application are discussed.

Molecular insight into the high selectivity of double-walled carbon nanotubes

Combining experimental knowledge with molecular simulations, we investigated the adsorption and separation properties of double-walled carbon nanotubes (DWNTs) against flue/synthetic gas mixture components (e.g. CO(2), CO, N(2), H(2), O(2), and CH(4)) at 300 K. Except molecular H(2), all studied nonpolar adsorbates assemble into single-file chain structures inside DWNTs at operating pressures below 1 MPa. Molecular wires of adsorbed molecules are stabilized by the strong solid-fluid potential generated from the cylindrical carbon walls. CO(2) assembly is formed at very low operating pressures in comparison to all other studied nonpolar adsorbates. The adsorption lock-and-key mechanism results from perfect fitting of rod-shaped CO(2) molecules into the cylindrical carbon pores. The enthalpy of CO(2) adsorption in DWNTs is very high and reaches 50 kJ mol(-1) at 300 K and low pore concentrations. In contrast, adsorption enthalpy at zero coverage is significantly lower for all other studied nonpolar adsorbates, for instance: 35 kJ mol(-1) for CH(4), and 14 kJ mol(-1) for H(2). Applying the ideal adsorption solution theory, we predicted that the internal pores of DWNTs have unusual ability to differentiate CO(2) molecules from other flue/synthetic gas mixture components (e.g. CO, N(2), H(2), O(2), and CH(4)) at ambient operating conditions. Computed equilibrium selectivity for equimolar CO(2)-X binary mixtures (where X: CO, N(2), H(2), O(2), and CH(4)) is very high at low mixture pressures. With an increase in binary mixture pressure, we predicted a decrease in equilibrium separation factor because of the competitive adsorption of the X binary mixture component. We showed that at 300 K and equimolar mixture pressures up to 1 MPa, the CO(2)-X equilibrium separation factor is higher than 10 for all studied binary mixtures, indicating strong preference for CO(2) adsorption. The overall selective properties of DWNTs seem to be superior, which may be beneficial for potential industrial applications of these novel carbon nanostructures.