The diabatic picture of electron transfer, reaction barriers, and molecular dynamics

A Multibox Splitting Scheme: Robust Approximation For ab Initio Molecular Dynamics

In this work, the multibox (M-box) simulation scheme is introduced, which can be considered as a generalization of the QM/MM scheme for multifragment (molecular) systems. This scheme exploits the natural locality of multifragment molecular-based systems by mapping the system into force-coupled block subspaces. Where defined in this way, the entire system can be fully modeled under a quantum mechanical force field. This allows the description of each subspace explicitly by means of a robust electronic structure theory without the requirement for large computational resources. An adequate block-to-block coupling by means of shared subsystem fragments is applied to preserve the long-distance structural correlation in the system during a molecular dynamic (MD) simulation. Since electronic structure descriptions play a central role in the formulation of several parametric models for charge or energy transport, we expect that this space-time correlated scheme can become a reliable computational tool for charge/energy transport/transfer applications. The efficiency of the method is demonstrated by performing statistical and time-resolved analysis using both the multifragment box and full ab initio approaches. We illustrate the method using as examples the melting process of a one-dimensional benzene chain (weak interaction situation) and NVE dynamics for the CnHn polymeric chain (strong interaction situation). We also have extended the threshold of applicability of our model, demonstrating how it can cope with MD simulation with more complex systems and processes.

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

Charge separation (CS) and charge recombination (CR) rates in photosynthetic architectures are difficult to control, yet their ratio can make or break photon-to-current conversion efficiencies. A rational design approach to the enhancement of CS over CR requires a mechanistic understanding of the underlying electron-transfer (ET) process, including the role of the environment. Toward this goal, we introduce a QM/MM protocol for ET simulations and use it to characterize CR in the formanilide-anthraquinone dyad (FAAQ). Our simulations predict fast recombination of the charge-transfer excited state, in agreement with recent experiments. The computed electronic couplings show an electronic state dependence and are weaker in solution than in the gas phase. We explore the role of cis-trans isomerization on the CR kinetics, and we find strong correlation between the vertical energy gaps of the full simulations and a collective solvent polarization coordinate. Our approach relies on constrained density functional theory to obtain accurate diabatic electronic states on the fly for molecular dynamics simulations, while orientational and electronic polarization of the solvent is captured by a polarizable force field based on a Drude oscillator model. The method offers a unified approach to the characterization of driving forces, reorganization energies, electronic couplings, and nonlinear solvent effects in light-harvesting systems.

Simulating picosecond iron K-edge X-ray absorption spectra by ab initio methods to study photoinduced changes in the electronic structure of Fe(II) spin crossover complexes

Recent time-resolved X-ray absorption experiments probing the low-spin to high-spin photoconversion in Fe(II) complexes have monitored the complex interplay between electronic and structural degrees of freedom on an ultrafast time scale. In this study, we use transition potential (TP) and time-dependent (TD) DFT to simulate the picosecond time-resolved iron K-edge X-ray absorption spectrum of the spin crossover (SCO) complex, [Fe(tren(py)(3))](2+). This is achieved by simulating the X-ray absorption spectrum of [Fe(tren(py)(3))](2+) in its low-spin (LS), (1)A(1), ground state and its high-spin (HS), (5)T(2), excited state. These results are compared with the X-ray absorption spectrum of the high-spin analogue (HSA), [Fe(tren(6-Me-py)(3))](2+), which has a (5)T(2) ground state. We show that the TP-DFT methodology can simulate a 40 eV range of the iron K-edge XANES spectrum reproducing all of the major features observed in the static and transient spectra of the LS, HS, and HSA complexes. The pre-edge region of the K-edge spectrum, simulated by TD-DFT, is shown to be highly sensitive to metal-ligand bonding. Changes in the intensity of the pre-edge region are shown to be sensitive to both symmetry and π-backbonding by analysis of relative electric dipole and quadrupole contributions to the transition moments. We generate a spectroscopic map of the iron 3d orbitals from our TD-DFT results and determine ligand field splitting energies of 1.55 and 1.35 eV for the HS and HSA complexes, respectively. We investigate the use of different functionals finding that hybrid functionals (such as PBE0) produce the best results. Finally, we provide a detailed comparison of our results with theoretical methods that have been previously used to interpret Fe K-edge spectroscopy of equilibrium and time-resolved SCO complexes.

Semiclassical dynamics simulations of charge transport in stacked π-systems

Charge transfer processes within stacked π-systems were examined for the stacked ethylene dimer radical cation with inclusion of a bridge containing up to three formaldehyde molecules. The electronic structure was treated at the complete active space self-consistent field and multireference configuration interaction levels. Nonadiabatic interactions between electronic and nuclear degrees of freedom were included through semiclassical surface hopping dynamics. The processes were analyzed according to fragment charge differences. Static calculations explored the dependence of the electronic coupling and on-site energies on varying geometric parameters and on the inclusion of a bridge. The dynamics simulations gave the possibility for directly observing complex charge transfer and diabatic trapping events.

Electronic coupling matrix elements from charge constrained density functional theory calculations using a plane wave basis set

We present a plane wave basis set implementation for the calculation of electronic coupling matrix elements of electron transfer reactions within the framework of constrained density functional theory (CDFT). Following the work of Wu and Van Voorhis [J. Chem. Phys. 125, 164105 (2006)], the diabatic wavefunctions are approximated by the Kohn-Sham determinants obtained from CDFT calculations, and the coupling matrix element calculated by an efficient integration scheme. Our results for intermolecular electron transfer in small systems agree very well with high-level ab initio calculations based on generalized Mulliken-Hush theory, and with previous local basis set CDFT calculations. The effect of thermal fluctuations on the coupling matrix element is demonstrated for intramolecular electron transfer in the tetrathiafulvalene-diquinone (Q-TTF-Q(-)) anion. Sampling the electronic coupling along density functional based molecular dynamics trajectories, we find that thermal fluctuations, in particular the slow bending motion of the molecule, can lead to changes in the instantaneous electron transfer rate by more than an order of magnitude. The thermal average, (<|H(ab)|(2)>)(1/2)=6.7 mH, is significantly higher than the value obtained for the minimum energy structure, |H(ab)|=3.8 mH. While CDFT in combination with generalized gradient approximation (GGA) functionals describes the intermolecular electron transfer in the studied systems well, exact exchange is required for Q-TTF-Q(-) in order to obtain coupling matrix elements in agreement with experiment (3.9 mH). The implementation presented opens up the possibility to compute electronic coupling matrix elements for extended systems where donor, acceptor, and the environment are treated at the quantum mechanical (QM) level.

Energy-transfer and charge-separation pathways in the reaction center of photosystem II revealed by coherent two-dimensional optical spectroscopy

The excited state dynamics and relaxation of electrons and holes in the photosynthetic reaction center of photosystem II are simulated using a two-band tight-binding model. The dissipative exciton and charge carrier motions are calculated using a transport theory, which includes a strong coupling to a harmonic bath with experimentally determined spectral density, and reduces to the Redfield, the Förster, and the Marcus expressions in the proper parameter regimes. The simulated third order two-dimensional signals, generated in the directions -k(1)+k(2)+k(3), k(1)-k(2)+k(3), and k(1)+k(2)-k(3), clearly reveal the exciton migration and the charge-separation processes.

Electronic properties of disordered organic semiconductors via QM/MM simulations

Organic semiconductors (OSCs) have recently received significant attention for their potential use in photovoltaic, light emitting diode, and field effect transistor devices. Part of the appeal of OSCs is the disordered, amorphous nature of these materials, which makes them more flexible and easier to process than their inorganic counterparts. In addition to their technological applications, OSCs provide an attractive laboratory for examining the chemistry of heterogeneous systems. Because OSCs are both electrically and optically active, researchers have access to a wealth of electrical and spectroscopic probes that are sensitive to a variety of localized electronic states in these materials. In this Account, we review the basic concepts in first-principles modeling of the electronic properties of disordered OSCs. There are three theoretical ingredients in the computational recipe. First, Marcus theory of nonadiabatic electron transfer (ET) provides a direct link between energy and kinetics. Second, constrained density functional theory (CDFT) forms the basis for an ab initio model of the diabatic charge states required in ET. Finally, quantum mechanical/molecular mechanical (QM/MM) techniques allow us to incorporate the influence of the heterogeneous environment on the diabatic states. As an illustration, we apply these ideas to the small molecule OSC tris(8- hydroxyquinolinato)aluminum (Alq(3)). In films, Alq(3) can possess a large degree of short-range order, placing it in the middle of the order-disorder spectrum (in this spectrum, pure crystals represent one extreme and totally amorphous structures the opposite extreme). We show that the QM/MM recipe reproduces the transport gap, charge carrier hopping integrals, optical spectra, and reorganization energies of Alq(3) in quantitative agreement with available experiments. However, one cannot specify any of these quantities accurately with a single number. Instead, one must characterize each property by a distribution that reflects the influence of the heterogeneous environment on the electronic states involved. For example, the hopping integral between a given pair of Alq(3) molecules can vary by as much as a factor of 5 on the nanosecond timescale, but the integrals for two different pairs can easily differ by a factor of 100. To accurately predict mesoscopic properties such as carrier mobilities based on these calculations, researchers must account for the dynamic range of the microscopic inputs, rather than just their average values. Thus, we find that many of the computational tools required to characterize these materials are now available. As we continue to improve this computational toolbox, we envision a future scenario in which researchers can use basic information about OSC deposition to simulate device operation on the atomic scale. This type of simulation could allow researchers to obtain data that not only aids in the interpretation of experimental results but also guides the design of more efficient devices.