Robust, Basis-Set Independent Method for the Evaluation of Charge-Transfer Energy in Noncovalent Complexes

Separation of the energetic contribution of charge transfer to interaction energy in noncovalent complexes would provide important insight into the mechanisms of the interaction. However, the calculation of charge-transfer energy is not an easy task. It is not a physically well-defined term, and the results might depend on how it is described in practice. Commonly, the charge transfer is defined in terms of molecular orbitals; in this framework, however, the charge transfer vanishes as the basis set size increases toward the complete basis set limit. This can be avoided by defining the charge transfer in terms of the spatial extent of the electron densities of the interacting molecules, but the schemes used so far do not reflect the actual electronic structure of each particular system and thus are not reliable. We propose a spatial partitioning of the system, which is based on a charge transfer-free reference state, namely superimposition of electron densities of the noninteracting fragments. We show that this method, employing constrained DFT for the calculation of the charge-transfer energy, yields reliable results and is robust with respect to the strength of the charge transfer, the basis set size, and the DFT functional used. Because it is based on DFT, the method is applicable to rather large systems

ATP Binding and Aspartate Protonation Enhance Photoinduced Electron Transfer in Plant Cryptochrome

Cryptochromes are flavoproteins encountered in most vegetal and animal species. They play a role of blue-light receptors in plants and in invertebrates. The putative resting state of the FAD cofactor in these proteins is its fully oxidized form, FAD_ox. Upon blue-light excitation, the isoalloxazine ring (ISO) may undergo an ultrafast reduction by a nearby tryptophan residue W400. This primary reduction triggers a cascade of electron and proton transfers, ultimately leading to the formation of the FADH° radical. A recent experimental study has shown that the yield of FADH° formation in <i>Arabidopsis</i> cryptochrome can be strongly modulated by ATP binding and by pH, affecting the protonation state of D396 (proton donor to FAD°^–). Here we provide a detailed molecular analysis of these effects by means of combined classical molecular dynamics simulations and time-dependent density functional theory calculations. When ATP is present and D396 protonated, FAD remains in close contact with W400, thereby enhancing electron transfer (ET) from W400 to ISO*. In contrast, deprotonation of D396 and absence of ATP introduce flexibility to the photoactive site prior to FAD excitation, with the consequence of increased ISO-W400 distance and diminished tunneling rate by almost two orders of magnitude. We show that under these conditions, ET from the adenine moiety of FAD becomes a competitive relaxation pathway. Overall, our data suggest that the observed effects of ATP and pH on the FAD photoreduction find their roots in the earliest stage of the photoreduction process; i.e., ATP binding and the protonation state of D396 determine the preferred pathway of ISO* relaxation

Electron Transfer, Decoherence, and Protein Dynamics: Insights from Atomistic Simulations

ConspectusElectron transfer in biological systems drives the processes of life. From cellular respiration to photosynthesis and enzymatic catalysis, electron transfers (ET) are chemical processes on which essential biological functions rely. Over the last 40 years, scientists have sought understanding of how these essential processes function in biology. One important breakthrough was the discovery that Marcus theory (MT) of electron transfer is applicable to biological systems. Chemists have experimentally collected both the reorganization energies (λ) and the driving forces (Δ<i>G</i>°), two parameters of Marcus theory, for a large variety of ET processes in proteins. At the same time, theoretical chemists have developed computational approaches that rely on molecular dynamics and quantum chemistry calculations to access numerical estimates of λ and Δ<i>G</i>°.Yet another crucial piece in determining the rate of an electron transfer is the electronic coupling between the initial and final electronic wave functions. This is an important prefactor in the nonadiabatic rate expression, since it reflects the probability that an electron tunnels from the electron donor to the acceptor through the intervening medium. The fact that a protein matrix supports electron tunneling much more efficiently than vacuum is now well documented, both experimentally and theoretically. Meanwhile, many chemists have provided examples of the rich physical chemistry that can be induced by protein dynamics.This Account describes our studies of the dynamical effects on electron tunneling. We present our analysis of two examples of natural biological systems through MD simulations and tunneling pathway analyses. Through these examples, we show that protein dynamics sustain efficient tunneling.Second, we introduce two time scales: τ_coh and τ_FC. The former characterizes how fast the electronic coupling varies with nuclear vibrations (which cause dephasing). The latter reflects the time taken by the system to leave the crossing region. In the framework of open quantum systems, τ_FC is a short time approximation of the characteristic decoherence time of the electronic subsystem in interaction with its nuclear environment. The comparison of the respective values of τ_coh and τ_FC allows us to probe the occurrence of non-Condon effects. We use <i>ab initio</i> MD simulations to analyze how decoherence appears in several biological cofactors. We conclude that we cannot account for its order of magnitude by considering only the atoms or bonds directly concerned with the transfer. Decoherence results from contributions from all atoms of the system appearing with a time delay that increases with the distance from the primarily concerned atoms or bonds. The delay and magnitude of the contributions depend on the chemical nature of the system.Finally, we present recent developments based on constrained DFT for efficient and accurate evaluations of the electronic coupling in <i>ab initio</i> MD simulations. These are promising methods to study the subtle fluctuations of the electronic coupling and the mechanisms of electronic decoherence in biological systems

Electron and Hydrogen Atom Transfers in the Hydride Carrier Protein EmoB

In this article, we investigate the mechanism of hydride transfer taking place within the EmoB protein of the <i>Mesorhizobium</i> species. The reaction involves the net transfer of one proton and two electrons from a reduced flavin mononucleotide (FMN) cofactor, which is anchored in the protein scaffold, to a diffusible oxidized FMN cofactor, both being held together by π-stacking interactions. To analyze the formal hydride transfer in terms of more elementary steps, electron transfer (ET), and hydrogen atom transfers (HAT), we employ a combination of classical molecular dynamics simulations and hybrid constrained Density Functional Theory/Molecular Mechanics (cDFT/MM) energy calculations to build the free energy profiles, for the ET before and after HAT occurs between the flavins. The main outcomes of our study are first to highlight the role of the protein in stabilizing the π-stacked FMN dimer and second to reveal the coupling between the ET and HAT. Before HAT has taken place, ET is unfavorable by 8 kcal/mol and become favorable by 8 kcal/mol after HAT. Our simulations show that such a coupling is not present for the analogous process in water (ET is almost athermal). This suggests a functional role for the protein matrix to ensure EmoB a role of hydride carrier in the <i>Mesorhizobium</i> species

Simulating Electron Dynamics in Polarizable Environments

We propose a methodology for simulating attosecond electron dynamics in large molecular systems. Our approach is based on the combination of real time time-dependent-density-functional theory (RT-TDDFT) and polarizable Molecular Mechanics (MMpol) with the point-charge-dipole model of electrostatic induction. We implemented this methodology in the software deMon2k that relies heavily on auxiliary fitted densities. In the context of RT-TDDFT/MMpol simulations, fitted densities allow the cost of the calculations to be reduced drastically on three fronts: (i) the Kohn–Sham potential, (ii) the electric field created by the (fluctuating) electron cloud which is needed in the QM/MM interaction, and (iii) the analysis of the fluctuating electron density on-the-fly. We determine conditions under which fitted densities can be used without jeopardizing the reliability of the simulations. Very encouraging results are found both for stationary and time-dependent calculations. We report absorption spectra of a dye molecule in the gas phase, in nonpolarizable water, and in polarizable water. Finally, we use the method to analyze the distance-dependent response of the environment of a peptide perturbed by an electric field. Different response mechanisms are identified. It is shown that the induction on MM sites allows excess energy to dissipate from the QM region to the environment. In this regard, the first hydration shell plays an essential role in absorbing energy. The methodology presented herein opens the possibility of simulating radiation-induced electronic phenomena in complex and extended molecular systems

Electronic Coupling Calculations for Bridge-Mediated Charge Transfer Using Constrained Density Functional Theory (CDFT) and Effective Hamiltonian Approaches at the Density Functional Theory (DFT) and Fragment-Orbital Density Functional Tight Binding (FODFTB) Level

In this article, four methods to calculate charge transfer integrals in the context of bridge-mediated electron transfer are tested. These methods are based on density functional theory (DFT). We consider two perturbative Green’s function effective Hamiltonian methods (first, at the DFT level of theory, using localized molecular orbitals; second, applying a tight-binding DFT approach, using fragment orbitals) and two constrained DFT implementations with either plane-wave or local basis sets. To assess the performance of the methods for through-bond (TB)-dominated or through-space (TS)-dominated transfer, different sets of molecules are considered. For through-bond electron transfer (ET), several molecules that were originally synthesized by Paddon-Row and co-workers for the deduction of electronic coupling values from photoemission and electron transmission spectroscopies, are analyzed. The tested methodologies prove to be successful in reproducing experimental data, the exponential distance decay constant and the superbridge effects arising from interference among ET pathways. For through-space ET, dedicated π-stacked systems with heterocyclopentadiene molecules were created and analyzed on the basis of electronic coupling dependence on donor–acceptor distance, structure of the bridge, and ET barrier height. The inexpensive fragment-orbital density functional tight binding (FODFTB) method gives similar results to constrained density functional theory (CDFT) and both reproduce the expected exponential decay of the coupling with donor–acceptor distances and the number of bridging units. These four approaches appear to give reliable results for both TB and TS ET and present a good alternative to expensive <i>ab initio</i> methodologies for large systems involving long-range charge transfers

Multidimensional Quantum Mechanical Modeling of Electron Transfer and Electronic Coherence in Plant Cryptochromes: The Role of Initial Bath Conditions

A multidimensional quantum mechanical protocol is used to describe the photoinduced electron transfer and electronic coherence in plant cryptochromes without any semiempirical, e.g., experimentally obtained, parameters. Starting from a two-level spin-boson Hamiltonian we look at the effect that the initial photoinduced nuclear bath distribution has on an intermediate step of this biological electron transfer cascade for two idealized cases. The first assumes a slow equilibration of the nuclear bath with respect to the previous electron transfer step that leads to an ultrafast decay with little temperature dependence; while the second assumes a prior fast bath equilibration on the donor potential energy surface leading to a much slower decay, which contrarily displays a high temperature dependence and a better agreement with previous theoretical and experimental results. Beyond Marcus and semiclassical pictures these results unravel the strong impact that the presence or not of equilibrium initial conditions has on the electronic population and coherence dynamics at the quantum dynamics level in this and conceivably in other biological electron transfer cascades