Tunneling Pathways Research Articles

Surface Adatom Conductance Filtering in Scanning Tunneling Spectroscopy of Co-dopedBaFe2As2Iron Pnictide Superconductors

We establish in a combination of ab initio theory and experiments that the tunneling process in scanning tunneling microscopy or spectroscopy on the A-122 iron pnictide superconductors-in this case BaFe(2-x)Co(x)As(2)-involves a strong adatom filtering of the differential conductance from the near-E(F) Fe-3d states, which in turn originates from the topmost subsurface Fe layer of the crystal. The calculations show that the dominance of surface Ba-related tunneling pathways leaves fingerprints found in the experimental differential conductance data, including large particle-hole asymmetry and energy-dependent contrast inversion in conductance maps.

Electronic and transport properties of azobenzene monolayer junctions as molecular switches

We investigate from first principles the change in transport properties of a two-dimensional azobenzene monolayer sandwiched between two Au electrodes that undergoes molecular switching. We focus on transport differences between a chemisorbed and physisorbed top monolayer-electrode contact. The conductance of the monolayer junction with a chemisorbed top contact is higher in the trans configuration, in agreement with the previous theoretical predictions of one-dimensional single-molecule junctions. However, with a physisorbed top contact, the ON state, with larger conductance, is associated with the cis configuration due to a reduced effective tunneling pathway, which successfully explains recent experimental measurements on azobenzene monolayer junctions. A simple model is developed to explain electron transmission across subsystems in the molecular junction. We also discuss the effects of monolayer packing density, molecule tilt angle, and contact geometry on the calculated transmission functions. In particular, we find that a tip-like contact with chemisorption significantly affects the electric current through the cis monolayer, leading to highly asymmetric current-voltage characteristics as well as large negative differential resistance behavior.

Theoretical Prediction of Triplet–Triplet Energy Transfer Rates in a Benzophenone–Fluorene–Naphthalene System

Triplet–triplet energy transfer in benzophenone–fluorene and benzophenone–fluorene–naphthalene molecules is theoretically investigated by using the rate theories and electronic structure calculations established for electron transfer. From the calculated electronic couplings for the single-step tunneling and multistep hopping pathways of the energy transfer from the donor benzophenone to the acceptor naphthalene, it is found that the tunneling comes from the direct electronic couplings between the donor and acceptor states, other than the coupling via the virtual bridge state in the conventional superexchange mechanism. The mode-specific reorganization energy calculations reveal that only the several high-frequency modes dominate the energy transfer, leading to an important nuclear tunneling effect. Succeedingly, with use of the obtained parameters, Fermi’s golden rule predicts the consistent energy transfer rates with experimental ones.

Electron Tunneling Pathways and Role of Adenine in Repair of Cyclobutane Pyrimidine Dimer by DNA Photolyase

Electron tunneling pathways in enzymes are critical to their catalytic efficiency. Through electron tunneling, photolyase, a photoenzyme, splits UV-induced cyclobutane pyrimidine dimer into two normal bases. Here, we report our systematic characterization and analyses of photoinitiated three electron transfer processes and cyclobutane ring splitting by following the entire dynamical evolution during enzymatic repair with femtosecond resolution. We observed the complete dynamics of the reactants, all intermediates and final products, and determined their reaction time scales. Using (deoxy)uracil and thymine as dimer substrates, we unambiguously determined the electron tunneling pathways for the forward electron transfer to initiate repair and for the final electron return to restore the active cofactor and complete the catalytic photocycle. Significantly, we found that the adenine moiety of the unusual bent flavin cofactor is essential to mediating all electron-transfer dynamics through a superexchange mechanism, leading to a delicate balance of time scales. The cyclobutane ring splitting takes tens of picoseconds, while electron-transfer dynamics all occur on a longer time scale. The active-site structural integrity, unique electron tunneling pathways, and the critical role of adenine ensure the synergy of these elementary steps in this complex photorepair machinery to achieve maximum repair efficiency which is close to unity. Finally, we used the Marcus electron-transfer theory to evaluate all three electron-transfer processes and thus obtained their reaction driving forces (free energies), reorganization energies, and electronic coupling constants, concluding that the forward and futile back-electron transfer is in the normal region and that the final electron return of the catalytic cycle is in the inverted region.

Exploring biological electron transfer pathway dynamics with the Pathways Plugin for VMD

We describe the new Pathways plugin for the molecular visualization program visual molecular dynamics. The plugin identifies and visualizes tunneling pathways and pathway families in biomolecules, and calculates relative electronic couplings. The plugin includes unique features to estimate the importance of individual atoms for mediating the coupling, to analyze the coupling sensitivity to thermal motion, and to visualize pathway fluctuations. The Pathways plugin is open source software distributed under the terms of the GNU's Not Unix (GNU) public license.

Computational Analysis of Electron Tunneling Pathways of Blue-Light Photoreceptors

DNA phtolyases and cryptochrome DASH (cry-DASH) enzymes in the blue-light photoreceptor family repair UV-damaged DNA by photo-induced electron transfer reaction. Recently (Miyazawa et al., 2008) we analyzed the electron tunneling pathways in a class I CPD photolyase derived from A. nidulans and identified a key residue, Met-353, which is perfectly conserved in the class I CPD photolyases. Interestingly, this site is switched to histidine in 6-4 photolyases, and to glutamine in cry-DASH enzymes. For instance, Met-353 is replaced to Gln-395 in cry-DASH. It is likely that the amino acid residue at the site controls the enzymatic functions of the blue-light photoreceptor family. Until now, the electron transfer pathways in cry-DASH enzymes remain unclear, while those of CPD photolyases are studied well.To characterize the roles of the amino acid residue at the site, we performed molecular dynamics simulation and electronic state calculations of the CPD photolyase of A. nidulans and the cry-DASH. We analyzed the electron tunneling pathways in the forward and backward electron transfer reactions between FADH- and CPD of these two enzymes. As a result, we observed busy trafficking of electron-tunneling current at both Met-353 of the CPD photolyase and Gln-395 of the cry-DASH.

Electron Tunneling in Respiratory Complex I

NADH:ubiquinone oxidoreductase (complex I) plays a central role in the respiratory electron transport chain by coupling the transfer of electrons from NADH to ubiquinone to proton pumping across the membrane. Until now, the atomistic details of electron transfer have remained unknown. In this study, electron tunneling along seven Fe/S clusters in complex I is examined in atomistic resolution by using the tunneling current theory and computer simulations [1]. Distinct electron tunneling pathways between neighboring Fe/S clusters are identified; the pathways primarily consist of two cysteine ligands and one additional key residue. The identified key residues are further characterized by sensitivity of electron transfer rates to their mutations, examined in simulations and their conservation among complex I homologues. Internal water between protein subunits is identified as an essential mediator enhancing drastically the overall electron transfer rate to achieve the physiologically significant value. With the water included, negative slope of the distance dependence of the electron transfer rates becomes close to a typical 1.4 in natural logarithm. The unusual electronic structure properties of Fe/S clusters in complex I explain their remarkable efficiency of electron transfer. [1] T.Hayashi, A.A.Stuchebrukhov, Proc. Natl. Acad. Sci. U.S.A. 107, 19157

Slow Magnetic Relaxation at Zero Field in the Tetrahedral Complex [Co(SPh)4]2–

The Ph(4)P(+) salt of the tetrahedral complex [Co(SPh)(4)](2-), possessing an S = (3)/(2) ground state with an axial zero-field splitting of D = -70 cm(-1), displays single-molecule magnet behavior in the absence of an applied magnetic field. At very low temperatures, ac magnetic susceptibility data show the magnetic relaxation time, τ, to be temperature-independent, while above 2.5 K thermally activated Arrhenius behavior is apparent with U(eff) = 21(1) cm(-1) and τ(0) = 1.0(3) × 10(-7) s. Under an applied field of 1 kOe, τ more closely approximates Arrhenius behavior over the entire temperature range. Upon dilution of the complex within a matrix of the isomorphous compound (Ph(4)P)(2)[Zn(SPh)(4)], ac susceptibility data reveal the molecular nature of the slow magnetic relaxation and indicate that the quantum tunneling pathway observed at low temperatures is likely mediated by intermolecular dipolar interactions.

Rotational Spectrum and Internal Dynamics of Tetrahydrofuran-Krypton

The rotational spectrum of the tetrahydrofuran-krypton van der Waals complex has been investigated by pulsed-jet Fourier transform microwave spectroscopy. The spectra of the (84)Kr and (86)Kr isotopologues have been assigned and the krypton atom is located nearly over the oxygen atom, almost perpendicular to the COC plane. Each rotational transition is split into two component lines due to, according to the observed Coriolis coupling term between the tunneling states, the residual pseudorotational effects of the ring in the complex. The splitting between the two vibrational sublevels is 87.462(2) and 87.062(2) MHz for the (84)Kr and (86)Kr isotopologues, respectively. These splittings have been used to determine the barrier to inversion, B(2) = 67 cm(-1). The dissociation energy has been estimated to be 3.7 kJ mol(-1) from centrifugal distortion effects.

Instanton calculations of tunneling splittings for water dimer and trimer

We investigate the ability of the recently developed ring-polymer instanton (RPI) method [J. O. Richardson and S. C. Althorpe, J. Chem. Phys. 134, 054109 (2011)] to treat tunneling in water clusters. We show that the RPI method is easy to extend to treat tunneling between more than two minima, using elementary graph theory. Tests of the method on water dimer and trimer yield a set of instanton periodic orbits which correspond to all known tunneling pathways in these systems. Splitting patterns obtained from the orbits are in good overall agreement with experiment. The agreement is closer for the deuterated than for the protonated clusters, almost certainly because the main approximation in the calculations is neglect of anharmonicity perpendicular to the tunneling path. All the calculations were performed on a desktop computer, which suggests that similar calculations will be possible on much larger clusters.

Electronic coupling calculation and pathway analysis of electron transfer reaction using ab initio fragment-based method. I. FMO–LCMO approach

By making use of an ab initio fragment-based electronic structure method, fragment molecular orbital-linear combination of MOs of the fragments (FMO-LCMO), developed by Tsuneyuki et al. [Chem. Phys. Lett. 476, 104 (2009)], we propose a novel approach to describe long-distance electron transfer (ET) in large system. The FMO-LCMO method produces one-electron Hamiltonian of whole system using the output of the FMO calculation with computational cost much lower than conventional all-electron calculations. Diagonalizing the FMO-LCMO Hamiltonian matrix, the molecular orbitals (MOs) of the whole system can be described by the LCMOs. In our approach, electronic coupling T(DA) of ET is calculated from the energy splitting of the frontier MOs of whole system or perturbation method in terms of the FMO-LCMO Hamiltonian matrix. Moreover, taking into account only the valence MOs of the fragments, we can considerably reduce computational cost to evaluate T(DA). Our approach was tested on four different kinds of model ET systems with non-covalent stacks of methane, non-covalent stacks of benzene, trans-alkanes, and alanine polypeptides as their bridge molecules, respectively. As a result, it reproduced reasonable T(DA) for all cases compared to the reference all-electron calculations. Furthermore, the tunneling pathway at fragment-based resolution was obtained from the tunneling current method with the FMO-LCMO Hamiltonian matrix.

Quantum tunneling switch in a planar four-well system

We investigate the tunneling dynamics of a single atom in a planar four-well potential driven by a high-frequency ac field. The quasienergy spectrum exhibits anticrossing and crossing, which are related to selective coherent destruction of tunneling (CDT) with several selectable directions. By using the CDTs of different directions, the switchlike effect is shown for the six tunneling pathways among the four wells. Applying the present results, we suggest a scheme for designing a single-atom quantum motor with the driving field as a quantum starter.

First principles studies of electron tunneling in proteins

A first principles study of electronic tunneling along the chain of seven Fe/S clusters in respiratory complex I, a key enzyme in the respiratory electron transport chain, is described. The broken-symmetry states of the Fe/S metal clusters calculated at both DFT and semi-empirical ZINDO levels were utilized to examine both the extremely weak electronic couplings between Fe/S clusters and the tunneling pathways, which provide a detailed atomistic-level description of the charge transfer process in the protein. One-electron tunneling approximation was found to hold within a reasonable accuracy, with only a moderate induced polarization of the core electrons. The method is demonstrated to be able to calculate accurately the coupling matrix elements as small as 10 −4 cm −1. A distinct signature of the wave properties of electrons is observed as quantum interferences of multiple tunneling pathways.

Quantum electron tunneling in respiratory complex I.

We have simulated the atomistic details of electronic wiring of all Fe/S clusters in complex I, a key enzyme in the respiratory electron transport chain. The tunneling current theory of many-electron systems is applied to the broken-symmetry (BS) states of the protein at the ZINDO level. While the one-electron tunneling approximation is found to hold in electron tunneling between the antiferromagnetic binuclear and tetranuclear Fe/S clusters without major orbital or spin rearrangement of the core electrons, induced polarization of the core electrons contributes significantly to decrease the electron transfer rates to 19-56 %. Calculated tunneling energy is about 3 eV higher than Fermi level in the band gap of the protein, which supports that the mechanism of electron transfer is quantum mechanical tunneling, as in the rest of the electron transport chain. Resulting electron tunneling pathways consist of up to three key contributing protein residues between neighboring Fe/S clusters. A signature of the wave properties of electrons is observed as distinct quantum interferences when multiple tunneling pathways exist. In N6a-N6b, electron tunnels along different pathways depending on the involved BS states, suggesting possible fluctuations of the tunneling pathways driven by the local protein environment. The calculated distance dependence of the electron transfer rates with internal water molecules included is in good agreement with a reported phenomenological relation.

Electron tunneling pathways in respiratory complex I: The role of the internal water between the enzyme subunits

Recently, the atomistic details of the electronic wiring of seven Fe/S clusters (N3,N1b,N4,N5,N6a,N6b,N2) of respiratory complex I, along which electrons are injected into the electron transport chain, have been revealed; the tunneling pathways between the clusters and the contributing key residues were identified [1]. In this study, the sensitivity of the electron tunneling pathways to the internal water at the protein subunit boundaries is investigated by simulating tunneling pathways of N3→N1b and N6b→N2 with and without the internal water. It is found that the hydrogen bonding networks formed along the internal water provide new efficient tunneling pathways. In N3→N1b, the tunneling pathway with the internal water is drastically different with a significantly shorter (3.4Å) total tunneling distance along the trajectory. In N6b→N2, the internal water contributes to the tunneling as a bridge between N6b and 9Ile99 with two shorter through-space jumps instead of one longer jump. The resulting enhancement of the rates of the individual electron tunneling process is two to three orders of magnitude. This study demonstrates that the tunneling pathways and tunneling rates are sensitive to the internal water, suggesting that the tunneling pathways change dynamically due to the water diffusion and the efficient electron tunneling occurs at the optimal positions of the internal water molecules.

Pathway analysis of super-exchange electronic couplings in electron transfer reactions using a multi-configuration self-consistent field method

We present a novel pathway analysis of super-exchange electronic couplings in electron transfer reactions using localized molecular orbitals from multi-configuration self-consistent field (MCSCF) calculations. In our analysis, the electronic coupling and the tunneling pathways can be calculated in terms of the configuration interaction (CI) Hamiltonian matrix obtained from the localized MCSCF wave function. Making use of the occupation restricted multiple active spaces (ORMAS) method can effectively produce the donor, acceptor, and intermediate configuration state functions (CSFs) and CIs among these CSFs. In order to express the electronic coupling as a sum of individual tunneling pathways contributions, we employed two perturbative methods: Löwdin projection-iteration method and higher-order super-exchange method. We applied them to anion couplings of butane-1,4-diyl and pentane-1,5-diyl. The results were (1) the electronic couplings calculated from the two perturbative methods were in reasonable agreement with those from a non-perturbative method (one-half value of the energy difference between the ground and first excited states), (2) the main tunneling pathways consisted of a small number of lower-order super-exchange pathways where bonding, anti-bonding, or extra-valence-shell orbitals were used once or twice, and (3) the interference among a huge number of higher-order super-exchange pathways significantly contributed to the overall electronic coupling, whereas each of them contributed only fractionally. Our method can adequately take into account both effects of non-dynamical electron correlation and orbital relaxation. Comparing with the analyses based on the Koopmans' theorem (ignoring both effects) and the ORMAS-CIs from frozen localized reference orbitals (ignoring the effect of orbital relaxation), we discuss these effects.

Coherence in electron transfer pathways

Central to the view of electron-transfer reactions is the idea that nuclear motion generates a transition state geometry at which the electron/hole amplitude propagates coherently from the electron donor to the electron acceptor. In the weakly coupled or nonadiabatic regime, the electron amplitude tunnels through an electronic barrier between the donor and acceptor. The structure of the barrier is determined by the covalent and noncovalent interactions of the bridge. Because the tunneling barrier depends on the nuclear coordinates of the reactants (and on the surrounding medium), the tunneling barrier is highly anisotropic, and it is useful to identify particular routes, or pathways, along which the transmission amplitude propagates. Moreover, when more than one such pathway exists, and the paths give rise to comparable transmission amplitude magnitudes, one may expect to observe quantum interferences among pathways if the propagation remains coherent. Given that the effective tunneling barrier height and width are affected by the nuclear positions, the modulation of the nuclear coordinates will lead to a modulation of the tunneling barrier and hence of the electron flow. For long distance electron transfer in biological and biomimetic systems, nuclear fluctuations, arising from flexible protein moieties and mobile water bridges, can become quite significant. We discuss experimental and theoretical results that explore the quantum interferences among coupling pathways in electron-transfer kinetics; we emphasize recent data and theories associated with the signatures of chirality and inelastic processes, which are manifested in the tunneling pathway coherence (or absence of coherence).

Electron tunneling in respiratory complex I

NADH:ubiquinone oxidoreductase (complex I) plays a central role in the respiratory electron transport chain by coupling the transfer of electrons from NADH to ubiquinone to the creation of the proton gradient across the membrane necessary for ATP synthesis. Here the atomistic details of electronic wiring of all Fe/S clusters in complex I are revealed by using the tunneling current theory and computer simulations; both density functional theory and semiempirical electronic structure methods were used to examine antiferromagnetically coupled spin states and corresponding tunneling wave functions. Distinct electron tunneling pathways between neighboring Fe/S clusters are identified; the pathways primarily consist of two cysteine ligands and one additional key residue. Internal water between protein subunits is identified as an essential mediator enhancing the overall electron transfer rate by almost three orders of magnitude to achieve a physiologically significant value. The identified key residues are further characterized by sensitivity of electron transfer rates to their mutations, examined in simulations, and their conservation among complex I homologues. The unusual electronic structure properties of Fe(4)S(4) clusters in complex I explain their remarkable efficiency of electron transfer.

Predicting Secondary Structural Folding Kinetics for Nucleic Acids

We report a new computational approach to the prediction of RNA secondary structure folding kinetics. In this approach, each elementary kinetic step is represented as the transformation between two secondary structures that differ by a helix. Based on the free energy landscape analysis, we identify three types of dominant pathways and the rate constants for the kinetic steps: 1), formation; 2), disruption of a helix stem; and 3), helix formation with concomitant partial melting of a competing (incompatible) helix. The third pathway, termed the tunneling pathway, is the low-barrier dominant pathway for the conversion between two incompatible helices. Comparisons with experimental data indicate that this new method is quite reliable in predicting the kinetics for RNA secondary structural folding and structural rearrangements. The approach presented here may provide a robust first step for further systematic development of a predictive theory for the folding kinetics for large RNAs.

Delocalization and electron transfer in polypeptides with different secondary structures

The polypeptide-mediated electron transfers (ET) in opposite directions are studied by analyzing the electronic structures. The electron delocalizations in polypeptides are mainly occurring from carboxyl end to amino end (direction A). The lowest unoccupied molecular orbital (LUMO) energies of the peptide subgroups decrease obviously along this direction. Accordingly, the ET in direction A would occur by the superexchange mechanism. The formation of intramolecular hydrogen bond may provide new tunneling pathway with lower energy barrier, and promotes the ET in direction A markedly. As to the ET in opposite direction, the thermally activated hopping mechanism should be adopted.