DOIT: a program to calculate thermal rate constants and mode‐specific tunneling splittings directly from quantum‐chemical calculations

In this contribution we discuss computational aspects of a recently introduced method for the calculation of proton tunneling rate constants, and tunneling splittings, which has been applied to molecules and complexes, and should apply equally well to bulk materials. The method is based on instanton theory, adapted so as to permit a direct link to the output of quantum‐chemical codes. It is implemented in the DOIT (dynamics of instanton tunneling) code, which calculates temperature‐dependent tunneling rate constants and mode‐specific tunneling splittings. As input, it uses the structure, energy, and vibrational force field of the stationary configurations along the reaction coordinate, computed by conventional quantum‐chemical programs. The method avoids the difficult problem of calculating the exact least‐action trajectory, known as the instanton path, and instead focusses on the corresponding instanton action, because it governs the dynamic properties. To approximate this action for a multidimensional system, the program starts from the one‐dimensional instanton action along the reaction coordinate, which can be obtained without difficulty. It then applies correction terms for the coupling to the other vibrational degrees of freedom, which are treated as harmonic oscillators (transverse normal modes). The couplings are assumed linear in these modes. Depending on the frequency and the character of the transverse modes, they may either decrease or increase the action, i.e., help or hinder the transfer. A number of tests have shown that the program is at least as accurate as alternative programs based on transition‐state theory with tunneling corrections, and is also much less demanding in computer time, thus allowing application to much larger systems. An outline of the instanton formalism is presented, some new developments are introduced, and special attention is paid to the connection with quantum‐chemical codes. Possible sources of error are investigated. To show the program in action, calculations are presented of tunneling rates and splittings associated with triple proton transfer in the chiral water trimer. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 787–801, 2001     

Deep nuclear resonant tunneling thermal rate constant calculations

A fast and robust time‐independent method to calculate thermal rate constants in the deep resonant tunneling regime for scattering reactions is presented. The method is based on the calculation of the cumulative reaction probability which, once integrated, gives the thermal rate constant. We tested our method with both continuous (single and double Eckart barriers) and discontinuous first derivative potentials (single and double rectangular barriers). Our results show that the presented method is robust enough to deal with extreme resonating conditions such as multiple barrier potentials. Finally, the calculation of the thermal rate constant for double Eckart potentials with several quasi‐bound states and the comparison with the time‐independent log‐derivative method are reported. An implementation of the method using the Mathematica Suite is included in the Supporting Information. © 2013 Wiley Periodicals, Inc.     

TUNNEX: An easy-to-use wentzel-kramers-brillouin (WKB) implementation to compute tunneling half-lives

Tunneling in experiments (TUNNEX) is a free open-source program with an easy-to-use graphical user interface to simplify the process of Wentzel-Kramers-Brillouin (WKB) computations. TUNNEX aims at experimental chemists with basic knowledge of computational chemistry, and it offers the computation of tunneling half-lives, visualization of data, and exporting of graphs. It also provides a helper tool for executing the zero-point vibrational energy correction along the path. The program also enables computing high-level single points along the intrinsic reaction path. TUNNEX is available at https://github.com/prs-group/TUNNEX . As the WKB approximation usually overestimates tunneling half-lives, it can be used to screen tunneling processes before proceeding with elaborate kinetic experiments or higher-level tunneling computations such as instanton theory and small curvature tunneling approaches. © 2018 Wiley Periodicals, Inc.     

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. © 2012 Wiley Periodicals, Inc.     

Electron Tunneling Rates in Respiratory Complex I Are Tuned for Efficient Energy Conversion

Respiratory complex I converts the free energy of ubiquinone reduction by NADH into a proton motive force, a redox reaction catalyzed by flavin mononucleotide(FMN) and a chain of seven iron–sulfur centers. Electron transfer rates between the centers were determined by ultrafast freeze‐quenching and analysis by EPR and UV/Vis spectroscopy. The complex rapidly oxidizes three NADH molecules. The electron‐tunneling rate between the most distant centers in the middle of the chain depends on the redox state of center N2 at the end of the chain, and is sixfold slower when N2 is reduced. The conformational changes that accompany reduction of N2 decrease the electronic coupling of the longest electron‐tunneling step. The chain of iron–sulfur centers is not just a simple electron‐conducting wire; it regulates the electron‐tunneling rate synchronizing it with conformation‐mediated proton pumping, enabling efficient energy conversion. Synchronization of rates is a principle means of enhancing the specificity of enzymatic reactions.     

Study of the electron standing wave states in scanning tunneling spectroscopy of Si(111) surface

Electron standing wave (ESW) states excited in the vacuum gap near sample surface by operating the scanning tunneling microscopy in field emission regime have been widely used to probe the local electronic properties of novel materials and structures. For accurate interpretation of the ESW states spectra, a simple numerical approach is developed based on a one‐dimensional model, and the transmission coefficient is accurately calculated using the transfer matrix method. Effects correlated with the potential distribution in the tunneling gap are discussed. By this method, main features of the experimental spectra obtained on Si(111)7 × 7 surfaces are successfully simulated. Factors affecting the spectra are discussed. Copyright © 2012 John Wiley & Sons, Ltd.     

Inside Cover: Switching the Chirality of Single Adsorbate Complexes (Angew. Chem. Int. Ed. 22/2009)

Wrong handedness? No problem! K.‐H. Ernst et al. describe in their Communication on page 4065 ff. how the chirality of single adsorbates can be switched into the opposite enantiomeric state. By using inelastically tunneling electrons from the tip of a scanning tunneling microscope in an ultra‐high vacuum, certain molecular vibrations are excited that, in turn, cause different actions such as hopping, rotation, and chirality conversion at the surface.

     

Ecoupling server: A tool to compute and analyze electronic couplings

Electron transfer processes are often studied through the evaluation and analysis of the electronic coupling (EC). Since most standard QM codes do not provide readily such a measure, additional, and user‐friendly tools to compute and analyze electronic coupling from external wave functions will be of high value. The first server to provide a friendly interface for evaluation and analysis of electronic couplings under two different approximations (FDC and GMH) is presented in this communication. Ecoupling server accepts inputs from common QM and QM/MM software and provides useful plots to understand and analyze the results easily. The web server has been implemented in CGI‐python using Apache and it is accessible at http://ecouplingserver.bsc.es . Ecoupling server is free and open to all users without login. © 2016 Wiley Periodicals, Inc.     

Particle Tunneling in the 7-Azaindole Dimer

Using a one dimensional quantum particle tunneling model, the proton and deuteron transfer lifetime was developed and computed in the 7-azaindole dimer, the results were compared with measurements by Douhal and thereby the effective barrier heights and widths extracted.     

Energy‐Level Alignment for Single‐Molecule Conductance of Extended Metal‐Atom Chains

The use of single‐molecule junctions for various functions constitutes a central goal of molecular electronics. The functional features and the efficiency of electron transport are dictated by the degree of energy‐level alignment (ELA), that is, the offset potential between the electrode Fermi level and the frontier molecular orbitals. Examples manifesting ELA are rare owing to experimental challenges and the large energy barriers of typical model compounds. In this work, single‐molecule junctions of organometallic compounds with five metal centers joined in a collinear fashion were analyzed. The single‐molecule i–V scans could be conducted in a reliable manner, and the E_FMO levels were electrochemically accessible. When the electrode Fermi level (E_F) is close to the frontier orbitals (E_FMO) of the bridging molecule, larger conductance was observed. The smaller |E_F?E_FMO| gap was also derived quantitatively, unambiguously confirming the ELA. The mechanism is described in terms of a two‐level model involving co‐tunneling and sequential tunneling processes.     

Heavy‐Atom Tunneling in Organic Reactions

In the past few years, numerous investigations have been reported on the role of heavy‐atom tunneling in the area of pericyclic reactions, π‐bond‐shifting, and other processes. These studies illustrate unique strategies for the experimental detection of heavy‐atom tunneling and the increased use of calculations to predict it. This Minireview focuses primarily on carbon tunneling in ground‐state processes but also highlights nitrogen tunneling and the first example of excited‐state heavy‐atom tunneling. Salient features of these reactions along with potential limitations are discussed, as well as challenges and directions for future investigation.     

Electron Transfer around a Molecular Corner

The distance dependence of electron transfer (ET) is commonly investigated in linear rigid rod‐like compounds, but studies of molecular wires with integrated corners imposing 90° angles are very rare. By using spirobifluorene as a key bridging element and by substituting it at different positions, two isomeric series of donor‐bridge‐acceptor compounds with either nearly linear or angled geometries were obtained. Photoinduced ET in both series is dominated by rapid through‐bond hole hopping across oligofluorene bridges over distances of up to 70 Å. Despite considerable conformational flexibility, direct through‐space and through‐solvent ET is negligible even in the angled series. The independence of the ET rate constant on the total number of fluorene units in the angled series is attributed to a rate‐limiting tunneling step through the spirobifluorene corner. This finding is relevant for multidimensional ET systems and grids in which individual molecular wires are interlinked at 90° angles.     

Quantum tunneling in a periodically driven double well system: Entangled trajectory molecular dynamics method

We study a wavepacket tunneling in one‐dimensional periodically driven double‐well system using entangled trajectory molecular dynamics method. The tunneling dynamics dependents on the amplitude and frequency of the driven force are present. Both resonant and nonresonant tunneling process are enhanced by the driven force when the system is chaotic under classical dynamics. We give entangled trajectory in phase space compared to corresponding classical trajectory with same initial state to visually show quantum tunneling process. The average values of quantum tunneling probability after long time evolution have been shown in the parameter spaces, the effect of resonance and chaos on the tunneling dynamics are present. The relation between chaos and the uncertainly product is discussed in the end. © 2016 Wiley Periodicals, Inc.     

Achieving Efficient Multichannel Conductance in Through‐Space Conjugated Single‐Molecule Parallel Circuits

Constructing single‐molecule parallel circuits with multiple conduction channels is an effective strategy to improve the conductance of a single molecular junction, but rarely reported. We present a novel through‐space conjugated single‐molecule parallel circuit (f‐4Ph‐4SMe) comprised of a pair of closely parallelly aligned p‐quaterphenyl chains tethered by a vinyl bridge and end‐capped with four SMe anchoring groups. Scanning‐tunneling‐microscopy‐based break junction (STM‐BJ) and transmission calculations demonstrate that f‐4Ph‐4SMe holds multiple conductance states owing to different contact configurations. When four SMe groups are in contact with two electrodes at the same time, the through‐bond and through‐space conduction channels work synergistically, resulting in a conductance much larger than those of analogous molecules with two SMe groups or the sum of two p‐quaterphenyl chains. The system is an ideal model for understanding electron transport through parallel π‐stacked molecular systems and may serve as a key component for integrated molecular circuits with controllable conductance.     

Vibrational stimulation of the coherent tunneling transition in the cyclopentanone molecule

The tunneling interconversion of the cyclopentanone molecule, which leads to the appearance of tunneling doublets in the microwave spectrum of the system, is studied. The dynamics of interconversion is described by two generalized coordinates, one of which corresponds to bending (non-tunneling promoting mode), while the other of which corresponds to twisting of the molecular plane (tunneling coordinate). The coupling between two coordinates is symmetric. A method for quasi-classical calculation of the wave functions in the tunneling region and of the tunneling splittings of the vibrationally excited states in a two-dimensional potential with symmetric coupling is proposed. The tunneling spectrum of cyclopentanone is calculated. It agrees well with the experimental one, and the tunneling splitting increases by 140 times when the transverse quantum number goes from 0 to 6. The dynamic effect of the vibrationally assisted tunneling is shown to be due to the increase in the width of the tunneling channel with the quantum number of bending mode, as well as to the simultaneous shortening of the tunneling distance. The transition state geometry is found using the wave function at the dividing line of the potential.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2098–2105, December, 1994.This work was supported by the Russian Foundation for Basic Research (Project 94-03-08863). The authors express their gratitude to W. Miller for helpful discussions and to H. Nakamura for a preprint of their work.     

Intermolecular H···O═C bonds induced 2D self‐assembly of thiophene based diketopyrrolopyrrole derivative

Compounds with diketopyrrolopyrrole (DPP) and thiophene moieties have attracted considerable attention because of their promising charge transport properties. The molecular conformation and self‐assembly of 2,5‐dihexadecyl‐3,6‐di(thiophen‐2‐yl)‐2,5‐dihydropyrrolo[3,4‐c]pyrrole‐1,4‐dione (TDPP‐C16) molecule have been investigated by scanning tunneling microscopy and density functional theory alculation. The TDPP‐C16 molecules adsorb with their optimized S‐shaped conformation and form a zipper‐like pattern on highly oriented pyrolytic graphite surface. R and S rotated structures are observed. The nanostructure is dominated by intermolecular double hydrogen bonds between C═O of the DPP units and hydrogen atom of thiophene rings in the neighboring molecules in each row. Atomic force microscopy and density functional theory calculation also display the existence of strong intermolecular hydrogen bonding. The results provide molecular evidence for the intermolecular interactions of the surface structure, which could benefit to the design of the organic semiconducting materials and understanding of underlying principle of charge transfer process. Copyright © 2017 John Wiley & Sons, Ltd.     

Heavy‐Atom Tunneling in the Ring Opening of a Strained Cyclopropene at Very Low Temperatures

The highly strained 1H‐bicyclo[3.1.0]‐hexa‐3,5‐dien‐2‐one 1 is metastable, and rearranges to 4‐oxacyclohexa‐2,5‐dienylidene 2 in inert gas matrices (neon, argon, krypton, xenon, and nitrogen) at temperatures as low as 3 K. The kinetics for this rearrangement show pronounced matrix effects, but in a given matrix, the reaction rate is independent of temperature between 3 and 20 K. This temperature independence means that the activation energy is zero in this temperature range, indicating that the reaction proceeds through quantum mechanical tunneling from the lowest vibrational level of the reactant. At temperatures above 20 K, the rate increases, resulting in curved Arrhenius plots that are also indicative of thermally activated tunneling. These experimental findings are supported by calculations performed at the CASSCF and CASPT2 levels by using the small‐curvature tunneling (SCT) approximation.     

Tunneling spectroscopy of single electron spin

The possibility of detection of the electron spin of a single paramagnetic species (an atom, a radical, or an ion) on the surface was discussed. The analysis was based on spin chemistry laws taking into account the statistics of the spin states of both the tunneling electron and paramagnetic center. The equations for the tunneling current as a function of temperature and magnetic field strength were derived. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1732–1734, September, 1998.     

Tunneling dynamics of a double‐well oscillator: Effects of barrier fluctuation and thermal modulation

The tunneling dynamics of a particle moving in a bistable potential with fluctuating barrier is studied. For barriers fluctuating randomly in time we show by exact numerical calculation the significant effect of barrier fluctuation on the tunneling behavior of the particle. At nonzero temperatures the computed tunneling rate constant passes through a maximum when plotted against fluctuation frequency. The resonant frequency (at which the maximum appears) slowly decreases with increase in temperature and attains a constant value at higher temperature and it increases linearly with increase in barrier height of the potential. Another important observation is that in presence of barrier fluctuation the dependence of tunneling rate constant on temperature is strongly guided by the barrier fluctuation frequency. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 280–285, 2003     

Fully adiabatic dissociative electrochemical electron transfer reactions induced by scanning tunneling microscopy

A theory of fully adiabatic dissociative electrochemical processes of the electron transfer that are induced by scanning tunneling microscopy is constructed. Adiabatic free energy surfaces are calculated and properties of their symmetry are examined under various conditions. Diagrams of kinetic regimes, which characterize possible kinetic processes, which may proceed in the system under consideration, are constructed in the space of model parameters. Dependence of activation free energy on the bias voltage, overvoltage, physical properties of a molecule, and intensity of interaction of a molecule with an electrode and the tip of the scanning tunneling microscope is explored.