Gate-controlled current and inelastic electron tunneling spectrum of benzene: a self-consistent study

We use density functional theory based nonequilibrium Green's function to self-consistently study the current through the 1,4-benzenedithiol (BDT). The elastic and inelastic tunneling properties through this Au-BDT-Au molecular junction are simulated, respectively. For the elastic tunneling case, it is found that the current through the tilted molecule can be modulated effectively by the external gate field, which is perpendicular to the phenyl ring. The gate voltage amplification comes from the modulation of the interaction between the electrodes and the molecules in the junctions. For the inelastic case, the electron tunneling scattered by the molecular vibrational modes is considered within the self-consistent Born approximation scheme, and the inelastic electron tunneling spectrum is calculated.     

Theoretical studies of electron transport in thiophene dimer: effects of substituent group and heteroatom

The electron-transport properties of various substituted molecules based on the thiol-ended thiophene dimer (2Th1DT) are investigated through density functional theory (DFT) combined with nonequilibrium Green's function (NEGF) method. The current-voltage (I-V) curves of all the Au/2Th1DT/Au systems in this work display similar steplike features, while their equilibrium conductances show a large difference and some of these I-V curves are asymmetric distinctly. The results reveal the dependence of conductance on the energy level of the substituted 2Th1DT molecules. Rectification ratios are computed to examine the asymmetric properties of the I-V curves. The rectifying behavior in the 2Th1DT molecule containing the amino group close to the molecular end is more prominent than that in the other molecules. The rectifying behavior is analyzed through transmission spectra and molecular projected self-consistent Hamiltonian (MPSH) states. Slight negative differential resistance (NDR) can be observed in some of the systems. The electron-transport properties of 2Th1DT molecules containing different heteroatoms are also investigated. The results indicate that the current in heteroatom-containing molecules is larger than that in their pristine analogues, and lighter heteroatoms are more favorable than heavier heteroatoms for electron transport of the thiophene dimer.     

Understanding the inelastic electron-tunneling spectra of alkanedithiols on gold

We present results for a simulated inelastic electron-tunneling spectra (IETS) from calculations using the "gDFTB" code. The geometric and electronic structure is obtained from calculations using a local-basis density-functional scheme, and a nonequilibrium Green's function formalism is employed to deal with the transport aspects of the problem. The calculated spectrum of octanedithiol on gold(111) shows good agreement with experimental results and suggests further details in the assignment of such spectra. We show that some low-energy peaks, unassigned in the experimental spectrum, occur in a region where a number of molecular modes are predicted to be active, suggesting that these modes are the cause of the peaks rather than a matrix signal, as previously postulated. The simulations also reveal the qualitative nature of the processes dominating IETS. It is highly sensitive only to the vibrational motions that occur in the regions of the molecule where there is electron density in the low-voltage conduction channel. This result is illustrated with an examination of the predicted variation of IETS with binding site and alkane chain length.     

A theoretical study of molecular conduction. III. A nonequilibrium-Green's-function-based Hartree-Fock approach

Many recent experimental and theoretical studies have paid attention to the conductivity of single molecule transport junctions, both because it is fundamentally important and because of its significance in the development of molecular-based electronics. In this paper, we discuss a nonequilibrium Green's function (NEGF)-based Hartree-Fock (HF) approach; the NEGF method can appropriately accommodate charge distributions in molecules connected to electrodes. In addition, we show that a NEGF-based density matrix can reduce to an ordinary HF density matrix for an isolated molecule if the molecule does not interact with electrodes. This feature of the NEGF-based density matrix also means that NEGF-based Mulliken charges can be reduced to ordinary Mulliken charges in those cases. Therefore, the NEGF-based HF approach can directly compare molecules that are connected to electrodes with isolated ones, and is useful in investigating complicated features of molecular conduction. We also calculated the transmission probability and conduction for benzenedithiol under finite electrode biases. The coupling between the electrodes and molecule causes electron transfer from the molecule to the electrodes, and the applied bias modifies this electron transfer. In addition, we found that the molecule responds capacitively to the applied bias, by shifting the molecular orbital energies.     

Carbon nanotube, graphene, nanowire, and molecule-based electron and spin transport phenomena using the nonequilibrium Green's function method at the level of first principles theory

Based on density functional theory, we have developed a program code to investigate the electron transport characteristics for a variety of nanometer scaled devices in the presence of an external bias voltage. We employed basis sets comprised of linear combinations of numerical type atomic orbitals, particularly focusing on k-point sampling for the realistic modeling of the bulk electrode. The scheme coupled with the matrix version of the nonequilibrium Green's function method enables calculation of the transmission coefficients at a given energy and voltage in a self-consistent manner as well as the corresponding current-voltage (I-V) characteristics. This scheme has advantages because it is applicable to large systems, easily transportable to different types of quantum chemistry packages, and extendable to time-dependent phenomena or inelastic scatterings. It has been applied to diverse types of practical electronic devices such as carbon nanotubes, graphene nanoribbons, metallic nanowires, and molecular electronic devices. The quantum conductance phenomena for systems involving quantum point contacts and I-V curves for a single molecule in contact with metal electrodes using the k-point sampling method are described.     

Linear optical response of current-carrying molecular junction: a nonequilibrium Green's function-time-dependent density functional theory approach

We propose a scheme for calculation of linear optical response of current-carrying molecular junctions for the case when electronic tunneling through the junction is much faster than characteristic time of external laser field. We discuss relationships between nonequilibrium Green's function (NEGF) and time-dependent density functional theory (TDDFT) approaches and derive expressions for optical response and linear polarizability within NEGF-TDDFT scheme. Corresponding results for isolated molecule, derived within TDDFT approach previously, are reproduced when coupling to contacts is neglected.     

Conduction modulation of π-stacked ethylbenzene wires on Si(100) with substituent groups

For the realization of molecular electronics, one essential goal is the ability to systematically fabricate molecular functional components in a well-controlled manner. Experimental techniques have been developed such that π-stacked ethylbenzene molecules can now be routinely induced to self-assemble on an H-terminated Si(100) surface at precise locations and along precise directions. Electron transport calculations predict that such molecular wires could indeed carry an electrical current, but the Si substrate may play a considerable role as a competing pathway for conducting electrons. In this work, we investigate the effect of placing substituent groups of varying electron donating or withdrawing strengths on the ethylbenzene molecules to determine how they would affect the transport properties of such molecular wires. The systems consist of a line of π-stacked ethylbenzene molecules covalently bonded to a Si substrate. The ethylbenzene line is bridging two Al electrodes to model current through the molecular stack. For our transport calculations, we employ a first-principles technique where density functional theory (DFT) is used within the non-equilibrium Green’s function formalism (NEGF). The calculated density of states suggest that substituent groups are an effective way to shift molecular states relative to the electronic states associated with the Si substrate. The electron transmission spectra obtained from the NEGF–DFT calculations reveal that the transport properties could also be extensively modulated by changing substituent groups. For certain molecules, it is possible to have a transmission peak at the Fermi level of the electrodes, corresponding to high conduction through the molecular wire with essentially no leakage into the Si substrate.     

Parallel implementation of efficient charge–charge interaction evaluation scheme in periodic divide‐and‐conquer density‐functional tight‐binding calculations

A low‐computational‐cost algorithm and its parallel implementation for periodic divide‐and‐conquer density‐functional tight‐binding (DC‐DFTB) calculations are presented. The developed algorithm enables rapid computation of the interaction between atomic partial charges, which is the bottleneck for applications to large systems, by means of multipole‐ and interpolation‐based approaches for long‐ and short‐range contributions. The numerical errors of energy and forces with respect to the conventional Ewald‐based technique can be under the control of the multipole expansion order, level of unit cell replication, and interpolation grid size. The parallel performance of four different evaluation schemes combining previous approaches and the proposed one are assessed using test calculations of a cubic water box on the K computer. The largest benchmark system consisted of 3,295,500 atoms. DC‐DFTB energy and forces for this system were obtained in only a few minutes when the proposed algorithm was activated and parallelized over 16,000 nodes in the K computer. The high performance using a single node workstation was also confirmed. In addition to liquid water systems, the feasibility of the present method was examined by testing solid systems such as diamond form of carbon, face‐centered cubic form of copper, and rock salt form of sodium chloride. © 2017 Wiley Periodicals, Inc.     

Can the transition from tunneling to hopping in molecular junctions be predicted by theoretical calculation?

The electron transport mechanism changes from tunneling to hopping as molecular length increases. To validate the theoretical simulation after the transition point and clarify influence of electronic structures on the transition, we calculated the conductance of a series of conjugated molecules by density functional theory together with the nonequilibrium Green's function. We found that the highest occupied molecular orbital energy level, transmission spectrum, and the reorganization energy are good indicators for the transition of the electron transport mechanism. The calculated resistances of short junctions (<50 Å, before the transition point) are consistent with the experimental result, following the tunneling mechanism. However, the theoretical predication failed for long molecules, indicating the limitation of the theoretical framework of elastic scattering when the electron transport mechanism changes to hopping. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Development of Divide‐and‐Conquer Density‐Functional Tight‐Binding Method for Theoretical Research on Li‐Ion Battery

The density‐functional tight‐binding (DFTB) method is one of the useful quantum chemical methods, which provides a good balance between accuracy and computational efficiency. In this account, we reviewed the basis of the DFTB method, the linear‐scaling divide‐and‐conquer (DC) technique, as well as the parameterization process. We also provide some refinement, modifications, and extension of the existing parameters that can be applicable for lithium‐ion battery systems. The diffusion constants of common electrolyte molecules and LiTFSA salt in solution have been estimated using DC‐DFTB molecular dynamics simulation with our new parameters. The resulting diffusion constants have good agreement to the experimental diffusion constants.     

Stability analysis of multiple nonequilibrium fixed points in self-consistent electron transport calculations

We present a method to perform stability analysis of nonequilibrium fixed points appearing in self-consistent electron transport calculations. The nonequilibrium fixed points are given by the self-consistent solution of stationary, nonlinear kinetic equation for single-particle density matrix. We obtain the stability matrix by linearizing the kinetic equation around the fixed points and analyze the real part of its spectrum to assess the asymptotic time behavior of the fixed points. We derive expressions for the stability matrices within Hartree-Fock and linear response adiabatic time-dependent density functional theory. The stability analysis of multiple fixed points is performed within the nonequilibrium Hartree-Fock approximation for the electron transport through a molecule with a spin-degenerate single level with local Coulomb interaction.     

Self-interaction and strong correlation in DFTB

The density functional based tight-binding (DFTB) method can benefit substantially from a number of developments in density functional theory (DFT) while also providing a simple analytical proving ground for new extensions. This contribution begins by demonstrating the variational nature of charge-self-consistent DFTB (SCC-DFTB), proving the presence of a defined ground-state in this class of methods. Because the ground state of the SCC-DFTB method itself can be qualitatively incorrect for some systems, suitable forms of the recent LDA+U functionals for SCC-DFTB are also presented. This leads to both a new semilocal self-interaction correction scheme and a new physical argument for the choice of parameters in the LDA+U method. The locality of these corrections can only partly repair the HOMO-LUMO gap and chemical potential discontinuity, hence a novel method for introducing this further physics into the method is also presented, leading to exact derivative discontinuities in this theory at low computational cost. The prototypical system NiO is used as an illustration for these developments.     

Inelastic electron tunneling spectroscopy by STM of phonons at solid surfaces and interfaces

Inelastic electron tunneling spectroscopy (IETS) combined with scanning tunneling microscopy (STM) allows the acquisition of vibrational signals at surfaces. In STM-IETS, a tunneling electron may excite a vibration, and opens an inelastic channel in parallel with the elastic one, giving rise to a change in conductivity of the STM junction. Until recently, the application of STM-IETS was limited to the localized vibrations of single atoms and molecules adsorbed on surfaces. The theory of the STM-IETS spectrum in such cases has been established. For the collective lattice dynamics, i.e., phonons, however, features of STM-IETS spectrum have not been understood well, though in principle STM-IETS should also be capable of detecting phonons. In this review, we present STM-IETS investigations for surface and interface phonons and provide a theoretical analysis. We take surface phonons on Cu(1?1?0) and interfacial phonons relevant to graphene on SiC substrate as illustrative examples. In the former, we provide a theoretical formalism about the inelastic phonon excitations by tunneling electrons based on the nonequilibrium Green’s function (NEGF) technique applied to a model Hamiltonian constructed in momentum space for both electrons and phonons. In the latter case, we discuss the experimentally observed spatial dependence of the STM-IETS spectrum and link it to local excitations of interfacial phonons based on ab-initio STM-IETS simulation.     

Identification of the atomic scale structures of the gold-thiol interfaces of molecular nanowires by inelastic tunneling spectroscopy

We examine theoretically the effects of the bonding geometries at the gold-thiol interfaces on the inelastic tunneling spectra of propanedithiolate (PDT) molecules bridging gold electrodes and show that inelastic tunneling spectroscopy combined with theory can be used to determine these bonding geometries experimentally. With the help of density functional theory, we calculate the relaxed geometries and vibrational modes of extended molecules each consisting of one or two PDT molecules connecting two gold nanoclusters. We formulate a perturbative theory of inelastic tunneling through molecules bridging metal contacts in terms of elastic transmission amplitudes, and use this theory to calculate the inelastic tunneling spectra of the gold-PDT-gold extended molecules. We consider PDT molecules with both trans and gauche conformations bound to the gold clusters at top, bridge, and hollow bonding sites. Comparing our results with the experimental data of Hihath et al. [Nano Lett. 8, 1673 (2008)], we identify the most frequently realized conformation in the experiment as that of trans molecules top-site bonded to both electrodes. We find the switching from the 42 meV vibrational mode to the 46 meV mode observed in the experiment to be due to the transition of trans molecules from mixed top-bridge to pure top-site bonding geometries. Our results also indicate that gauche molecular conformations and hollow site bonding did not contribute significantly to the experimental inelastic tunneling spectra. For pairs of PDT molecules connecting the gold electrodes in parallel we find total elastic conductances close to twice those of single molecules bridging the contacts with similar bonding conformations and small splittings of the vibrational mode energies for the modes that are the most sensitive to the molecule-electrode bonding geometries.     

Rapid and accurate assessment of GPCR–ligand interactions Using the fragment molecular orbital‐based density‐functional tight‐binding method

The reliable and precise evaluation of receptor–ligand interactions and pair‐interaction energy is an essential element of rational drug design. While quantum mechanical (QM) methods have been a promising means by which to achieve this, traditional QM is not applicable for large biological systems due to its high computational cost. Here, the fragment molecular orbital (FMO) method has been used to accelerate QM calculations, and by combining FMO with the density‐functional tight‐binding (DFTB) method we are able to decrease computational cost 1000 times, achieving results in seconds, instead of hours. We have applied FMO‐DFTB to three different GPCR–ligand systems. Our results correlate well with site directed mutagenesis data and findings presented in the published literature, demonstrating that FMO‐DFTB is a rapid and accurate means of GPCR–ligand interactions. © 2017 Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Validation of the density-functional based tight-binding approximation method for the calculation of reaction energies and other data

We investigated the performance of the approximative density functional method DFTB versus BLYP and G2 with respect to zero-point corrected reaction energies, vibrational frequencies, and geometry parameters for a set of 28 reactions and 22 representative molecules containing C, H, N, and O (DFTB--density-functional based tight-binding approximation). The DFTB reaction energies show a mean absolute deviation versus the G2 reference of 4.3 kcalmol only. The corresponding value for the vibrational frequencies amounts to 75 cm(-1) versus BLYP/cc-pVTZ. With very few exceptions bond lengths and angles are in excellent agreement with the results of higher-level methods.