A theoretical study of molecular conduction. II. A Hartree-Fock approach to transmission probability

In this paper, we discuss molecular conductivity based on Green's function methods. In our calculations, we adopted the self-energy formalism to accommodate semi-infinite electrodes connected to a molecule, and the self-energy was obtained from the surface Green's function of the electrodes. We adopted the formalism of the surface Green's function derived by Sanvito et al. [Phys. Rev. B 59, 11936 (1999)] and Krstic et al. [Phys. Rev. B 66, 205319 (2002)], and although their formalisms for the surface Green's function were different, we were able to demonstrate that these formalisms are mathematically identical. We analyzed the electron transmission probability by using the spectrum expression of Green's function, instead of using the inverse matrix of the effective Hamiltonian that includes an isolated molecule and the electrodes. Finally, we calculated the transmission probability of benzenedithiol based on the Hartree-Fock method and analyzed the disappearance of the transmission probability due to the orbital interference.     

Effect of bond-length alternation in molecular wires

Current-voltage (I-V) characteristics for metal-molecule-metal junctions formed from three classes of molecules measured with a simple crossed-wire molecular electronics test-bed are reported. Junction conductance as a function of molecular structure is consistent with I-V characteristics calculated from extended Hückel theory coupled with a Green's function approach, and can be understood on the basis of bond-length alternation.     

Self-consistent solution of the Dyson equation for atoms and molecules within a conserving approximation

We have calculated the self-consistent Green's function for a number of atoms and diatomic molecules. This Green's function is obtained from a conserving self-energy approximation, which implies that the observables calculated from the Green's functions agree with the macroscopic conservation laws for particle number, momentum, and energy. As a further consequence, the kinetic and potential energies agree with the virial theorem, and the many possible methods for calculating the total energy all give the same result. In these calculations we use the finite temperature formalism and calculate the Green's function on the imaginary time axis. This allows for a simple extension to nonequilibrium systems. We have compared the energies from self-consistent Green's functions to those of nonselfconsistent schemes and also calculated ionization potentials from the Green's functions by using the extended Koopmans' theorem.     

GW方法: 基本原理, 最新进展及其在d-和f-电子体系中的应用

基于格林函数的多体微扰理论提供了描述材料基态和激发态性质的一个严格理论框架. 格林函数依赖于交换关联自能, 后者满足一组复杂的被称为Hedin方程的积分微分方程. GW方法是由对自能算符根据屏蔽库仑作用做多体微扰理论展开到第一项得到, 是目前描述扩展体系准粒子电子激发性质最为准确的第一原理方法. 本文概述了GW方法的基本原理, 并对最新的理论方法进展在一个统一的框架下进行了评述. 最后, 通过对若干典型实例的分析展示了针对d/f-电子体系的GW方法的现状.     

Nonequilibrium superoperator GW equations

Hedin's equations [Phys. Rev. 139, 796 (1965)] for the one-particle equilibrium Green's function of a many-electron system are generalized to nonequilibrium open systems using two fields that separately control the evolution of the bra and the ket of the density matrix. A closed hierarchy is derived for the Green's function, the self-energy, the screened potential, the polarization, and the vertex function, all expressed as Keldysh matrices in Liouville space.     

Thermoelectrics in an array of molecular junctions

The room temperature thermoelectric properties of a three-dimensional array of molecular junctions are calculated. The array is composed of n-doped silicon nanoparticles where the surfaces are partially covered with polar molecules and the nanoparticles are bridged by trans-polyacetylene molecules. The role of the polar molecules is to reduce the band bending in the n-doped silicon nanoparticles and to shift the electronic resonances of the bridging molecules to the nanoparticle conduction band edges where the molecular resonances act as electron energy filters. The transmission coefficients of the bridging molecules that appear in the formulas for the Seebeck coefficient, the electrical conductance, and the electronic thermal conductance, are calculated using the nonequilibrium Green's function technique. A simple tight-binding Hamiltonian is used to describe the bridging molecules, and the self-energy term is calculated using the parabolic conduction band approximation. The dependencies of the thermoelectric properties of the molecular junctions on the silicon doping concentration and on the molecule-nanoparticle coupling are discussed. The maximal achievable thermoelectric figure of merit ZT of the array is estimated as a function of the phononic thermal conductance of the bridging molecules and the doping of the nanoparticles. The power factor of the array is also calculated. For sufficiently small phononic thermal conductances of the bridging molecules, very high ZT values are predicted.     

Switching mechanism of photochromic diarylethene derivatives molecular junctions

The electronic transport properties and switching mechanism of single photochromic diarylethene derivatives sandwiched between two gold surfaces with closed and open configurations are investigated by a fully self-consistent nonequilibrium Green's function method combined with density functional theory. The calculated transmission spectra of two configurations are strikingly distinctive. The open form lacks any significant transmission peak within a wide energy window, while the closed structure has two significant transmission peaks on both sides of the Fermi level. The electronic transport properties of the molecular junction with closed structure under a small bias voltage are mainly determined by the tail of the transmission peak contributed unusually by the perturbed lowest perturbed unoccupied molecular orbital. The calculated on-off ratio of currents between the closed and open configurations is about two orders of magnitude, which reproduces the essential features of the experimental measured results. Moreover, we find that the switching behavior within a wide bias voltage window is extremely robust to both substituting F or S for H or O and varying end anchoring atoms from S to Se and Te.     

Observation and assignment of phonon combination bands in the far infrared dielectric response of GaAs

A determination by dispersive Fourier transform spectroscopy of the frequency dependence of the anharmonic self-energy of the q??O transverse optic phonon in GaAs at 300 and 6 K is presented. The measured self-energy function is compared with the two-phonon density of states function calculated from an 11-parameter rigid ion model, and the model is found to account satisfactorily for all features in the measured spectrum as phonon combination bands.     

Theoretical investigation of electron transport modulation through benzenedithiol by substituent groups

Density functional theory combined with nonequilibrium Green's function techniques was used to model the conduction through disubstituted benzenedithiol molecules bonded to leads composed of 3x3, 5x5 gold and 3x3 aluminum. For the disubstituted 3x3 Au-benzenedithiol-Au systems, the small lead cross section results in a region of nearly zero transmission from -0.4 to -0.2 eV, relative to E(F), due to the absence of lead states. This feature results in negative differential resistance in the current-voltage curves and also causes the main peaks in the transmission spectra, which are dominated by the highest occupied molecular orbitals, to be centered near E(F). The zero-bias transmissions for the disubstituted benzenedithiol, as well as currents at applied biases, correlate very well with the Hammett parameter sigma(p), a quantity that relates the electron donating or withdrawing strength of a substituent. Calculations on disubstituted benzenedithiol connected to 5x5 Au leads produced transmission spectra that showed no gaps over the energy range considered and no negative differential resistance. The transmission in these cases also predominately involves the highest occupied molecular orbitals, and electron donating and withdrawing groups are able to increase and decrease current, respectively. However, there is no strong correlation between current and sigma(p) for this system. This suggests that the correlation observed in the 3x3 Au systems arises from the abrupt cutoff of the main transmission peaks near E(F). The disubstituted 3x3 Al-benzenedithiol-Al systems displayed markedly different behavior from the Au analogs. Electron donating groups and H benzenedithiol-substituted systems display almost no transmission over the energy range considered. However, electron withdrawing group disubstituted benzenedithiol systems had significant peaks in the transmission spectra near E(F), which are associated with the lowest-energy, unoccupied pi-type molecular orbitals. Higher currents are calculated for cases where the substituents have pi-type orbitals that are conjugated with the ring moiety of benzenedithiol. In all cases, the current through the 3x3 Al-benzenedithiol-Al systems is about a factor of 2 less than that through the analogous Au systems. These simulations reveal that the electrical conductance behavior through nanosystems of the type investigated in this work depends on the nature of the molecule as well as the size and composition of the leads to which it is connected. The results suggest that rational design of nanoelectronic systems might be possible under certain conditions but that structure-function relationships cannot be transferred from one system to another.     

METHOD OF INTEGRATED GREEN''''S FUNCTION FOR THE CALCULATION OF TILT LOAD TIDE CAUSED BY THE OCEANIC TIDES

The method of integrated Green's function for the calculation of the tilt(?)load tide proposed by this paper is sn improvement and s development of the current widely used method proposed by Farrell, and it is s new method of calculation. According to this method, the integrated Green's function of tilt load tide has been calculated first, then on the basis of the cotidal charts the tilt load tide caused by the oceanic tides at any point on the continent can be easily calculated through algebraic procedures. As an example of application of this method the tilt load tides of M_2 have been calculated on the basis of cotidal charts of Schwiderski for the following three stations: Wuchang, Tai'an and Xuzhou.     

Ab initio electron propagator calculations on the ionization energies of free base porphine, magnesium porphyrin, and zinc porphyrin

Ab initio electron propagator methods are applied to the prediction, assignment, and interpretation of the valence photoelectron spectra of free base porphine and of magnesium and zinc porphyrins. Tests of various approximate self-energies, including the partial third (P3), the outer valence Green's function, and the nondiagonal, renormalized second-order (NR2) methods are performed. Basis set effects and reduced active orbital spaces are examined as well. The P3 method and the one-electron picture of ionization that accompanies it are validated for the first two cationic states and for states with sigma holes that are localized in nitrogen, lone pair regions. In the remaining pi-hole states, there is significant shake-up character and NR2 results provide useful diagnostics of correlation effects.     

Optical properties of current carrying molecular wires

We consider several fundamental optical phenomena involving single molecules in biased metal-molecule-metal junctions. The molecule is represented by its highest occupied and lowest unoccupied molecular orbitals, and the analysis involves the simultaneous consideration of three coupled fluxes: the electronic current through the molecule, energy flow between the molecule and electron-hole excitations in the leads, and the incident and/or emitted photon flux. Using a unified theoretical approach based on the nonequilibrium Green's function method we derive expressions for the absorption line shape (not an observable but a useful reference for considering yields of other optical processes) and for the current induced molecular emission in such junctions. We also consider conditions under which resonance radiation can induce electronic current in an unbiased junction. We find that current driven molecular emission and resonant light induced electronic currents in single molecule junctions can be of observable magnitude under appropriate realizable conditions. In particular, light induced current should be observed in junctions involving molecular bridges that are characterized by strong charge-transfer optical transitions. For observing current induced molecular emission we find that in addition to the familiar need to control the damping of molecular excitations into the metal substrate the phenomenon is also sensitive to the way in which the potential bias is distributed on the junction.     

Simple STM tip functionalization for rapid DNA sequencing: an Ab initio Green's function study

An ab initio nonequilibrium Green's function study of the electron-transport properties of the adenine, thymine, cytosine, and guanine DNA bases located between gold electrodes has been performed. One-electron transmission spectra were calculated for both gold and sulfur-modified gold electrodes, which are model conditions of scanning tunneling microscopy (STM) experiments with the different tips. It is shown that the nature of chemical bonding between molecules and metal electrodes plays the most significant role in the overall conductance of the systems. The distance between electrodes and the size of molecules are less important, at least when both sides of the molecule form chemical contact with the electrodes. On the basis of the obtained results, a simple two-pass DNA sequencing scheme is suggested.     

On the quantum chemical origin for the nonvalidity of Koopmans' theorem in transitionmetal compounds

The quantum chemical origin for the nonvalidity of Koopmans' theorem in transitionmetal compounds of the 3d series is analyzed by means of the Green's function formalism applied in the framework of a semiempirical INDO Hamiltonian. In the case of ferrocene (1), cyclobutadiene iron tricarbonyl (2) and irontetracarbonyl dihydride (3) the self-energy part of a geometric approximation has been partitioned into relaxation and correlation (pair removal, pair relaxation) increments. The breakdown of Koopmans' theorem for strongly localized MOs with large Fe 3d amplitudes is predominantly the result of electronic relaxation lowering the calculated ionization potentials. On the other hand the variation of the pair correlation energy in the cationic hole-state is by no means negligible and acts into the opposite direction as the relaxation increment. These significant pair relaxation contributions explain the wellknown failtures of the ΔSCF approach in combination with large scaleab initio bases. The loss of ground state pair correlation in the outer valence region is small in comparison to relaxation and pair relaxation. The magnitude of the aforementioned reorganization increments has been studied as a function of the localization properties of the MOs and as a function of the one-electron energies of the available particle- and hole-states. The computational findings derived with the INDO model are compared with recentab initio studies.     

Vertical ionization potential in hydrogen molecule with many-body Green's function method

The many-body Green's function method is applied to the vertical ionization potential of the hydrogen molecule. The ionization potential is calculated iteratively by expanding the self-energy part up to third order. The effects of higher-order correlation corrections and nondiagonal self-energy elements on the solutions of the Dyson equation are examined with some techniques and approximations, by means of which a Koopmans' defect of 97.7% of the accurate value is obtained.     

Single quintuple bond [PhCrCrPh] molecule as a possible molecular switch

The electronic transport properties of a single quintuple bond [PhCrCrPh] molecule sandwiched between two Au(111) surfaces with the trans-bent and linear configurations are studied by a fully self-consistent nonequilibrium Green's function method combined with density functional theory. The calculated transmission spectra of two chemical isomers are remarkably distinctive. Theoretical results suggest that the current through the trans-bent configuration is significantly larger than the corresponding linear one. The predicted on-off ratio of currents ranging from around 50 to 200 in the applied bias window [-1.5 V, 1.5 V] suggests that multiple bond compounds have attractive potential in molecular switch technology.     

Comparison of perturbative and multiconfigurational electron propagator methods

Ionization energies below 20 eV of 10 molecules calculated with electron propagator techniques employing Hartree-Fock orbitals and multiconfigurational self-consistent field orbitals are compared. Diagonal and nondiagonal self-energy approximations are used in the perturbative formalism. Three diagonal methods based on second- and third-order self-energy terms, all known as the outer valence Green's function, are discussed. A procedure for selecting the most reliable of these three versions for a given calculation is tested. Results with a polarized, triple ζ basis produce root mean square errors with respect to experiment of approximately 0.3 eV. Use of the selection procedure has a slight influence on the quality of the results. A related, nondiagonal method, known as ADC (3), performs infinite-order summations on several types of self-energy contributions, is complete through third-order, and produces similar accuracy. These results are compared to ionization energies calculated with the multiconfigurational spin-tensor electron propagator method. Complete active space wave functions or close approximations constitute the reference states. Simple field operators and transfer operators pertaining to the active space define the operator manifold. With the same basis sets, these methods produce ionization energies with accuracy that is comparable to that of the perturbative techniques. © 1996 John Wiley & Sons, Inc.     

First Principle Study on the Rectification of Molecular Junctions Based on the Thiol-ended Oligosilane

The electron transport properties of various molecular junctions based on the thiol-ended oligosilane are investigated through density functional theory combined with non-equilibrium Green's function formalism. Our calculations show that oligosilanes doped by the phenyl and-C10H6 groups demonstrate better rectifying effect and their rectification ratios are up to 15.41 and 65.13 for their molecular junctions. The current-voltage(I-V) curves of all the Au/ modified oligosilane/Au systems in this work are illustrated by frontier molecular orbitals, transmission spectra and density of states under zero bias. And their rectifying behaviors are analyzed through transmission spectra.