Electron Transport through Single Molecules: Scattering Treatment Using Density Functional and Green Function Theories

The eigenfunction expansion of the infinite depth free surface Green function in three dimensions

ABSTRACTA new method is proposed for a fast evaluation of high-dimensional integrals of potential energy surfaces (PES) that arise in many areas of quantum dynamics. It decomposes a PES into a canonical low-rank tensor format, reducing its integral into a relatively short sum of products of low-dimensional integrals. The decomposition is achieved by the alternating least squares (ALS) algorithm, requiring only a small number of single-point energy evaluations. Therefore, it eradicates a force-constant evaluation as the hotspot of many quantum dynamics simulations and also possibly lifts the curse of dimensionality. This general method is applied to the anharmonic vibrational zero-point and transition energy calculations of molecules using the second-order diagrammatic vibrational many-body Green's function (XVH2) theory with a harmonic-approximation reference. In this application, high dimensional PES and Green's functions are both subjected to a low-rank decomposition. Evaluating the molecular integrals over a low-rank PES and Green's functions as sums of low-dimensional integrals using the Gauss–Hermite quadrature, this canonical-tensor-decomposition-based XVH2 (CT-XVH2) achieves an accuracy of 0.1 cm−1 or higher and nearly an order of magnitude speedup as compared with the original algorithm using force constants for water and formaldehyde.

We combine the recently developed many-body Green's function theory for electrons and nuclei with the exact factorization of the wave function. The existing Born-Oppenheimer Green's functions are shown to be special cases of our exact approach. We consider the limitations of the laboratory frame formulation of the Green's function theory and discuss why the body-fixed frame formulation is needed in order to go beyond the Born-Oppenheimer theory. We give exact forms of the electronic and nuclear Green's functions written in terms of the exact factorized states, providing a systematic approach beyond the Born-Oppenheimer approximation. The lowest order approximation to the exact electronic Green's function is found to be an expected value of the Born-Oppenheimer electronic Green's function with respect to the nuclear density.

Nonequilibrium superoperator Green's function theory is used to calculate the fluorescence signal of molecules induced by currents in scanning tunneling microscope junctions. The spectrum of benzene and its variation with tip position and bias are simulated at the density functional theory level. The formal analogy with laser-induced fluorescence is pointed out. Many-body effects can be accounted for through self-energies and the Keldysh Dyson equations. The sum-over-orbital expressions obtained within density functional theory may not be expressed as an amplitude square. This is due to dephasing effects induced by the many-electron excitations, which act as a bath.

Spin-dependent transport in graphene nanoribbons adsorbed with vanadium in different positions

In using the spectral theorem of many-body Green's function theory in order to relate correlations to commutator Green's functions, it is necessary in the standard procedure to consider the anti-commutator Green's functions as well whenever the matrix governing the equations of motion for the commutator Green's functions has zero eigenvalues. We show that a singular-value decomposition of this matrix allows one to reformulate the problem in terms of a smaller set of Green's functions with an associated matrix having no zero eigenvalues, thus eliminating the need for the anti-commutator functions. The procedure is quite general and easy to apply. It is illustrated for the field-induced reorientation of the magnetization of a ferromagnetic Heisenberg monolayer and it is expected to work for more complicated cases as well.

ABSTRACTThe Green's function theory and high-temperature series expansions technical have been developed for magnetic systems GeNi2−xCoxO4. We have applied the Green's function theory to evaluate thermal magnetization and magnetic susceptibility for different values of magnetic field and dilution x, considering all components of the magnetization when an external magnetic field is applied in (x,z)-plane. The second theory combined with the Padé approximants method for a randomly diluted Heisenberg magnet is used to deduce the magnetic phase diagram of GeNi2 − xCoxO4 systems. The critical exponents and associated with the magnetic susceptibility and the correlation length ξ, respectively, have been deduced. The theoretical results are compared with those given by magnetic measurements.

Nuclear structure theory has recently gone through a major renewal with the development of ab initio techniques that can be applied to a large number of atomic nuclei, well beyond the light sector that had been traditionally targeted in the past. Self-consistent Green's function theory is one among these techniques. The present work aims to give an overview of the self-consistent Green's function approach for atomic nuclei, including examples of recent applications and a discussion on the perspectives for extending the method to nuclear reactions, doubly open-shell systems and heavy nuclei.

We present a scalable single-particle framework to treat electronic correlation in molecules and materials motivated by Green's function theory. We derive a size-extensive Brillouin-Wigner perturbation theory from the single-particle Green's function by introducing the Goldstone self-energy. This new ground state correlation energy, referred to as Quasi-Particle MP2 theory (QPMP2), avoids the characteristic divergences present in both second-order Møller-Plesset perturbation theory and Coupled Cluster Singles and Doubles within the strongly correlated regime. We show that the exact ground state energy and properties of the Hubbard dimer are reproduced by QPMP2 and demonstrate the advantages of the approach for larger Hubbard models where the metal-to-insulator transition is qualitatively reproduced, contrasting with the complete failure of traditional methods. We apply this formalism to characteristic strongly correlated molecular systems and show that QPMP2 provides an efficient, size-consistent regularization of MP2.

Excitonic contributions to absorption and photocurrent generation in semiconductor nanostructures are described theoretically and simulated numerically using steady-state non-equilibrium Green's function theory. In a first approach, the coherent interband polarization including Coulomb corrections is determined from a Bethe-Salpeter-type equation for the equal time interband single-particle charge carrier Green's function. The effects of excitonic absorption on photocurrent generation are considered on the same level of approximation via the derivation of the corresponding corrections to the electron-photon self-energy.

Tight gas reservoirs with matrix permeabilities in the microdarcy range sometimes contain zones of natural fractures with relatively high permeabilities. The development of these reservoirs requires great care in that it is essential to connect the wells with the natural fracture system in order to ensure economic well productivities. To assess the feasibility of developing such reservoirs, a study was undertaken to investigate the relative attractiveness of connecting a well to a vertical zone of high permeability either by a horizontal hole or by a massive hydraulic fracture (MHF). The first phase of the work assumed single-phase compressible flow and utilised Green's function theory to derive the transient pressure response in such complex situations. The results indicate that a horizontal hole draining a natural fracture zone compares well with connecting the well to the naturally fractured zone by a MHF, particularly in the case of short MHFs. The calculations also resulted in new principles for the interpretation of well tests for the two situations described above. For example, interpretation of the formation linear flow period when there are multiple fractures indicates fracture areas that are larger than the area of the MHF. The second phase involved numerical simulation, with mobile water both in the matrix and in the fracture systems taken into account. The results, which agree qualitatively with those of analytical methods, indicate under which conditions coning or cusping of water from the fractures into the well perforations might be expected.

We explore the impact of point defects, including oxygen vacancies (Ov), cerium interstitials (Ce-int), and hydroxyl groups (Hy), on the electronic and optical properties of bulk CeO2 using many-body Green's function theory (GW method and Bethe-Salpeter equation). Although these three defects all produce occupied electronic levels near the conduction band minimum, they impose quite different effects. Ov and Ce-intinduce strong peaks in the low-energy region of the imaginary part of the microscopic dielectric function, indicating stronger electronic screening compared to the pristine CeO2. This causes pronounced narrowing of the bandgap, e.g., by 0.8eV in G0W0 and 1.6eV in the eigenvalue self-consistent GW for Ov. Comparatively, Hy affects little electronic screening and bandgap at different levels of GW calculations. For the lowest several 4f orbitals, the exchange part of the self-energy (|Σx| > 9eV) in GW is much stronger than the correlation part (|Σc| < 5eV) for Ov and Ce-int, while |Σc| is much stronger than |Σx| instead for the pristine CeO2 and Hy. Quasiparticle weights in Ov and Ce-intdecrease by a large quantity compared to the pristine CeO2. Consideration of Ov and Ce-intmight to some extent relieve the discrepancy between the GW bandgap of the pristine CeO2 and the experimental gap. Ov and Ce-intcould reduce the excitonic binding energy several times and result in optical absorption, which corresponds to the experiments.

New silicon hydrogen infrared vibrational band associated to HSiCl configurations in an amorphous silicon matrix : Green's function theory approach

With the experimental advances in microscale fabrication technology, the designing of functional devices by using single molecules has become one of the most promising methods for the next generation of electronic devices. Molecular rectifier, as a basic component almost for any electronic device, has become a research hotspot in molecular electronics. Recently, one-dimensional graphene nanoribbons (GNRs) which cut off from the novel two-dimensional material-graphene were used as the electrodes for several molecular devices due to their unique electronic structures and transport characteristics. The GNRs have less serious contact problems than metallic electrode materials like gold. In this paper, we investigate the rectifying performances of oligo phenylene ethynylene molecular devices based on graphene electrodes by using the density-functional theory and the non-equilibrium Green's function method. The effect of functional group on the rectifying performances of molecular device is discussed. The results show that the functional group plays a significant role in determining the rectifying performances of oligo phenylene ethynylene molecular device. The rectifying ratio can be effectively tuned by the functional group: adding the donor group (NH2) can lead to the positive rectifying phenomenon, adding the acceptor group (NO2) can trigger the negative rectifying phenomenon, and simultaneously adding NH2 and NO2 groups can bring about an alternate phenomenon between positive and reverse rectifying . The physical mechanism of the rectifying behavior is explained based on the transmission spectra and molecular projected self-consistent Hamiltonian. The transmission spectra of four models (M1-M4) bias voltages in range from-1.0 V to 1.0 V are given. The main transmission peak of M1 for positive bias is similar to that for negative bias, resulting in a weak rectification ratio. However, for M2 and M3, the main transmission peaks for positive and negative bias are significantly different from each other, which shows obviously a rectifying behavior. For M4, the main transmission peak is higher for the bias of (0.44-0.83 V) and also for the bias (0.95-1.00 V), showing an alternate phenomenon between positive and reverse rectifying. The maximum rectification ratio reaches 2.71 by adding an acceptor group (NO2), which suggests that this system has attractive potential applications in future molecular circuit.

The solid electrolyte interphase (SEI) is a solid that forms between the anode and electrolyte in batteries. It is made up electrolyte species that have decomposed due to reduction by the anode, but its growth is self-limited as its very presence inhibits further electrolyte decomposition. The SEI is made up of numerous inorganic and organic species, and its composition and properties can vary drastically. For the proper operation of the battery, it needs to be ionically conducting while being electronically insulating. These two properties are often correlated, so it is important to understand how to decouple them to achieve desired battery performance.In this presentation, we will discuss results from our group on studying electron transport through simplified models of the SEI from first-principles atomistic modeling. Our approach uses the non-equilibrium Green's function technique in combination with density functional theory (NEGF-DFT) to calculate electron transport through SEI structures. We first applied this method to compare the electronic conductivity of single-crystal versus polycrystalline LiF, a common inorganic SEI component. The grain boundaries in polycrystalline LiF are known to be essential for Li ion transport, but they also make for leakage pathways for electrons to pass through the material. Next, we apply the same method to investigate the SEI in Ca ion batteries, with a study of electron transport through CaF2. In this study, we considered single-crystal CaF2, as well as several grain boundaries and an amorphous version of CaF2. We found the amorphous version of this SEI component to be orders of magnitude more electronically conductive than the crystalline counterparts.Finally, we used ab initio molecular dynamics (AIMD) to contrast the reductive decomposition of two electrolyte solvents: tetrahydrofuran (THF) and ethylene carbonate (EC) at a Ca anode. The former does not decompose in the timescales of our simulations (ca. 50 ps), while the latter undergoes rapid decomposition. We extracted structural atomistic snapshots from our AIMD trajectories and fed them through the NEGF-DFT code to obtain time-dependent electron transport for the THF and EC solvents near the Ca anode, while decompositions are occurring in the EC system. While THF is more conductive than EC, its conductivity has relatively small variation in time. EC has drastic fluctuations in its conductivity, part of which can be attributed to individual molecular decomposition events, which may be useful to develop diagnostic or characterization techniques.The SEI plays an essential role in maintaining long-term battery stability. Understanding how electron transport occurs through this battery component will help develop SEIs with desired properties for ultimate performance in both Li-ion batteries and beyond Li-ion batteries such as Ca ion and other multivalent systems.