Renormalization of Molecular Quasiparticle Levels at Metal-Molecule Interfaces: Trends Across Binding Regimes

When an electron or a hole is added into an orbital of an adsorbed molecule the substrate electrons will rearrange in order to screen the added charge. This results in a reduction of the electron addition/removal energies as compared to the free molecule case. In this work we use a simple model to illustrate the universal trends of this renormalization mechanism as a function of the microscopic key parameters. Insight of both fundamental and practical importance is obtained by comparing GW quasiparticle energies with Hartree-Fock and Kohn-Sham calculations. We identify two different polarization mechanisms: (i) polarization of the metal (image charge formation) and (ii) polarization of the molecule via charge transfer across the interface. The importance of (i) and (ii) is found to increase with the metal density of states at the Fermi level and metal-molecule coupling strength, respectively.Comment: 4 pages, 3 figure

Extending the random-phase approximation for electronic correlation energies: The renormalized adiabatic local density approximation

The adiabatic connection fluctuation-dissipation theorem with the random phase approximation (RPA) has recently been applied with success to obtain correlation energies of a variety of chemical and solid state systems. The main merit of this approach is the improved description of dispersive forces while chemical bond strengths and absolute correlation energies are systematically underestimated. In this work we extend the RPA by including a parameter-free renormalized version of the adiabatic local density (ALDA) exchange-correlation kernel. The renormalization consists of a (local) truncation of the ALDA kernel for wave vectors $q>2k_F$, which is found to yield excellent results for the homogeneous electron gas. In addition, the kernel significantly improves both the absolute correlation energies and atomization energies of small molecules over RPA and ALDA. The renormalization can be straightforwardly applied to other adiabatic local kernels.Comment: 5 page

Towards quantitative accuracy in first-principles transport calculations: The GW method applied to alkane/gold junctions

The calculation of electronic conductance of nano-scale junctions from first principles is a long standing problem in molecular electronics. Here we demonstrate excellent agreement with experiments for the transport properties of the gold/alkanediamine benchmark system when electron-electron interactions are described using the many-body GW approximation. The main difference from standard density functional theory (DFT) calculations is a significant reduction of the contact conductance, G_c, due an improved alignment of the molecular energy levels with the metal Fermi energy. The molecular orbitals involved in the tunneling process comprise states delocalized over the carbon backbone and states localized on the amine end groups. We find that dynamical screening effects renormalize the two types of states in qualitatively different ways when the molecule is inserted in the junction. Consequently, the GW transport results cannot be mimicked by DFT calculations employing a simple scissors operator.Comment: 7 page

Dynamical Image Charge Effect in Molecular Tunnel Junctions: Beyond Energy Level Alignment

When an electron tunnels between two metal contacts it temporarily induces an image charge (IC) in the electrodes which acts back on the tunneling electron. It is usually assumed that the IC forms instantaneously such that a static model for the image potential applies. Here we investigate how the finite IC formation time affects charge transport through a molecule suspended between two electrodes. For a single level model, an analytical treatment shows that the conductance is suppressed by a factor $Z^2$ (compared to the static IC approximation) where $Z$ is the quasiparticle renormalization factor. We show that $Z$ can be expressed either in terms of the plasma frequency of the electrode or as the overlap between the ground states of the electrode with and without an electron on the molecule. First-principles GW calculations for benzene-diamine connected to gold electrodes show that the dynamical corrections can reduce the conductance by more than a factor of two.Comment: 5 pages, 3 figure

Static correlation beyond the random phase approximation: Dissociating H2 with the Bethe-Salpeter equation and time-dependent GW

We investigate various approximations to the correlation energy of a H$_2$ molecule in the dissociation limit, where the ground state is poorly described by a single Slater determinant. The correlation energies are derived from the density response function and it is shown that response functions derived from Hedin's equations (Random Phase Approximation (RPA), Time-dependent Hartree-Fock (TDHF), Bethe-Salpeter equation (BSE), and Time-Dependent GW (TDGW)) all reproduce the correct dissociation limit. We also show that the BSE improves the correlation energies obtained within RPA and TDHF significantly for intermediate binding distances. A Hubbard model for the dimer allow us to obtain exact analytical results for the various approximations, which is readily compared with the exact diagonalization of the model. Moreover, the model is shown to reproduce all the qualitative results from the \textit{ab initio} calculations and confirms that BSE greatly improves the RPA and TDHF results despite the fact that the BSE excitation spectrum breaks down in the dissociation limit. In contrast, Second Order Screened Exchange (SOSEX) gives a poor description of the dissociation limit, which can be attributed to the fact that it cannot be derived from an irreducible response function

Adiabatic-connection fluctuation-dissipation DFT for the structural properties of solids-the renormalized ALDA and electron gas kernels

We present calculations of the correlation energies of crystalline solids and isolated systems within the adiabatic-connection fluctuation-dissipation formulation of density-functional theory. We perform a quantitative comparison of a set of model exchange-correlation kernels originally derived for the homogeneous electron gas (HEG), including the recently-introduced renormalized adiabatic local-density approximation (rALDA) and also kernels which (a) satisfy known exact limits of the HEG, (b) carry a frequency dependence or (c) display a 1/$k^2$ divergence for small wavevectors. After generalizing the kernels to inhomogeneous systems through a reciprocal-space averaging procedure, we calculate the lattice constants and bulk moduli of a test set of 10 solids consisting of tetrahedrally-bonded semiconductors (C, Si, SiC), ionic compounds (MgO, LiCl, LiF) and metals (Al, Na, Cu, Pd). We also consider the atomization energy of the H$_2$ molecule. We compare the results calculated with different kernels to those obtained from the random-phase approximation (RPA) and to experimental measurements. We demonstrate that the model kernels correct the RPA's tendency to overestimate the magnitude of the correlation energy whilst maintaining a high-accuracy description of structural properties.Comment: 41 pages, 7 figure

Interference and k-point sampling in the supercell approach to phase-coherent transport

We present a systematic study of interference and k-point sampling effects in the supercell approach to phase-coherent electron transport. We use a representative tight-binding model to show that interference between the repeated images is a small effect compared to the error introduced by using only the Gamma-point for a supercell containing (3,3) sites in the transverse plane. An insufficient k-point sampling can introduce strong but unphysical features in the transmission function which can be traced to the presence of van Hove singularities in the lead. We present a first-principles calculation of the transmission through a Pt contact which shows that the k-point sampling is also important for realistic systems.Comment: 4 pages, 5 figures. Accepted for Phys. Rev. B (Brief Report

Four-atom period in the conductance of monatomic Al wires

We present first principles calculations based on density functional theory for the conductance of monatomic Al wires between Al(111) electrodes. In contrast to the even-odd oscillations observed in other metallic wires, the conductance of the Al wires is found to oscillate with a period of 4 atoms as the length of the wire is varied. Although local charge neutrality can account for the observed period it leads to an incorrect phase. We explain the conductance behavior using a resonant transport model based on the electronic structure of the infinite wire.Comment: 4 pages, 5 figure

Excitons in van der Waals heterostructures: The important role of dielectric screening

The existence of strongly bound excitons is one of the hallmarks of the newly discovered atomically thin semi-conductors. While it is understood that the large binding energy is mainly due to the weak dielectric screening in two dimensions (2D), a systematic investigation of the role of screening on 2D excitons is still lacking. Here we provide a critical assessment of a widely used 2D hydrogenic exciton model which assumes a dielectric function of the form {\epsilon}(q) = 1 + 2{\pi}{\alpha}q, and we develop a quasi-2D model with a much broader applicability. Within the quasi-2D picture, electrons and holes are described as in-plane point charges with a finite extension in the perpendicular direction and their interaction is screened by a dielectric function with a non-linear q-dependence which is computed ab-initio. The screened interaction is used in a generalized Mott-Wannier model to calculate exciton binding energies in both isolated and supported 2D materials. For isolated 2D materials, the quasi-2D treatment yields results almost identical to those of the strict 2D model and both are in good agreement with ab-initio many-body calculations. On the other hand, for more complex structures such as supported layers or layers embedded in a van der Waals heterostructure, the size of the exciton in reciprocal space extends well beyond the linear regime of the dielectric function and a quasi-2D description has to replace the 2D one. Our methodology has the merit of providing a seamless connection between the strict 2D limit of isolated monolayer materials and the more bulk-like screening characteristics of supported 2D materials or van der Waals heterostructures.Comment: 14 pages, 13 figure

Non-equilibrium GW approach to quantum transport in nano-scale contacts

Correlation effects within the GW approximation have been incorporated into the Keldysh non-equilibrium transport formalism. We show that GW describes the Kondo effect and the zero-temperature transport properties of the Anderson model fairly well. Combining the GW scheme with density functional theory and a Wannier function basis set, we illustrate the impact of correlations by computing the I-V characteristics of a hydrogen molecule between two Pt chains. Our results indicate that self-consistency is fundamental for the calculated currents, but that it tends to wash out satellite structures in the spectral function.Comment: 5 pages, 4 figure