The exact density functional for the ground-state energy is strictly self-interaction-free (i.e., orbitals demonstrably do not self-interact), but many approximations to it, including the local-spin-density (LSD) approximation for exchange and correlation, are not. We present two related methods for the self-interaction correction (SIC) of any density functional for the energy; correction of the self-consistent one-electron potenial follows naturally from the variational principle. Both methods are sanctioned by the Hohenberg-Kohn theorem. Although the first method introduces an orbital-dependent single-particle potential, the second involves a local potential as in the Kohn-Sham scheme. We apply the first method to LSD and show that it properly conserves the number content of the exchange-correlation hole, while substantially improving the description of its shape. We apply this method to a number of physical problems, where the uncorrected LSD approach produces systematic errors. We find systematic improvements, qualitative as well as quantitative, from this simple correction. Benefits of SIC in atomic calculations include (i) improved values for the total energy and for the separate exchange and correlation pieces of it, (ii) accurate binding energies of negative ions, which are wrongly unstable in LSD, (iii) more accurate electron densities, (iv) orbital eigenvalues that closely approximate physical removal energies, including relaxation, and (v) correct longrange behavior of the potential and density. It appears that SIC can also remedy the LSD underestimate of the band gaps in insulators (as shown by numerical calculations for the rare-gas solids and CuCl), and the LSD overestimate of the cohesive energies of transition metals. The LSD spin splitting in atomic Ni and $s\ensuremath{-}d$ interconfigurational energies of transition elements are almost unchanged by SIC. We also discuss the admissibility of fractional occupation numbers, and present a parametrization of the electron-gas correlation energy at any density, based on the recent results of Ceperley and Alder.

Self-interaction correction to density-functional approximations for many-electron systems

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Self-assembled monolayers of thiolates on metals as a form of nanotechnology.

A scheme that reduces the calculations of ground-state properties of systems of interacting particles exactly to the solution of single-particle Hartree-type equations has obvious advantages. It is not surprising, then, that the density functional formalism, which provides a way of doing this, has received much attention in the past two decades. The quality of the energy surfaces calculated using a simple local-density approximation for exchange and correlation exceeds by far the original expectations. In this work, the authors survey the formalism and some of its applications (in particular to atoms and small molecules) and discuss the reasons for the successes and failures of the local-density approximation and some of its modifications.

The density functional formalism, its applications and prospects

Molecules of benzene-1,4-dithiol were self-assembled onto the two facing gold electrodes of a mechanically controllable break junction to form a statically stable gold-sulfur-aryl-sulfur-gold system, allowing for direct observation of charge transport through the molecules. Current-voltage measurements at room temperature demonstrated a highly reproducible apparent gap at about 0.7 volt, and the conductance-voltage curve showed two steps in both bias directions. This study provides a quantative measure of the conductance of a junction containing a single molecule, which is a fundamental step in the emerging area of molecular-scale electronics.

https://www.eng.yale.edu/reedlab/publications/83%20BDT%20Science97.pdf

Conductance of a Molecular Junction

The semiconductor industry has seen a remarkable miniaturization trend, driven by many scientific and technological innovations. But if this trend is to continue, and provide ever faster and cheaper computers, the size of microelectronic circuit components will soon need to reach the scale of atoms or molecules—a goal that will require conceptually new device structures. The idea that a few molecules, or even a single molecule, could be embedded between electrodes and perform the basic functions of digital electronics—rectification, amplification and storage—was first put forward in the mid-1970s. The concept is now realized for individual components, but the economic fabrication of complete circuits at the molecular level remains challenging because of the difficulty of connecting molecules to one another. A possible solution to this problem is ‘mono-molecular’ electronics, in which a single molecule will integrate the elementary functions and interconnections required for computation.

Electronics using hybrid-molecular and mono-molecular devices

The first part of this paper deals with the jellium model of a metal surface. The theory of the inhomogeneous electron gas, with local exchange and correlation energies, is used. Self-consistent electron density distributions are obtained. The surface energy is found to be negative for high densities (${\mathcal{r}}_{s}\ensuremath{\le}2.5$). In the second part, two corrections to the surface energy are calculated which arise when the positive background model is replaced by a pseudopotential model of the ions. One correction is a cleavage energy of a classical neutralized lattice, the other an interaction energy of the pseudopotentials with the electrons. Both of these corrections are essential at higher densities (${\mathcal{r}}_{s}\ensuremath{\le}4$). The resulting surface energy is in semiquantitative agreement with surface-tension measurements for eight simple metals (Li, Na, K, Rb, Cs, Mg, Zn, Al), typical errors being about 25%. For Pb there is a serious disagreement.

Theory of Metal Surfaces: Charge Density and Surface Energy

In a recent paper we presented a contribution to the theory of metal surfaces with emphasis on the shape of the electron-density distribution and the surface energy. The present paper extends this analysis to a consideration of the work function. Some general theoretical relationships are established. Effects of the ions are included using a simple pseudopotential theory, permitting the calculation of the variation of the work function from one crystal face to another. For simple metals (Li, Na, K, Rb, Cs, Al, Pb, Zn, and Mg), agreement with available experimental data is good (5-10%); for the noble metals, the computed work functions are 15-30% too low.

Theory of Metal Surfaces: Work Function

Recent years have shown steady progress towards molecular electronics, in which molecules form basic components such as switches, diodes and electronic mixers. Often, a scanning tunnelling microscope is used to address an individual molecule, although this arrangement does not provide long-term stability. Therefore, metal-molecule-metal links using break-junction devices have also been explored; however, it is difficult to establish unambiguously that a single molecule forms the contact. Here we show that a single hydrogen molecule can form a stable bridge between platinum electrodes. In contrast to results for organic molecules, the bridge has a nearly perfect conductance of one quantum unit, carried by a single channel. The hydrogen bridge represents a simple test system in which to understand fundamental transport properties of single-molecule devices.

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Measurement of the conductance of a hydrogen molecule.

We report first-principles calculations of the current-voltage ( $I\ensuremath{-}V$) characteristics of a molecular device and compare with experiment. We find that the shape of the $I\ensuremath{-}V$ curve is largely determined by the electronic structure of the molecule, while the presence of single atoms at the molecule-electrode interface play a key role in determining the absolute value of the current. The results show that such simulations would be useful for the design of future microelectronic devices for which the Boltzmann-equation approach is no longer applicable.

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First-Principles Calculation of Transport Properties of a Molecular Device

This paper contributes to the theory of the electron density distribution induced at a metal surface by a small static external charge distribution. As a first application, profiles of the charge induced by a uniform external electric field are obtained for metals of different bulk electron densities. A quantity of particular interest is the position of the center of mass, ${x}_{0}$, of these profiles, for which we present numerical values. (The $x$ axis is taken along the surface normal.) Next, the case of a small point charge $q$ with $x$ coordinate ${x}_{1}$ well outside the surface is treated. It is shown that the image potential experienced by such a charge has the form $\ensuremath{-}\frac{{q}^{2}}{[4({x}_{1}\ensuremath{-}{x}_{0})]}$, where ${x}_{0}$ is the above-mentioned quantity. We locate ${x}_{0}$, the effective position of the metal surface, relative to the last lattice plane of the crystal. We discuss the implications of these results for alkali adsorption on metal substrates, the capacitances of small-gap condensers, and field-emission experiments.

Norton D. Lang

Papers

Theory of Metal Surfaces: Charge Density and Surface Energy

Theory of Metal Surfaces: Work Function

Measurement of the conductance of a hydrogen molecule.

First-Principles Calculation of Transport Properties of a Molecular Device

Theory of Metal Surfaces: Induced Surface Charge and Image Potential