Describing static correlation in bond dissociation by Kohn-Sham density functional theory

We show that density functional theory within the RPA (random phase approximation for the exchange-correlation energy) provides a correct description of bond dissociation in H$_2$ in a spin-restricted Kohn-Sham formalism, i.e. without artificial symmetry breaking. We present accurate adiabatic connection curves both at equilibrium and beyond the Coulson-Fisher point. The strong curvature at large bond length implies important static (left-right) correlation, justifying modern hybrid functional constructions but also demonstrating their limitations. Although exact at infinite and accurate around the equilibrium bond length, the RPA dissociation curve displays unphysical repulsion at larger but finite bond lengths. Going beyond the RPA by including the exact exchange kernel (RPA+X), we find a similar repulsion. We argue that this deficiency is due to the absence of double excitations in adiabatic linear response theory. Further analyzing the H$_2$ dissociation limit we show that the RPA+X is not size-consistent, in contrast to the RPA.Comment: 15 pages, 5 figure

Rationale for a new class of double-hybrid approximations in density-functional theory

We provide a rationale for a new class of double-hybrid approximations introduced by Br\'emond and Adamo [J. Chem. Phys. 135, 024106 (2011)] which combine an exchange-correlation density functional with Hartree-Fock exchange weighted by \l and second-order M{\o}ller-Plesset (MP2) correlation weighted by \l^3. We show that this double-hybrid model can be understood in the context of the density-scaled double-hybrid model proposed by Sharkas et al. [J. Chem. Phys. 134, 064113 (2011)], as approximating the density-scaled correlation functional E_c[n_{1/\l}] by a linear function of \l, interpolating between MP2 at \l=0 and a density-functional approximation at \l=1. Numerical results obtained with the Perdew-Burke-Ernzerhof density functional confirms the relevance of this double-hybrid model.Comment: 4 pages, 2 figures, to appear in Journal of Chemical Physic

Mechanical modulation of single-electron tunneling through molecular-assembled metallic nanoparticles

We present a microscopic study of single-electron tunneling in nanomechanical double-barrier tunneling junctions formed using a vibrating scanning nanoprobe and a metallic nanoparticle connected to a metallic substrate through a molecular bridge. We analyze the motion of single electrons on and off the nanoparticle through the tunneling current, the displacement current and the charging-induced electrostatic force on the vibrating nanoprobe. We demonstrate the mechanical single-electron turnstile effect by applying the theory to a gold nanoparticle connected to the gold substrate through alkane dithiol molecular bridge and probed by a vibrating platinum tip.Comment: Accepted by Phys. Rev.

Exchange and correlation as a functional of the local density of states

A functional $E_{xc}[\rho(\r,\epsilon)]$ is presented, in which the exchange and correlation energy of an electron gas depends on the local density of occupied states. A simple local parametrization scheme is proposed, entirely from first principles, based on the decomposition of the exchange-correlation hole in scattering states of different relative energies. In its practical Kohn-Sham-like form, the single-electron orbitals become the independent variables, and an explicit formula for the functional derivative is obtained.Comment: 5 pages. Expanded version. Will appear in Phys. Rev.

Comparative study of density functional theories of the exchange-correlation hole and energy in silicon

We present a detailed study of the exchange-correlation hole and exchange-correlation energy per particle in the Si crystal as calculated by the Variational Monte Carlo method and predicted by various density functional models. Nonlocal density averaging methods prove to be successful in correcting severe errors in the local density approximation (LDA) at low densities where the density changes dramatically over the correlation length of the LDA hole, but fail to provide systematic improvements at higher densities where the effects of density inhomogeneity are more subtle. Exchange and correlation considered separately show a sensitivity to the nonlocal semiconductor crystal environment, particularly within the Si bond, which is not predicted by the nonlocal approaches based on density averaging. The exchange hole is well described by a bonding orbital picture, while the correlation hole has a significant component due to the polarization of the nearby bonds, which partially screens out the anisotropy in the exchange hole.Comment: 16 pages, 5 figures, RevTeX, added conten

Resonance Lifetimes from Complex Densities

The ab-initio calculation of resonance lifetimes of metastable anions challenges modern quantum-chemical methods. The exact lifetime of the lowest-energy resonance is encoded into a complex "density" that can be obtained via complex-coordinate scaling. We illustrate this with one-electron examples and show how the lifetime can be extracted from the complex density in much the same way as the ground-state energy of bound systems is extracted from its ground-state density

Hybrid exchange-correlation functional for accurate prediction of the electronic and structural properties of ferroelectric oxides

Using a linear combination of atomic orbitals approach, we report a systematic comparison of various Density Functional Theory (DFT) and hybrid exchange-correlation functionals for the prediction of the electronic and structural properties of prototypical ferroelectric oxides. It is found that none of the available functionals is able to provide, at the same time, accurate electronic and structural properties of the cubic and tetragonal phases of BaTiO$_3$ and PbTiO$_3$. Some, although not all, usual DFT functionals predict the structure with acceptable accuracy, but always underestimate the electronic band gaps. Conversely, common hybrid functionals yield an improved description of the band gaps, but overestimate the volume and atomic distortions associated to ferroelectricity, giving rise to an unacceptably large $c/a$ ratio for the tetragonal phases of both compounds. This super-tetragonality is found to be induced mainly by the exchange energy corresponding to the Generalized Gradient Approximation (GGA) and, to a lesser extent, by the exact exchange term of the hybrid functional. We thus propose an alternative functional that mixes exact exchange with the recently proposed GGA of Wu and Cohen [Phys. Rev. B 73, 235116 (2006)] which, for solids, improves over the treatment of exchange of the most usual GGA's. The new functional renders an accurate description of both the structural and electronic properties of typical ferroelectric oxides.Comment: 13 pages, 4 figures, 7 table

Global hybrids from the semiclassical atom theory satisfying the local density linear response

We propose global hybrid approximations of the exchange-correlation (XC) energy functional which reproduce well the modified fourth-order gradient expansion of the exchange energy in the semiclassical limit of many-electron neutral atoms and recover the full local density approximation (LDA) linear response. These XC functionals represent the hybrid versions of the APBE functional [Phys. Rev. Lett. 106, 186406, (2011)] yet employing an additional correlation functional which uses the localization concept of the correlation energy density to improve the compatibility with the Hartree-Fock exchange as well as the coupling-constant-resolved XC potential energy. Broad energetical and structural testings, including thermochemistry and geometry, transition metal complexes, non-covalent interactions, gold clusters and small gold-molecule interfaces, as well as an analysis of the hybrid parameters, show that our construction is quite robust. In particular, our testing shows that the resulting hybrid, including 20\% of Hartree-Fock exchange and named hAPBE, performs remarkably well for a broad palette of systems and properties, being generally better than popular hybrids (PBE0 and B3LYP). Semi-empirical dispersion corrections are also provided.Comment: 12 pages, 4 figure

Energy densities in the strong-interaction limit of density functional theory

We discuss energy densities in the strong-interaction limit of density functional theory, deriving an exact expression within the definition (gauge) of the electrostatic potential of the exchange-correlation hole. Exact results for small atoms and small model quantum dots are compared with available approximations defined in the same gauge. The idea of a local interpolation along the adiabatic connection is discussed, comparing the energy densities of the Kohn-Sham, the physical, and the strong-interacting systems. We also use our results to analyze the local version of the Lieb-Oxford bound, widely used in the construction of approximate exchange-correlation functionals.Comment: 12 page

Observation of Quantum Interference in Molecular Charge Transport

As the dimensions of a conductor approach the nano-scale, quantum effects will begin to dominate its behavior. This entails the exciting possibility of controlling the conductance of a device by direct manipulation of the electron wave function. Such control has been most clearly demonstrated in mesoscopic semiconductor structures at low temperatures. Indeed, the Aharanov-Bohm effect, conductance quantization and universal conductance fluctuations are direct manifestations of the electron wave nature. However, an extension of this concept to more practical emperatures has not been achieved so far. As molecules are nano-scale objects with typical energy level spacings (~eV) much larger than the thermal energy at 300 K (~25 meV), they are natural candidates to enable such a break-through. Fascinating phenomena including giant magnetoresistance, Kondo effects and conductance switching, have previously been demonstrated at the molecular level. Here, we report direct evidence for destructive quantum interference in charge transport through two-terminal molecular junctions at room temperature. Furthermore, we show that the degree of interference can be controlled by simple chemical modifications of the molecule. Not only does this provide the experimental demonstration of a new phenomenon in quantum charge transport, it also opens the road for a new type of molecular devices based on chemical or electrostatic control of quantum interference