797 publications from this institution
In recent work, generalized gradient approximations (GGA's) have been constructed from the energy density of the Airy gas for exchange but not for correlation. We report the random phase approximation (RPA) conventional correlation energy density of the Airy gas, the simplest edge electron gas, in which the auxiliary noninteracting electrons experience a linear potential. By fitting the Airy-gas RPA exchange-correlation energy density and making an accurate short-range correction to RPA, we propose a simple beyond-RPA GGA density functional ("ARPA+") for the exchange-correlation energy. Our functional, tested for jellium surfaces, atoms, molecules and solids, improves mildly over the local spin density approximation for atomization energies and lattice constants without much worsening the already-good surface exchange-correlation energies.
We construct a nonlocal density functional approximation with full exact exchange, while preserving the constraint-satisfaction approach and justified error cancellations of simpler semilocal functionals. This is achieved by interpolating between different approximations suitable for two extreme regions of the electron density. "Normal" regions are well described by semilocal approximations, because of proper accuracy for a slowly-varying density or because of error cancellation between exchange and correlation. "Abnormal" regions, where nonlocality is unveiled, include those in which exchange can dominate correlation (one-electron, nonuniform high-density, and rapidly-varying limits), and those open subsystems of fluctuating electron number over which the exact exchange-correlation hole integrates to a value greater than -1. Regions between these extremes are described by a hybrid functional mixing exact and semilocal exchange energy densities locally. Because our mixing fraction tends to 1 in the high-density limit, we rigorously employ full exact exchange. However, the nonlocality of exchange also requires balanced nonlocality of correlation, which can demand at least five empirical parameters. Our local hybrid functional is perhaps the first size-consistent fourth-rung density functional or hyper-GGA with full exact exchange, is exact for all one-electron densities, and provides an excellent fit to the 223 molecular enthalpies of formation of the G3/99 set and the 42 reaction barrier heights of the BH42/03 set, improving both (but especially the latter) over most semilocal functionals and global hybrids.
Range-separated (screened) hybrid functionals provide a powerful strategy for incorporating nonlocal exact (Hartree-Fock-type) exchange into density functional theory. Existing implementations of range separation use a fixed system-independent screening parameter. Here, we propose a novel method that uses a position-dependent screening function. These locally range-separated hybrids add substantial flexibility for describing diverse electronic structures and satisfy a high-density scaling constraint better than the fixed screening approximation does.
Due to size-dependent non-additivity, the van der Waals interaction (vdW) between nanostructures remains elusive. Here we first develop a model dynamic multipole polarizability for an inhomogeneous system that allows for a cavity. The model recovers the exact zero- and high-frequency limits and respects the paradigms of condensed matter physics (slowly varying density) and quantum chemistry (one- and two-electron densities). We find that the model can generate accurate vdW coefficients for both spherical and non-spherical clusters, with an overall mean absolute relative error of 4%, without any fitting. Based on this model, we study the non-additivity of vdW interactions. We find that there is strong non-additivity of vdW interactions between nanostructures, arising from electron delocalization, inequivalent contributions of atoms, and non-additive many-body interactions. Furthermore, we find that the non-additivity can have increasing size dependence as well as decreasing size dependence with cluster size.
Received 4 January 2018DOI:https://doi.org/10.1103/PhysRevB.98.079903©2018 American Physical SocietyPhysics Subject Headings (PhySH)TechniquesDensity functional theory developmentCondensed Matter, Materials & Applied Physics
Fullerene molecules such as C(60) are large nearly spherical shells of carbon atoms. Pairs of such molecules have a strong long-range van der Waals attraction that can produce scattering or binding into molecular crystals. A simplified classical-electrodynamics model for a fullerene is a spherical metal shell, with uniform electron density confined between outer and inner radii (just as a simplified model for a nearly spherical metallic nanocluster is a solid metal sphere or filled shell). For the spherical-shell model, the exact dynamic multipole polarizabilities are all known analytically. From them, we can derive exact analytic expressions for the van der Waals coefficients of all orders between two spherical metal shells. The shells can be identical or different, and hollow or filled. To connect the model to a real fullerene, we input the static dipole polarizability, valence electron number and estimated shell thickness t of the real molecule. Our prediction for the leading van der Waals coefficient C(6) between two C(60) molecules ((1.30 ± 0.22) × 10(5) hartree bohr(6)) agrees well with a prediction for the real molecule from time-dependent density functional theory. Our prediction is remarkably insensitive to t. Future work might include the prediction of higher-order (e.g. C(8) and C(10)) coefficients for C(60), applications to other fullerenes or nearly spherical metal clusters, etc. We also make general observations about the van der Waals coefficients.
Received 12 January 2010DOI:https://doi.org/10.1103/PhysRevB.81.169902©2010 American Physical Society
While the exact total energy of a separated open system varies linearly as a function of average electron number between adjacent integers, the energy predicted by semilocal density-functional approximations is concave up and the exact-exchange-only or Hartree-Fock energy is concave down. As a result, semilocal density functionals fail for separated open systems of fluctuating electron number, as in stretched molecular ions $\mathrm{A}_{2}{}^{+}$ and in solid transition-metal oxides. We develop an exact-exchange theory and an exchange-hole sum rule that explain these failures and we propose a way to correct them via a local hybrid functional.
In recent work, generalized gradient approximations (GGAs) have been constructed from the energy density of the Airy gas for exchange but not for correlation. We report the random-phase approximation (RPA) conventional correlation energy density of the Airy gas, the simplest edge electron gas, in which the auxiliary noninteracting electrons experience a linear potential. By fitting the Airy-gas RPA exchange-correlation energy density and making an accurate short-range correction to RPA, we propose a simple beyond RPA GGA density functional (``$\text{ARPA}+$'') for the exchange-correlation energy. Our functional, tested for jellium surfaces, atoms, molecules, and solids, improves mildly over the local spin-density approximation for atomization energies and lattice constants without much worsening the already good surface exchange-correlation energies.
Electrodeposition of an amorphous cobalt catalyst layer over a high-surface-area alpha-Fe(2)O(3) photoanode causes a more than 350 mV cathodic shift in the onset potential for photoelectrochemical water oxidation using this anode and simulated solar irradiation. The catalyst layer is shown to deposit conformally onto the mesostructured alpha-Fe(2)O(3), leading to a large contact area at the interface between the two halves of the composite photoanode. Photoelectrochemical measurements show that the photocurrent generated from this composite photoanode still derives from alpha-Fe(2)O(3) excitation but is now accessible at an external bias several hundred millivolts below what is typically required for alpha-Fe(2)O(3) photoanodes alone, indicating a reduced external bias would be needed to drive overall water splitting. These results demonstrate modification of this prototypical photoanode material with a conformal layer of a competent electrocatalyst to separate the tasks of photon absorption and redox catalysis, a strategy that may have important and general ramifications for solar photoelectrochemical hydrogen generation.
While the short-range part of the van der Waals (vdW) interaction can be described by semilocal density functionals, the long range cannot. By respecting two uniform electron gas and other exact limits, we construct a nonlocal density functional for the long-range coefficient ${C}_{6}$. ${C}_{8}$ and ${C}_{10}$ may be determined empirically from ${C}_{6}$. Then we estimate the effect of the core-core vdW attraction upon the lattice constants of the alkali metals, including dynamic valence-electron screening. This attraction is important for the softest metals, shrinking the lattice constant of Cs by $0.1\text{ }\text{\AA{}}$.
