Publications

Strongly Constrained and Appropriately Normed Semilocal Density Functional

The ground-state energy, electron density, and related properties of ordinary matter can be computed efficiently when the exchange-correlation energy as a functional of the density is approximated semilocally. We propose the first meta-GGA (meta-generalized gradient approximation) that is fully constrained, obeying all 17 known exact constraints that a meta-GGA can. It is also exact or nearly exact for a set of appropriate norms, including rare-gas atoms and nonbonded interactions. This SCAN (strongly constrained and appropriately normed) meta-GGA achieves remarkable accuracy for systems where the exact exchange-correlation hole is localized near its electron, and especially for lattice constants and weak interactions.

Data-driven discovery of functional 2D materials utilizing a computational database for electronic structures

Phonon Frequencies from a Local Pseudopotential

Friction and Wear Behavior of Polyetherimide(PEI) Filled With Polytetrafluoroethylene(PTFE)

The tribological performance of Polyetherimide (PEI) composites filled with different Polytetrafluoroethylene (PTFE) content was comparatively evaluated on MM-200 test rig in block-on-ring configuration under dry friction condition. The microstructures of worn surfaces, fractured surfaces and wear mechanisms of the PEI composite were examined under scanning electron microscope (SEM). The variations of elastic modulus and surface hardness with variation in composition were also investigated. The results showed that under conditions of dry friction the PTFE can lower the friction coefficient and reduce wear of the PEI composites. When filled with 10 wt. % PTFE, the composite had the lowest wear rate. For PEI filled with 5wt. % PTFE the friction coefficient was about 0.3 and remained comparatively stable with increase of the PTFE content.

What Do We Learn from the Classical Turning Surface of the Kohn-Sham Potential as Electron Number Is Varied Continuously?

The classical turning radius Rt of an atom can be defined as the radius where the KS potential is equal to the negative ionisation potential of the atom, i.e. where v_s(R_t)=\epsilon_h. It was recently shown [P.N.A.S. 115, E11578 (2018)] to yield chemically relevant bonding distances, in line with known empirical values. In this work we show that extension of the concept to non-integer electron number yields additional information about atomic systems, and can be used to detect the difficulty of adding or subtracting electrons. Notably, it reflects the ease of bonding in open p-shells, and its greater difficulty in open s-shells. The latter manifests in significant discontinuities in the turning radius as the electron number changes the principal quantum number of the outermost electronic shell (e.g. going from Na to Na^{2+}). We then show that a non-integer picture is required to correctly interpret bonding and dissociation in H_2^+. Results are consistent when properties are calculated exactly, or via an appropriate approximation. They can be interpreted in the context of conceptual density functional theory.

Short-range Cut-Off of the Summed-Up van der Waals Series

Exchange-correlation energy of a metallic surface: Wave-vector analysis

The exchange-correlation energy of a jellium metal surface is analyzed in terms of the wavelength of the fluctuations that contribute to it, using a three-dimensional scheme different from that used by other authors. It is shown that with this scheme there exists an exact limiting form at long wavelengths which includes all many-body correlations and which is independent of the surface density profile. The local-density approximation is formulated as a function of wavelength, and it is shown to be exact at short wavelength. The interpolation scheme between these limits, which was discussed previously, is formulated and checked more completely and used to calculate surface energies.

A step in the direction of resolving the paradox of Perdew-Zunger self-interaction correction. II. Gauge consistency of the energy density at three levels of approximation

The Perdew-Zunger (PZ) self-interaction correction (SIC) was designed to correct the one-electron limit of any approximate density functional for the exchange-correlation (xc) energy, while yielding no correction to the exact functional. Unfortunately, it spoils the slowly varying (in space) limits of the uncorrected approximate functionals, where those functionals are right by construction. The right limits can be restored by locally scaling down the energy density of the PZ SIC in many-electron regions, but then a spurious correction to the exact functional would be found unless the self-Hartree and exact self-xc terms of the PZ SIC energy density were expressed in the same gauge. Only the local density approximation satisfies the same-gauge condition for the energy density, which explains why the recent local-scaling SIC is found here to work excellently for atoms and molecules only with this basic approximation and not with the more advanced generalized gradient approximations (GGAs) and meta-GGAs, which lose the Hartree gauge via simplifying integrations by parts. The transformation of energy density that achieves the Hartree gauge for the exact xc functional can also be applied to approximate functionals. Doing so leads to a simple scaled-down self-interaction correction that is typically much more accurate than PZ SIC in tests for many molecular properties (including equilibrium bond lengths). The present work unambiguously shows that the largest errors of PZ SIC applied to standard functionals at three levels of approximation can be removed by restoring their correct slowly varying density limits. It also confirms the relevance of these limits to atoms and molecules.

Stretched or noded orbital densities and self-interaction correction in density functional theory

Semilocal approximations to the density functional for the exchange-correlation energy of a many-electron system necessarily fail for lobed one-electron densities, including not only the familiar stretched densities but also the less familiar but closely related noded ones. The Perdew-Zunger (PZ) self-interaction correction (SIC) to a semilocal approximation makes that approximation exact for all one-electron ground- or excited-state densities and accurate for stretched bonds. When the minimization of the PZ total energy is made over real localized orbitals, the orbital densities can be noded, leading to energy errors in many-electron systems. Minimization over complex localized orbitals yields nodeless orbital densities, which reduce but typically do not eliminate the SIC errors of atomization energies. Other errors of PZ SIC remain, attributable to the loss of the exact constraints and appropriate norms that the semilocal approximations satisfy, suggesting the need for a generalized SIC. These conclusions are supported by calculations for one-electron densities and for many-electron molecules. While PZ SIC raises and improves the energy barriers of standard generalized gradient approximations (GGAs) and meta-GGAs, it reduces and often worsens the atomization energies of molecules. Thus, PZ SIC raises the energy more as the nodality of the valence localized orbitals increases from atoms to molecules to transition states. PZ SIC is applied here, in particular, to the strongly constrained and appropriately normed (SCAN) meta-GGA, for which the correlation part is already self-interaction-free. This property makes SCAN a natural first candidate for a generalized SIC.

Predicting Magnetic Coupling and Spin-Polarization Energy in Triangulene Analogues

Triangulene and its analogue metal-free magnetic systems have garnered increasing attention since their discovery. Predicting the magnetic coupling and spin-polarization energy with quantitative accuracy is beyond the predictive power of today's density functional theory (DFT) due to their intrinsic multireference character. Herein, we create a benchmark dataset of 25 magnetic systems with nonlocal spin densities, including the triangulene monomer, dimer, and their analogues. We calculate the magnetic coupling (<i>J</i>) and spin-polarization energy (Δ<i>E</i>_spin) of these systems using complete active space self-consistent field (CASSCF) and coupled-cluster methods as high-quality reference values. This reference data is then used to benchmark 22 DFT functionals commonly used in material science. Our results show that, while some functionals consistently correctly predict the qualitative character of the ground state, achieving quantitative accuracy with small relative errors is currently not feasible. PBE0, M06-2X, and MN15 are predicting the correct electronic ground state for all systems investigated here and also have the lowest mean absolute error for predicting both Δ<i>E</i>_spin (0.34, 0.32, and 0.31 eV) and <i>J</i> (11.74, 12.66, and 10.64 meV). They may therefore also serve as starting points for higher-level methods such as the <i>GW</i> or the random phase approximation. As other functionals fail for the prediction of the ground state, they cannot be recommended for metal-free magnetic systems.

Assessment of a density functional with full exact exchange and balanced non-locality of correlation

Abstract The recently proposed non-local functional of Perdew, Staroverov, Tao, and Scuseria (PSTS) [Phys. Rev. A 78, 052513 (2008)] belongs to the general family of local hybrids and hyper-generalized gradient approximations for the ground-state exchange-correlation energy. It is distinguished from other functionals of this family by the use of formally full exact exchange, balanced non-locality of correlation, and satisfaction of many exact constraints. We report here a self-consistent, generalized Kohn–Sham implementation of PSTS using the exact exchange energy density in the less-than-optimal conventional gauge. We extensively benchmark this version of PSTS for a series of properties against other well-established density functional approximations. It is shown that PSTS in the conventional gauge performs well for most of the properties under study. Keywords: density functionallocal hybrid Acknowledgements CAJH thanks Dr Thomas Henderson for helpful discussions. This work was supported by NSF under grants DMR-0501588 (JPP) and CHE-0807194 (GES), the Welch Foundation (C-0036), and by the Shared University Grid at Rice funded by NSF under grant EIA-0216467, and a partnership between Rice University, Sun Microsystems, and Sigma Solutions, Inc. One of the authors (BGJ) additionally acknowledges a training fellowship from the National Library of Medicine to the Keck Center for Interdisciplinary Bioscience Training of the Gulf Coast Consortium (NLM grant No. 5T15LM07093).

Ranking the Physics Departments: Use Citation Analysis

Landscape of competing stripe and magnetic phases in cuprates

Realistic modeling of competing phases in complex quantum materials has proven extremely challenging. For example, much of the existing density-functional-theory-based first-principles framework fails in the cuprate superconductors. Various many-body approaches involve generic model Hamiltonians and do not account for the couplings between spin, charge, and lattice. Here, by deploying the recently constructed strongly-constrained-and-appropriately-normed density functional, we show how landscapes of competing stripe and magnetic phases can be addressed on a first-principles basis in YBa2Cu3O6 and YBa2Cu3O7 as archetype cuprate compounds. We invoke no free parameters such as the Hubbard U, which has been the basis of much of the cuprate literature. Lattice degrees of freedom are found to be crucially important in stabilizing the various phases.

Ionization energy and electron affinity of a metal cluster in the stabilized jellium model: Size effect and charging limit

We report the first reliable theoretical calculation of the quantum size correction c which yields the asymptotic ionization energy I(R)=W+(12+c)/R+O(R−2) of a simple-metal cluster of radius R. Restricted-variational electronic density profiles are used to evaluate two sets of expressions for the bulk work function W and quantum size correction c: the Koopmans expressions, and the more accurate and profile-insensitive ΔSCF expressions. We find c≈−0.08 for stabilized (as for ordinary) jellium, and thus for real simple metals. We present parameters from which the density profiles may be reconstructed for a wide range of cluster sizes, including the planar surface. We also discuss how many excess electrons can be bound by a neutral cluster of given size. Within a continuum picture, the criterion for total-energy stability of a negatively charged cluster is less stringent than that for existence of a self-consistent solution.

Assessing the Performance of Recent Density Functionals for Bulk Solids

We assess the performance of recent density functionals for the exchange-correlation energy of a nonmolecular solid, by applying accurate calculations with the GAUSSIAN, BAND, and VASP codes to a test set of 24 solid metals and non-metals. The functionals tested are the modified Perdew-Burke-Ernzerhof generalized gradient approximation (PBEsol GGA), the second-order GGA (SOGGA), and the Armiento-Mattsson 2005 (AM05) GGA. For completeness, we also test more-standard functionals: the local density approximation, the original PBE GGA, and the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA. We find that the recent density functionals for solids reach a high accuracy for bulk properties (lattice constant and bulk modulus). For the cohesive energy, PBE is better than PBEsol overall, as expected, but PBEsol is actually better for the alkali metals and alkali halides. For fair comparison of calculated and experimental results, we consider the zero-point phonon and finite-temperature effects ignored by many workers. We show how Gaussian basis sets and inaccurate experimental reference data may affect the rating of the quality of the functionals. The results show that PBEsol and AM05 perform somewhat differently from each other for alkali metal, alkaline earth metal and alkali halide crystals (where the maximum value of the reduced density gradient is about 2), but perform very similarly for most of the other solids (where it is often about 1). Our explanation for this is consistent with the importance of exchange-correlation nonlocality in regions of core-valence overlap.

Density functionals for non-relativistic coulomb systems

Laplacian-level meta-GGA for the exchange-correlation energies of metals

Some Fundamental Issues in Ground-State Density Functional Theory: A Guide for the Perplexed

Some fundamental issues in ground-state density functional theory are discussed without equations: (1) The standard Hohenberg-Kohn and Kohn-Sham theorems were proven for a Hamiltonian that is not quite exact for real atoms, molecules, and solids. (2) The density functional for the exchange-correlation energy, which must be approximated, arises from the tendency of electrons to avoid one another as they move through the electron density. (3) In the absence of a magnetic field, either spin densities or total electron density can be used, although the former choice is better for approximations. (4) "Spin contamination" of the determinant of Kohn-Sham orbitals for an open-shell system is not wrong but right. (5) Only to the extent that symmetries of the interacting wave function are reflected in the spin densities should those symmetries be respected by the Kohn-Sham noninteracting or determinantal wave function. Functionals below the highest level of approximations should however sometimes break even those symmetries, for good physical reasons. (6) Simple and commonly used semilocal (lower-level) approximations for the exchange-correlation energy as a functional of the density can be accurate for closed systems near equilibrium and yet fail for open systems of fluctuating electron number. (7) The exact Kohn-Sham noninteracting state need not be a single determinant, but common approximations can fail when it is not. (8) Over an open system of fluctuating electron number, connected to another such system by stretched bonds, semilocal approximations make the exchange-correlation energy and hole-density sum rule too negative. (9) The gap in the exact Kohn-Sham band structure of a crystal underestimates the real fundamental gap but may approximate the first exciton energy in the large-gap limit. (10) Density functional theory is not really a mean-field theory, although it looks like one. The exact functional includes strong correlation, and semilocal approximations often overestimate the strength of static correlation through their semilocal exchange contributions. (11) Only under rare conditions can excited states arise directly from a ground-state theory.