Publications

Visualizing atomic sizes and molecular shapes with the classical turning surface of the Kohn–Sham potential

The Kohn-Sham potential [Formula: see text] is the effective multiplicative operator in a noninteracting Schrödinger equation that reproduces the ground-state density of a real (interacting) system. The sizes and shapes of atoms, molecules, and solids can be defined in terms of Kohn-Sham potentials in a nonarbitrary way that accords with chemical intuition and can be implemented efficiently, permitting a natural pictorial representation for chemistry and condensed-matter physics. Let [Formula: see text] be the maximum occupied orbital energy of the noninteracting electrons. Then the equation [Formula: see text] defines the surface at which classical electrons with energy [Formula: see text] would be turned back and thus determines the surface of any electronic object. Atomic and ionic radii defined in this manner agree well with empirical estimates, show regular chemical trends, and allow one to identify the type of chemical bonding between two given atoms by comparing the actual internuclear distance to the sum of atomic radii. The molecular surfaces can be fused (for a covalent bond), seamed (ionic bond), necked (hydrogen bond), or divided (van der Waals bond). This contribution extends the pioneering work of Z.-Z. Yang et al. [Yang ZZ, Davidson ER (1997) <i>Int J Quantum Chem</i> 62:47-53; Zhao DX, et al. (2018) <i>Mol Phys</i> 116:969-977] by our consideration of the Kohn-Sham potential, protomolecules, doubly negative atomic ions, a bond-type parameter, seamed and necked molecular surfaces, and a more extensive table of atomic and ionic radii that are fully consistent with expected periodic trends.

Right band gaps for the right reason at low computational cost with a meta-GGA

In density functional theory, traditional explicit density functionals such as the local density approximation and generalized gradient approximations cannot accurately predict the band gap of solids for a fundamental reason: They lack the exchange-correlation derivative discontinuity. By comparing Kohn-Sham and generalized Kohn-Sham calculations, we here show that the nonempirical meta-generalized-gradient-approximation (meta-GGA) TASK from Aschebrock and K\"ummel [Phys. Rev. Res. 1, 033082 (2019)] predicts the right gaps for the right reason, i.e., as a combination of a proper Kohn-Sham gap and a substantial derivative discontinuity contribution. For many materials from small-gap semiconductors to large-gap insulators, the proper band gap is thus obtained. We further study a group of metal-halide perovskites for which the band gap is notoriously hard to predict. For these materials, TASK yields band gaps very similar to the nonlocal screened hybrid Heyd-Scuseria-Ernzerhof functional, yet at a fraction of the hybrid functional's computational cost. We discuss the influence of correlation functionals, and open questions in the comparison of calculated band gaps with experimental ones.

Can desorption be described by the local density formalism?

Large Topological Hall Effect and Spiral Magnetic Order in the Weyl Semimetal SmAlSi

The first demonstration of spiral magnetic order in a Weyl semimetal sets the stage for finding other materials with these structures, which could be used for high-density magnetic information storage.

Self-interaction corrected dipole polarizabilites of free atoms and their ions

High yield production of ultrathin fibroid semiconducting nanowire of Ta2Pd3Se8

Immediately after the demonstration of the high-quality electronic properties in various two dimensional (2D) van der Waals (vdW) crystals fabricated with mechanical exfoliation, many methods have been reported to explore and control large scale fabrications. Comparing with recent advancements in fabricating 2D atomic layered crystals, large scale production of one dimensional (1D) nanowires with thickness approaching molecular or atomic level still remains stagnant. Here, we demonstrate the high yield production of a 1D vdW material, semiconducting Ta2Pd3Se8 nanowires, by means of liquid-phase exfoliation. The thinnest nanowire we have readily achieved is around 1 nm, corresponding to a bundle of one or two molecular ribbons. Transmission electron microscopy (TEM) and transport measurements reveal the as-fabricated Ta2Pd3Se8 nanowires exhibit unexpected high crystallinity and chemical stability. Our low-frequency Raman spectroscopy reveals clear evidence of the existing of weak inter-ribbon bindings. The fabricated nanowire transistors exhibit high switching performance and promising applications for photodetectors.

Combinations of coupled cluster, density functionals, and the random phase approximation for describing static and dynamic correlation, and van der Waals interactions

Contrary to standard coupled cluster doubles (CCD) and Brueckner doubles (BD), singlet-paired analogues of CCD and BD (denoted here as CCD0 and BD0) do not break down when static correlation is present, but neglect substantial amounts of dynamic correlation. In fact, CCD0 and BD0 do not account for any contributions from multielectron excitations involving only same-spin electrons at all. We exploit this feature to add---without introducing double counting, self-interaction, or increase in cost---the missing correlation to these methods via meta-GGA density functionals (TPSS and SCAN). Furthermore, we improve upon these CCD0+DFT blends by invoking range separation: the short- and long-range correlations absent in CCD0/BD0 are evaluated with DFT and the direct random phase approximation (dRPA), respectively. This corrects the description of long-range van der Waals forces. Comprehensive benchmarking shows that the combinations presented here are very accurate for weakly correlated systems, while also providing a reasonable description of strongly correlated problems without resorting to symmetry breaking.

Calculation of the band structure, Fermi surface, and interband optical conductivity of lithium

The band structure of lithium has been calculated by the OPW method using the Seitz potential for the ions and the selfconsistent Hartree potential due to the conduction electrons. Use of the same potential for the 'core state' as for the conduction-electron states is found to be of some importance. A novel method is presented to transform the OPW generalized eigenvalue problem into standard eigenvalue form. The band structure so obtained agrees with previous calculations, particularly that of Rudge (1969). The calculated Fermi surface distortions are less than 4%, while the density of states and optical masses are 1.50 and 1.47 respectively. The direct interband optical conductivity has also been calculated; its overall magnitude is in reasonable agreement with measurements by Mathewson and Myers (1973). The calculation predicts a sharp absorption edge at 3.4 eV, in agreement with the measurement by Hodgson (1966), and in contrast to the much slower rise in the optical conductivity beginning at 2.4 eV reported by Mathewson and Myers.

The general-purpose SCAN meta-GGA for ferroelectric materials

Data for "Laplacian-level meta-GGA for the weakly-nonlocal solid and liquid metals"

This dataset contains all VASP inputs and outputs for the paper "Improved Laplacian-level meta-GGA for the weakly-nonlocal solid and liquid metals." For the preprint, see arXiv:2203.09403, and for the reference densities, fitting routines, and analysis scripts, see the Gitlab code repository.\n\nDescription of individual tarballs:\n\n\n\tAE6: 6-molecule set of atomization energies\n\tferro: relaxed geometries and magnetic moments for the ferromagnetic solids Fe, Ni, and Co\n\tintermetallics: formation energies of three intermetallic solids, HfOs, ScPt, and VPt2\n\tLC20: relaxed geometries and equilibrium bulk moduli for the LC20 set of cubic solids. Equilibrium geometries by equation of state fit. Bandgaps for select insulators are included here.\n\tLC20_stress_tensor: same as LC20, but equilibrium geometries found by minimizing forces on unit cell computed with Laplacian-dependent stress tensor\n\tLC23: equilibrium geometries, bulk moduli, and cohesive energies for the LC23 set (LC20 + K, Rb, and Cs) found by equation of state fit. Bandgaps for select insulators are included here.\n\tPt_monovac: monovacancy formation energies for Pt, computed in a few different ways described in the text\n

Role of the exchange-correlation energy: Nature's glue

In the Kohn–Sham density functional theory of ground-state electronic structure, only the exchange–correlation energy Exc must be approximated. Although Exc is not typically a large component of the total energy, it is the principal ingredient of the glue that binds atoms together to form molecules and solids. To illustrate this fact, we present self-consistent results for atomization energies of molecules and for surface energies and work functions of jellium, calculated within the “Hartree” approximation, which neglects Exc. The Hartree world displays weak bonding between atoms, low or negative surface energies, and work functions that are close to zero. Other aspects of the Hartree world can be deduced from known size–effect relationships. The mechanism behind the glue role of exchange and correlation is the suppression of Hartree charge fluctuations. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 814–818, 2000

New Meta-Generalized Gradient Approximation for Exchange and Correlation

Enhancing the accuracy of interior-scaled Perdew-Zunger self-interaction correction

Coupling-constant dependence of atomization energies

The local spin-density (LSD) functional and Perdew–Wang 91 (PW91) generalized gradient approximations to atomization energies of molecules are investigated. We discuss the coupling-constant dependence of the atomization energy and why exchange errors of the functionals are greater than exchange–correlation errors. This fact helps to justify hybrid schemes which mix some exact exchange with density functional approximations for exchange and correlation. It is shown that the biggest errors in the atomization energies occur when there is a strong interaction between different electron pairs, which vanishes upon atomization. We argue that the amount of exchange character of a molecular property, such as the atomization energy, depends on the property itself. We define an exact mixing coefficient b, which measures this exchange character, and show that both LSD and PW91 typically overestimate this quantity. Thus, nonempirical hybrid schemes which approximate this quantity by its LSD or PW91 value typically do not improve the exchange–correlation energy. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64: 285–295, 1997

Comparing Meta-GGAs, +U Corrections, and Hybrid Functionals for Polaronic Point Defects in Layered MnO$_2$, NiO$_2$, and KCoO$_2$

Defects in a material can significantly tune properties and enhance utility. Hybrid functionals like HSE06 are often used to describe solids with such defects. However, geometry optimization (including accounting for effects such as Jahn-Teller distortion) using hybrid functionals is challenging for the large supercells needed for defect study. The proposed r$^2$SCAN+rVV10+U+$\mathrm{U_d}$ method, which is computationally much cheaper and faster than hybrid functionals, can successfully describe defects in materials with the proper choice of U (for the d orbitals of the host atom) and $\mathrm{U_d}$ (for those of the defect atom), as shown here for small polaron defects in layered transition-metal oxides. For a range of U and $\mathrm{U_d}$ around literature values (from solid-state reaction energies) for a given transition-metal ion and its oxidation state, we find that this approach predicts localized polaronic states in band gaps, as hybrid functionals do. The layered materials birnessite ($\mathrm{K_nMnO_2}, n=0.03 $) and $\mathrm{K_nNiO_2},n=0.03$, with one K atom intercalated between layers in a supercell, are found to have one localized occupied $\mathrm{e_g}$ polaronic state on the transition metal ion reduced by the insertion of the K atom, when the geometry is calculated as above using published U values. The expected Jahn-Teller distortion is not observed when U=$\mathrm{U_d}$=0. Layered cobalt oxide with additional potassium ions intercalated ($\mathrm{K_nCoO_2},n=1.03$) is different, due to a dramatic difference in electronic configuration of the defected Co(II) ion: A single extra K atom in the supercell leads to four localized electrons in the band gap, using standard U values, and even for U=$\mathrm{U_d}$=0.

Comparing first-principles density functionals plus corrections for the lattice dynamics of YBa2Cu3O6

The enigmatic mechanism underlying unconventional high-temperature superconductivity, especially the role of lattice dynamics, has remained a subject of debate. Theoretical insights have long been hindered due to the lack of an accurate first-principles description of the lattice dynamics of cuprates. Recently, using the r2SCAN meta-generalized gradient approximation (meta-GGA) functional, we have been able to achieve accurate phonon spectra of an insulating cuprate YBa2Cu3O6 and discover significant magnetoelastic coupling in experimentally interesting Cu-O bond stretching optical modes [Ning et al., Phys. Rev. B 107, 045126 (2023)]. We extend this work by comparing Perdew-Burke-Ernzerhof and r2SCAN performances with corrections from the on-site Hubbard U and the D4 van der Waals (vdW) methods, aiming at further understanding on both the materials science side and the density functional side. We demonstrate the importance of vdW and self-interaction corrections for accurate first-principles YBa2Cu3O6 lattice dynamics. Since r2SCAN by itself partially accounts for these effects, the good performance of r2SCAN is now more fully explained. In addition, the performances of the Tao-Mo series of meta-GGAs, which are constructed in a different way from the strongly constrained and appropriately normed (SCAN) meta-GGA and its revised version r2SCAN, are also compared and discussed.

Accuracy of first-principles interatomic interactions and predictions of ferroelectric phase transitions in perovskite oxides: Energy functional and effective Hamiltonian

While first-principles density functional theory (DFT)-based models have been effective in capturing the physics of ferroelectric phase transitions in ${\mathrm{BaTiO}}_{3}, {\mathrm{PbTiO}}_{3}$, and ${\mathrm{KNbO}}_{3}$, quantitative estimates of the transition temperatures (${T}_{C}$) suffer from errors that are believed to originate from the errors in estimating lattice constants obtained within the local density approximation (LDA) and generalized gradient approximation (GGA) of DFT. The recently developed strongly constrained and appropriately normed (SCAN) meta-GGA functional has been shown to be quite accurate in the estimation of lattice constants. Here, we present a quantitative analysis of the estimates of ferroelectric ground-state properties of eight perovskite oxides and transition temperatures of ${\mathrm{BaTiO}}_{3}, {\mathrm{PbTiO}}_{3}$, and ${\mathrm{KNbO}}_{3}$ obtained with molecular dynamics simulations using an effective Hamiltonian derived from the SCAN meta-GGA-based DFT. Relative to LDA, we find an improvement in the estimates of ${T}_{C}$, which arises from the changes in the calculated strain-phonon, anharmonic coupling constants, and strength of ferroelectric instabilities, i.e., frequencies of the soft modes. We also assess the errors in ${T}_{C}$ originating from approximately integrating out the high-energy phonons during construction of the model Hamiltonian through estimates of the effects of fourth-order couplings between the soft mode and higher-energy modes of ${\mathrm{BaTiO}}_{3}, {\mathrm{PbTiO}}_{3}$, and ${\mathrm{KNbO}}_{3}$. We find that inclusion of these anharmonic couplings results in deeper double-well energy functions of ferroelectric distortions and further improvement in the estimates of transition temperatures. Consistently improved estimates of lattice constants and transition temperatures with the SCAN meta-GGA calculations augur well for their use in simulations of superlattices or heterostructures of perovskite oxides, in which the effects of lattice matching are critical.

Erratum: Nonempirical density functionals investigated for jellium: Spin-polarized surfaces, spherical clusters, and bulk linear response [Phys. Rev. B<b>77</b>, 245107 (2008)]

Received 10 December 2008DOI:https://doi.org/10.1103/PhysRevB.78.239906©2008 American Physical Society

Density functional for short-range correlation: Is the random phase approximation accurate for iso-electronic energy changes?