Publications

Comparative first-principles study of clean-surface properties of metals

Reducing Self-Interaction Error in Transition-Metal Oxides with Different Exact-Exchange Fractions for Energy and Density

Density functional theory (DFT) in chemistry and materials science aims for "chemical accuracy," but this goal is challenged by the need to approximate the exact exchange-correlation (XC) energy functional. The r$^2$SCAN, meta-generalized gradient approximation to the XC functional fulfills 17 exact constraints of the XC energy, and has significantly boosted prediction accuracy for molecules and materials. However, r$^2$SCAN remains inadequate at predicting properties of open \textit{d} and \textit{f} transition-metal strongly correlated compounds, such as band gaps, magnetic moments, and oxidation energies. Prediction inaccuracies of r$^2$SCAN energies arise from functional and density-driven errors, mainly resulting from the DFT self-interaction error. We propose the r$^2$SCANY@r$^2$SCANX method to mitigate the self-interaction error of XC functionals for the accurate simulations of electronic, magnetic, and thermochemical properties of transition metal oxides. r$^2$SCANY@r$^2$SCANX uses different fractions of exact Hartree-Fock exchange: X for the electronic density and Y for the density functional approximation of the total energy, thereby simultaneously addressing functional-driven and density-driven inaccuracies. Building just on 1 (or maximum 2) parameters that apply unchanged to \emph{s-p}-bonded systems, we demonstrate that, r$^2$SCANY@r$^2$SCANX improves upon the r$^2$SCAN predictions for 20 highly correlated oxides and even outperforms the highly parameterized DFT(r$^2$SCAN)+\emph{U} method -- the state-of-the-art approach to predict strongly correlated materials. Prediction uncertainties for oxidation energies and magnetic moments of transition metal oxides are significantly reduced by r$^2$SCAN10@r$^2$SCAN50 and band gaps with r$^2$SCAN10@r$^2$SCAN. r$^2$SCAN10@r$^2$SCAN50 diminishes the density-driven error of the energy in r$^2$SCAN and r$^2$SCAN10.

Hartree-Fock density functional theory works through error cancellation for the interaction energies of halogen and chalcogen bonded complexes

Spin scaling of the electron-gas correlation energy in the high-density limit

The ground-state correlation energy per particle in a uniform electron gas with spin densities ${\mathit{n}}_{\mathrm{\ensuremath{\uparrow}}}$ and ${\mathit{n}}_{\mathrm{\ensuremath{\downarrow}}}$ may be expressed as ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}$(\ensuremath{\zeta},${\mathit{r}}_{\mathit{s}}$)=I(\ensuremath{\zeta},${\mathit{r}}_{\mathit{s}}$)${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}$(0,${\mathit{r}}_{\mathit{s}}$), where ${\mathit{r}}_{\mathit{s}}$=[3/4\ensuremath{\pi}(${\mathit{n}}_{\mathrm{\ensuremath{\uparrow}}}$+${\mathit{n}}_{\mathrm{\ensuremath{\downarrow}}}$)${]}^{1/3}$ is the density parameter and \ensuremath{\zeta}=(${\mathit{n}}_{\mathrm{\ensuremath{\uparrow}}}$-${\mathit{n}}_{\mathrm{\ensuremath{\downarrow}}}$)/(${\mathit{n}}_{\mathrm{\ensuremath{\uparrow}}}$+${\mathit{n}}_{\mathrm{\ensuremath{\downarrow}}}$) is the relative spin polarization. We find an analytic expression for the spin-scaling factor (SSF) I(\ensuremath{\zeta},${\mathit{r}}_{\mathit{s}}$) in the high-density limit ${\mathit{r}}_{\mathit{s}}$\ensuremath{\rightarrow}0. It decreases from the value 1 at \ensuremath{\zeta}=0, approaching the value 1/2 with slope -\ensuremath{\infty} as \ensuremath{\zeta} approaches 1. A simple approximation to this SSF which displays the correct qualitative behavior is ${\mathit{g}}^{3}$(\ensuremath{\zeta}), where g(\ensuremath{\zeta})=[(1+\ensuremath{\zeta}${)}^{2/3}$+(1-\ensuremath{\zeta}${)}^{2/3}$]/2. We find that g(\ensuremath{\zeta}) is the SSF for the coefficient of the \ensuremath{\Vert}\ensuremath{\nabla}n${\mathrm{\ensuremath{\Vert}}}^{2}$/${\mathit{n}}^{4/3}$ term of the spin-density gradient expansion of the exchange energy, and a good approximation to the SSF for that of correlation: ${\mathit{scrC}}_{\mathit{x}}$(\ensuremath{\zeta})/${\mathit{scrC}}_{\mathit{x}}$(0)=g(\ensuremath{\zeta}) and ${\mathit{scrC}}_{\mathit{c}}$(\ensuremath{\zeta},${\mathit{r}}_{\mathit{s}}$\ensuremath{\rightarrow}0)/${\mathit{scrC}}_{\mathit{c}}$(0, ${\mathrm{r}}_{\mathrm{s}}$\ensuremath{\rightarrow}0)\ensuremath{\approxeq}g(\ensuremath{\zeta}). We also find that the \ensuremath{\Vert}\ensuremath{\nabla}\ensuremath{\zeta}${\mathrm{\ensuremath{\Vert}}}^{2}$ contribution to the correlation energy is always negligible.

Risk factors and intervention strategies for post-traumatic stress disorder following spinal cord injury: a retrospective multivariate analysis of 195 cases

Prompt recognition and specific interventions for high-risk spinal cord injury patients are crucial for minimizing PTSD and enhancing results.

Meta-generalized gradient approximation: Explanation of a realistic nonempirical density functional

Tao, Perdew, Staroverov, and Scuseria (TPSS) have constructed a nonempirical meta-generalized gradient approximation (meta-GGA) [Phys. Rev. Lett. 91, 146401 (2003)] for the exchange-correlation energy, imposing exact constraints relevant to the paradigm densities of condensed matter physics and quantum chemistry. Results of their extensive tests on molecules, solids, and solid surfaces are encouraging, suggesting that this density functional achieves uniform accuracy for diverse properties and systems. In the present work, this functional is explained and details of its construction are presented. In particular, the functional is constructed to yield accurate energies under uniform coordinate scaling to the low-density or strong-interaction limit. Its nonlocality is displayed by plotting the factor F(xc) that gives the enhancement relative to the local density approximation for exchange. We also discuss an apparently harmless order-of-limits problem in the meta-GGA. The performance of this functional is investigated for exchange and correlation energies and shell-removal energies of atoms and ions. Non-self-consistent molecular atomization energies and bond lengths of the TPSS meta-GGA, calculated with GGA orbitals and densities, agree well with those calculated self-consistently. We suggest that satisfaction of additional exact constraints on higher rungs of a ladder of density functional approximations can lead to further progress.

Perdew-Zunger Self-Interaction Correction in Neutral, Protonated, and Deprotonated Water Clusters

Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation

Generalized gradient approximations (GGA's) seek to improve upon the accuracy of the local-spin-density (LSD) approximation in electronic-structure calculations. Perdew and Wang have developed a GGA based on real-space cutoff of the spurious long-range components of the second-order gradient expansion for the exchange-correlation hole. We have found that this density functional performs well in numerical tests for a variety of systems: (1) Total energies of 30 atoms are highly accurate. (2) Ionization energies and electron affinities are improved in a statistical sense, although significant interconfigurational and interterm errors remain. (3) Accurate atomization energies are found for seven hydrocarbon molecules, with a rms error per bond of 0.1 eV, compared with 0.7 eV for the LSD approximation and 2.4 eV for the Hartree-Fock approximation. (4) For atoms and molecules, there is a cancellation of error between density functionals for exchange and correlation, which is most striking whenever the Hartree-Fock result is furthest from experiment. (5) The surprising LSD underestimation of the lattice constants of Li and Na by 3--4 % is corrected, and the magnetic ground state of solid Fe is restored. (6) The work function, surface energy (neglecting the long-range contribution), and curvature energy of a metallic surface are all slightly reduced in comparison with LSD. Taking account of the positive long-range contribution, we find surface and curvature energies in good agreement with experimental or exact values. Finally, a way is found to visualize and understand the nonlocality of exchange and correlation, its origins, and its physical effects.

Identifying Practical DFT Functionals for Predicting 0D and 1D Organic Metal-Halide Hybrids

Low-dimensional organic metal-halide hybrids (LD-OMHHs) are a promising class of materials for applications in optical, magnetic, and quantum information technologies. Computational understanding of these materials necessitates reliable and efficient methods for property prediction, such as predicting the electronic band gap. This work systematically benchmarks three density functional theory (DFT) functionals as well as the impact of spin–orbital coupling on the band gap predictions for 110 experimentally reported LD-OMHHs. Surprisingly, the band gap predicted by the generalized gradient approximation (GGA) aligns similarly or better with experimentally measured values compared to two meta-GGA methods. Furthermore, spin–orbital coupling shows a limited impact on these predictions. The potential existence of significant excitonic effects might explain the discrepancies between meta-GGA and experimental band gaps. Our research also reveals that the direct use of the GGA functional can already be practical and efficient for high-throughput screening of LD-OMHHs with reasonable band gaps.

Phonon Frequencies from a Local Pseudopotential

Short-range correlation in the uniform electron gas: Extended Overhauser model

We use the two-electron wave functions (geminals) and the simple screened Coulomb potential proposed by Overhauser [Can. J. Phys. 73, 683 (1995)] to compute the pair-distribution function $g(r)$ for a uniform electron gas, finding the exact $g(0)$ for this model and extending the results from $g(0)$ to $g(r).$ We find that the short-range $(r<{r}_{s})$ part of this $g(r)$ is in excellent agreement with quantum Monte Carlo simulations for a wide range of electron densities. We are thus able to estimate the value of the second-order ${(r}^{2})$ coefficient of the small interelectronic-distance expansion of the pair-distribution function. The coefficients of the small-$r$ expansion of the spin-resolved ${g}_{\ensuremath{\sigma}{\ensuremath{\sigma}}^{\ensuremath{'}}}(r)$ have density or ${r}_{s}$ dependencies which we parametrize in a way that makes it easy to find their coupling-constant averages. Their spin-polarization or $\ensuremath{\zeta}$ dependencies are estimated from a proposed spin-scaling relation.

Energies of isoelectronic atomic ions from a successful metageneralized gradient approximation and other density functionals

We show that the poor performance of approximate Kohn-Sham (KS) density functional theory for highly charged atomic ions is improved dramatically by ensuring that (i) the exchange functional recovers the correct leading term in the $Z$ expansion of the exchange energy ($Z$ is the nuclear charge) and (ii) the correlation functional is bounded under uniform scaling of the density to the high-density limit---i.e., ${\mathrm{lim}}_{\ensuremath{\lambda}\ensuremath{\rightarrow}\ensuremath{\infty}}{E}_{\mathrm{c}}^{\mathrm{KS}}[{n}_{\ensuremath{\lambda}}]>\ensuremath{-}\ensuremath{\infty}$, where ${n}_{\ensuremath{\lambda}}(\mathbf{r})={\ensuremath{\lambda}}^{3}n(\ensuremath{\lambda}\mathbf{r})$. The performance of several density functionals (BLYP, BP86, VS98, HCTH/407, PBE, PKZB, and TPSS) is compared for the 4-, 10-, and 18-electron atomic series spanning values of $Z$ from 4 to 28. Especially accurate results are obtained with the nonempirical metageneralized gradient approximation of Tao, Perdew, Staroverov, and Scuseria (TPSS). High-$Z$ limits of selected exchange and correlation functionals are evaluated and compared with the exact values.

Symmetry Breaking with the SCAN Density Functional Describes Strong Correlation in the Singlet Carbon Dimer

The SCAN (strongly constrained and appropriately normed) meta-generalized gradient approximation (meta-GGA), which satisfies all 17 exact constraints that a meta-GGA can satisfy, accurately describes equilibrium bonds that are normally correlated. With symmetry breaking, it also accurately describes some sd equilibrium bonds that are strongly correlated. While sp equilibrium bonds are nearly always normally correlated, the C2 singlet ground state is known to be a rare case of strong correlation in an sp equilibrium bond. Earlier work that calculated atomization energies of the molecular sequence B2, C2, O2, and F2 in the local spin density approximation (LSDA), the Perdew-Burke-Ernzerhof (PBE) GGA, and the SCAN meta-GGA, without symmetry breaking in the molecule, found that only SCAN was accurate enough to reveal an anomalous under-binding for C2. This work shows that spin symmetry breaking in singlet C2, the appearance of net up- and down-spin densities on opposite sides (not ends) of the bond, corrects that under-binding, with a small SCAN atomization-energy error more like that of the other three molecules, suggesting that symmetry-breaking with an advanced density functional might reliably describe strong correlation. This article also discusses some general aspects of symmetry breaking, and the insights into strong correlation that symmetry-breaking can bring.

Wave-vector analysis of the jellium exchange-correlation surface energy in the random-phase approximation: Support for nonempirical density functionals

We report a three-dimensional wave-vector analysis of the jellium exchange-correlation (xc) surface energy in the random-phase approximation (RPA). The RPA accurately describes long-range xc effects which are challenging for semilocal approximations, since it includes the universal small-wave-vector behavior derived by Langreth and Perdew. We use these rigorous RPA calculations for jellium slabs to test RPA versions of nonempirical semilocal density-functional approximations for the xc energy. The local spin density approximation displays canceling errors in the small- and intermediate-wave-vector regions. The Perdew-Burke-Ernzerhof generalized gradient approximation improves the analysis for intermediate wave vectors, but remains too low for small wave vectors (implying too-low jellium xc surface energies). The nonempirical metageneralized gradient approximation of Tao, Perdew, Staroverov, and Scuseria gives a realistic wave-vector analysis, even for small wave vectors or long-range effects. We also study the effects of slab thickness and of short-range corrections to the RPA.

Full self-consistency in the Fermi-orbital self-interaction correction

The Perdew-Zunger self-interaction correction cures many common problems associated with semilocal density functionals, but suffers from a size-extensivity problem when Kohn-Sham orbitals are used in the correction. Fermi-L\"owdin-orbital self-interaction correction (FLOSIC) solves the size-extensivity problem, allowing its use in periodic systems and resulting in better accuracy in finite systems. Although the previously published FLOSIC algorithm Pederson et al., J. Chem. Phys. 140, 121103 (2014). appears to work well in many cases, it is not fully self-consistent. This would be particularly problematic for systems where the occupied manifold is strongly changed by the correction. In this paper, we demonstrate a different algorithm for FLOSIC to achieve full self-consistency with only marginal increase of computational cost. The resulting total energies are found to be lower than previously reported non-self-consistent results.

CCDC 902392: Experimental Crystal Structure Determination

An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.

Simple Iterative Construction of the Optimized Effective Potential for Orbital Functionals, Including Exact Exchange

For exchange-correlation functionals that depend explicitly on the Kohn-Sham orbitals, the potential V(xcsigma)(r) must be obtained as the solution of the optimized effective potential (OEP) integral equation. This is very demanding and has limited the use of orbital functionals. We demonstrate that instead the OEP can be obtained iteratively by solving the partial differential equations for the orbital shifts that exactify the Krieger-Li-Iafrate approximation. Unoccupied orbitals do not need to be calculated. Accuracy and efficiency of the method are shown for atoms and clusters using the exact-exchange energy. Counterintuitive asymptotic limits of the exact OEP are presented.

Damped Zaremba-Kohn (dZK) model: van der Waals Corrected Density Functionals for Cylindrical Surfaces