Publications

Diminished gradient dependence of density functionals: Constraint satisfaction and self-interaction correction

The Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation for the exchange-correlation energy functional has two nonempirical constructions, based on satisfaction of universal exact constraints on the hole density or on the energy. We show here that, by identifying one possible free parameter in exchange and a second in correlation, we can continue to satisfy these constraints while diminishing the gradient dependence almost to zero (i.e., almost recovering the local spin density approximation or LSDA). This points out the important role played by the Perdew-Wang 1991 nonempirical hole construction in shaping PBE and later constructions. Only the undiminished PBE is good for atoms and molecules, for reasons we present, but a somewhat diminished PBE could be useful for solids; in particular, the surface energies of solids could be improved. Even for atoms and molecules, a strongly diminished PBE works well when combined with a scaled-down self-interaction correction (although perhaps not significantly better than LSDA). This shows that the undiminished gradient dependence of PBE and related functionals works somewhat like a scaled-down self-interaction correction to LSDA.

Competing stripe and magnetic phases in the cuprates from first principles

Realistic description 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 interplay between the spin, charge, and lattice degrees of freedom. Here, by deploying the recently constructed strongly constrained and appropriately normed (SCAN) density functional, we show how the landscape of competing stripe and magnetic phases can be addressed on a first-principles basis both in the parent insulator YBa₂Cu₃O₆ and the near-optimally doped YBa₂Cu₃O₇ as archetype cuprate compounds. In YBa₂Cu₃O₇, we find many stripe phases that are nearly degenerate with the ground state and may give rise to the pseudogap state from which the high-temperature superconducting state emerges. We invoke no free parameters such as the Hubbard <i>U</i>, which has been the basis of much of the existing cuprate literature. Lattice degrees of freedom are found to be crucially important in stabilizing the various phases.

Theory of nonuniform electronic systems. I. Analysis of the gradient approximation and a generalization that works

A complete wave-vector analysis has been made of the gradient coefficient for the exchange-correlation energy of a nonuniform electronic system. It is shown that the majority of the contribution comes from a very small but universal region of $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ space near the origin. From this it can be concluded that random-phase-approximation-like calculations, like the present one or that of Rasolt and Geldart, which treat this region correctly, are likely to provide accurate results for the gradient coefficient and hence for the energy and structure of a system whose density is truly slowly varying. However, it also shows that the criterion for the validity of the gradient approximation itself is much more severe than previously supposed, so that the usual type of application, to say a surface or bulk material, is incorrect. For the surface case this is verified in unequivocal detail. On the other hand, a generalization of the gradient scheme based on an average slope instead of a local slope is proposed. This gives good agreement with limiting cases where they exist, and rough agreement with the interpolation scheme proposed previously by the authors.

Redox properties of birnessite from a defect perspective

Birnessite, a layered-structure MnO₂, is an earth-abundant functional material with potential for various energy and environmental applications, such as water oxidation. An important feature of birnessite is the existence of Mn(III) within the MnO₂ layers, accompanied by interlayer charge-neutralizing cations. Using first-principles calculations, we reveal the nature of Mn(III) in birnessite with the concept of the small polaron, a special kind of point defect. Further taking into account the effect of the spatial distribution of Mn(III), we propose a theoretical model to explain the structure-performance dependence of birnessite as an oxygen evolution catalyst. We find an internal potential step which leads to the easy switching of the oxidation state between Mn(III) and Mn(IV) that is critical for enhancing the catalytic activity of birnessite. Finally, we conduct a series of comparative experiments which support our model.

First-principles study of band topology for f -electron materials: Ce 3 (Pt/Pd) 3 Bi 4

Coulomb correlation in noncollinear antiferromagnetic α-Mn

We discuss the interplay between magnetic and structural degrees of freedom in elemental Mn. The equilibrium volume is shown to be sensitive to magnetic interactions between the Mn atoms. While the standard generalized gradient approximation underestimates the equilibrium volume, a more accurate treatment of the effects of electronic localization and magnetism is found to solve this longstanding problem. Our calculations also reveal the presence of a magnetic phase in strained $\ensuremath{\alpha}$-Mn that has been reported previously in experiments. This new phase of strained $\ensuremath{\alpha}$-Mn exhibits a noncollinear spin structure with large magnetic moments.

Density functional theory and the band gap problem

In Eq. ( 32), the fmt factor of the integrand should be "e2k~/47r3."In Eq. (51), the second "=" should be a "+."In Eq. ( 5 5 ) , the first " . 1 " should be a '' t ," In Eq. (75), the second "=" should be a minus ("-").In Eq. ( 83), the "u" should be "xc."

A SCAN perspective on the puzzle of the α ↔γ phase transition of Ce

Rethinking CO adsorption on transition-metal surfaces: Effect of density-driven self-interaction errors

Adsorption of the molecule CO on metallic surfaces is an important unsolved problem in Kohn-Sham density functional theory (KS-DFT). We present a detailed study of carbon monoxide adsorption on fcc (111) surfaces of $3d, 4d$, and $5d$ metals using nonempirical semilocal density functionals for the exchange-correlation energy: the local-density approximation (LDA), two generalized gradient approximations or GGAs [Perdew-Burke-Ernzerhof (PBE) and PBE for solids (PBEsol)], and a meta-GGA [strongly constrained and appropriately normed (SCAN) functional]. The typical error pattern (as found earlier for free molecules and for free transition-metal surfaces), in which results improve from LDA to PBE or PBEsol to SCAN, due to the satisfaction of more exact constraints, is not found here. Instead, for CO adsorption on transition-metal surfaces, we find that, while SCAN overbinds much less than LDA, it overbinds slightly more than PBE. Moreover, the tested functionals often predict the wrong adsorption site, as first pointed out for LDA and GGA in the CO/Pt (111) puzzle. This abnormal pattern leads us to suspect that the errors of PBE and SCAN for this problem are density-driven self-interaction errors associated with incorrect charge transfer between molecule and metal surface. We point out that, by the variational principle, overbinding by an approximate functional would be reduced if that functional were applied not to its self-consistent density for the adsorbed system but to an exact or more correct density for that system. Finally, we show for CO on Pt(111) that the site preference is corrected and the adsorption energy is improved for the PBE functional by using not the self-consistent PBE density but a $\text{PBE}+U$ density. The resulting correction to the PBE total energy is much larger for the adsorbed system than for its desorbed components, showing that the error is in the density of the adsorbed system. This seems to solve the Feibelman 2001 CO/Pt(111) puzzle, in principle if not fully in practice.

First-principles study of band topology for f -electron materials: Ce 3 (Pt/Pd) 3 Bi 4

METAL-SURFACE CORRELATION ENERGY FROM THE LIQUID DROP MODEL: A BACK-OF-THE-ENVELOPE ESTIMATE

The liquid drop model applied to the one-electron problem provides an elementary estimate of the correlation contribution to the surface and curvature energies of jellium, in terms of bulk electron density and bulk correlation energy. Within the random phase approximation (RPA), this estimate correctly predicts the size of the surface correlation energy, its strong dependence upon bulk density, and its weak dependence upon surface density profile. The local density approximation (LDA) to RPA predicts surface correlation energies that are far too small, as a consequence of the LDA self-interaction error. Possible implications beyond RPA are discussed. The power and limitations of the liquid drop expansion are illustrated by the example of one-electron jellium spheroids.

Ab initio theory and modeling of water

Water is of the utmost importance for life and technology. However, a genuinely predictive ab initio model of water has eluded scientists. We demonstrate that a fully ab initio approach, relying on the strongly constrained and appropriately normed (SCAN) density functional, provides such a description of water. SCAN accurately describes the balance among covalent bonds, hydrogen bonds, and van der Waals interactions that dictates the structure and dynamics of liquid water. Notably, SCAN captures the density difference between water and ice I<i>h</i> at ambient conditions, as well as many important structural, electronic, and dynamic properties of liquid water. These successful predictions of the versatile SCAN functional open the gates to study complex processes in aqueous phase chemistry and the interactions of water with other materials in an efficient, accurate, and predictive, ab initio manner.

Accurate and numerically efficient r$^2$SCAN meta-generalized gradient approximation

The recently proposed rSCAN functional [J. Chem. Phys. 150, 161101 (2019)] is a regularized form of the SCAN functional [Phys. Rev. Lett. 115, 036402 (2015)] that improves SCAN's numerical performance at the expense of breaking constraints known from the exact exchange-correlation functional. We construct a new meta-generalized gradient approximation by restoring exact constraint adherence to rSCAN. The resulting functional maintains rSCAN's numerical performance while restoring the transferable accuracy of SCAN.

New Meta-Generalized Gradient Approximation for Exchange and Correlation

Initial Fermi orbital descriptors for FLOSIC calculations: The quick-FOD method

Energies of curved metallic surfaces from the stabilized-jellium model

In the liquid-drop model, the total energy of a system is expanded as a sum of volume, surface, and curvature terms. We derive an expression for the curvature energy of a metal in terms of the electron-density profile for a planar surface, and show that the resulting values agree with the fits of calculated or measured total energies to the liquid-drop expansion. In particular, this expansion accurately describes the formation energies of microscopic voids (including monovacancies) in metals. In our calculations, the curvature energy is determined by the bulk density. It is nearly the same for restricted trial density profiles as for self-consistent Kohn-Sham profiles, for the fourth-order gradient expansion as for the exact kinetic energy, and for jellium as for stabilized jellium. We also report Kohn-Sham results for the surface energy and work function. The stabilized-jellium model, while retaining the simplicity and nonempirical character of jellium, gives a significantly more realistic description of the simple metals, especially those with high bulk densities.

Anisotropic Conductivity at the Single‐Molecule Scale

Abstract In most junctions built by wiring a single molecule between two electrodes, the electrons flow along only one axis: between the two anchoring groups. However, molecules can be anisotropic, and an orientation‐dependent conductance is expected. Here, we fabricated single‐molecule junctions by using the electrode potential to control the molecular orientation and access individual elements of the conductivity tensor. We measured the conductance in two directions, along the molecular plane as the benzene ring bridges two electrodes using anchoring groups (upright) and orthogonal to the molecular plane with the molecule lying flat on the substrate (planar). The perpendicular (planar) conductance is about 400 times higher than that along the molecular plane (upright). This offers a new method for designing a reversible room‐temperature single‐molecule electromechanical switch that controllably employs the electrode potential to orient the molecule in the junction in either “ON” or “OFF” conductance states.

Density functionals that are one- and two- are not always many-electron self-interaction-free, as shown for H2+, He2+, LiH+, and Ne2+

The common density functionals for the exchange-correlation energy make serious self-interaction errors in the molecular dissociation limit when real or spurious noninteger electron numbers N are found on the dissociation products. An "M-electron self-interaction-free" functional for positive integer M is one that produces a realistic linear variation of total energy with N in the range of M-1<N<or=M, and so can avoid these errors. This desideratum is a natural generalization to all M of the more familiar one of one-electron self-interaction freedom. The intent of this paper is not to advocate for any functional, but to understand what is required for a functional to be M-electron self-interaction-free and thus correct even for highly stretched bonds. The original Perdew-Zunger self-interaction correction (SIC) and our scaled-down variant of it are exactly one- and nearly two-electron self-interaction-free, but only the former is nearly so for atoms with M>2. Thus all these SIC's produce an exact binding energy curve for H2+, and an accurate one for He2+, but only the unscaled Perdew-Zunger SIC produces an accurate one for Ne2+, where there are more than two electrons on each fragment Ne+0.5. We also discuss LiH+, which is relatively free from self-interaction errors. We suggest that the ability of the original and unscaled Perdew-Zunger SIC to be nearly M-electron self-interaction-free for atoms of all M stems in part from its formal resemblance to the Hartree-Fock theory, with which it shares a sum rule on the exchange-correlation hole of an open system.