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.

Revealing quasi-excitations in the low-density homogeneous electron gas with model exchange-correlation kernels.

Time-dependent density functional theory within the linear response regime provides a solid mathematical framework to capture excitations. The accuracy of the theory, however, largely depends on the approximations for the exchange-correlation (xc) kernels. Away from the long-wavelength (or q = 0 short wave-vector) and zero-frequency (ω = 0) limit, the correlation contribution to the kernel becomes more relevant and dominant over exchange. The dielectric function, in principle, can encompass xc effects relevant to describe low-density physics. Furthermore, besides collective plasmon excitations, the dielectric function can reveal collective electron-hole excitations, often dubbed "ghost excitons." Besides collective excitons, the physics of the low-density regime is rich, as exemplified by a static charge-density wave that was recently found for rs > 69, and was shown to be associated with softening of the plasmon mode. These excitations are seen to be present in much higher density 2D homogeneous electron gases of rs ≳ 4. In this work, we perform a thorough analysis with xc model kernels for excitations of various nature. The uniform electron gas, as a useful model of real metallic systems, is used as a platform for our analysis. We highlight the relevance of exact constraints as we display and explain screening and excitations in the low-density region.

Spin-crossover complexes: Self-interaction correction vs density correction.

Complexes containing a transition metal atom with a 3d4-3d7 electron configuration typically have two low-lying, high-spin (HS) and low-spin (LS) states. The adiabatic energy difference between these states, known as the spin-crossover energy, is small enough to pose a challenge even for electronic structure methods that are well known for their accuracy and reliability. In this work, we analyze the quality of electronic structure approximations for spin-crossover energies of iron complexes with four different ligands by comparing energies from self-consistent and post-self-consistent calculations for methods based on the random phase approximation and the Fermi-Löwdin self-interaction correction. Considering that Hartree-Fock densities were found by Song et al., J. Chem. Theory Comput. 14, 2304 (2018), to eliminate the density error to a large extent, and that the Hartree-Fock method and the Perdew-Zunger-type self-interaction correction share some physics, we compare the densities obtained with these methods to learn their resemblance. We find that evaluating non-empirical exchange-correlation energy functionals on the corresponding self-interaction-corrected densities can mitigate the strong density errors and improves the accuracy of the adiabatic energy differences between HS and LS states.

Tunable band gaps and optical absorption properties of bent MoS2 nanoribbons.

The large tunability of band gaps and optical absorptions of armchair MoS2 nanoribbons of different widths under bending is studied using density functional theory and many-body perturbation GW and Bethe-Salpeter equation approaches. We find that there are three critical bending curvatures, and the non-edge and edge band gaps generally show a non-monotonic trend with bending. The non-degenerate edge gap splits show an oscillating feature with ribbon width n, with a period [Formula: see text], due to quantum confinement effects. The complex strain patterns on the bent nanoribbons control the varying features of band structures and band gaps that result in varying exciton formations and optical properties. The binding energy and the spin singlet-triplet split of the exciton forming the lowest absorption peak generally decrease with bending curvatures. The large tunability of optical properties of bent MoS2 nanoribbons is promising and will find applications in tunable optoelectronic nanodevices.

Self-interaction-corrected Kohn-Sham effective potentials using the density-consistent effective potential method.

Density functional theory (DFT) and beyond-DFT methods are often used in combination with photoelectron spectroscopy to obtain physical insights into the electronic structure of molecules and solids. The Kohn-Sham eigenvalues are not electron removal energies except for the highest occupied orbital. The eigenvalues of the highest occupied molecular orbitals often underestimate the electron removal or ionization energies due to the self-interaction (SI) errors in approximate density functionals. In this work, we adapt and implement the density-consistent effective potential method of Kohut, Ryabinkin, and Staroverov [J. Chem. Phys. 140, 18A535 (2014)] to obtain SI-corrected local effective potentials from the SI-corrected Fermi-Löwdin orbitals and density in the Fermi-Löwdin orbital self-interaction correction scheme. The implementation is used to obtain the density of states (photoelectron spectra) and HOMO-LUMO gaps for a set of molecules and polyacenes. Good agreement with experimental values is obtained compared to a range of SI uncorrected density functional approximations.

Describing adsorption of benzene, thiophene, and xenon on coinage metals by using the Zaremba-Kohn theory-based model.

Semilocal (SL) density functional approximations (DFAs) are widely applied but have limitations due to their inability to incorporate long-range van der Waals (vdW) interaction. Non-local functionals (vdW-DF, VV10, and rVV10) or empirical methods (DFT+D, DFT+vdW, and DFT+MBD) are used with SL-DFAs to account for such missing interaction. The physisorption of a molecule on the surface of the coinage metals (Cu, Ag, and Au) is a typical example of systems where vdW interaction is significant. However, it is difficult to find a general method that reasonably describes both adsorption energy and geometry of even the simple prototypes of cyclic and heterocyclic aromatic molecules such as benzene (C6H6) and thiophene (C4H4S), respectively, with reasonable accuracy. In this work, we present an alternative scheme based on Zaremba-Kohn theory, called DFT+vdW-dZK. We show that unlike other popular methods, DFT+vdW-dZK and particularly SCAN+vdW-dZK give an accurate description of the physisorption of a rare-gas atom (xenon) and two small albeit diverse prototype organic molecules on the (111) surfaces of the coinage metals.

Self-Interaction-Corrected Random Phase Approximation.

The short-range correlation energy of the random phase approximation (RPA) is too negative and is often corrected by local or nonlocal methods. These beyond-RPA corrections usually lead to a mixed performance for thermodynamics and dissociation properties. RPA+ is an additive correction based on density functional approximations that often gives realistic total energies for atoms or solids. RPA+ adds a moderate correction to the ionization energies/electron affinities of RPA but does not yield an improvement beyond RPA for atomization energies of molecules. This incompleteness results in severely underestimated atomization energies just like in RPA. Exchange-correlation kernels within the Dyson equation could simultaneously improve atomization, ionization energies, and electron affinities, but their implementation is computationally less feasible in localized basis set codes. In preceding work ( Phys. Rev. A 100, 2019022515), two of the authors proposed a computationally efficient generalized RPA+ (gRPA+) that changes RPA+ only for spin-polarized systems by making gRPA+ exact for all one-electron densities. gRPA+ was found to yield a large improvement of ionization energies and electron affinities of light atoms over RPA, and a smaller improvement over RPA+. Within this work, we investigate to what extent this improvement transfers to atomization energies, ionization energies, and electron affinities of molecules, using a modified gRPA+ (mgRPA+) method that can be applied in codes with localized basis functions. We thereby aim to understand the applicability of beyond-RPA corrections based on density functional approximations.

Exploring and enhancing the accuracy of interior-scaled Perdew-Zunger self-interaction correction.

The Perdew-Zunger self-interaction correction (PZ-SIC) improves the performance of density functional approximations for the properties that involve significant self-interaction error (SIE), as in stretched bond situations, but overcorrects for equilibrium properties where SIE is insignificant. This overcorrection is often reduced by local scaling self-interaction correction (LSIC) of the PZ-SIC to the local spin density approximation (LSDA). Here, we propose a new scaling factor to use in an LSIC-like approach that satisfies an additional important constraint: the correct coefficient of the atomic number Z in the asymptotic expansion of the exchange-correlation (xc) energy for atoms. LSIC and LSIC+ are scaled by functions of the iso-orbital indicator zσ, which distinguishes one-electron regions from many-electron regions. LSIC+ applied to the LSDA works better for many equilibrium properties than LSDA-LSIC and the Perdew, Burke, and Ernzerhof generalized gradient approximation (GGA), and almost close to the strongly constrained and appropriately normed (SCAN) meta-GGA. LSDA-LSIC and LSDA-LSIC+, however, fail to predict interaction energies involving weaker bonds, in sharp contrast to their earlier successes. It is found that more than one set of localized SIC orbitals can yield a nearly degenerate energetic description of the same multiple covalent bond, suggesting that a consistent chemical interpretation of the localized orbitals requires a new way to choose their Fermi orbital descriptors. To make a locally scaled down SIC to functionals beyond the LSDA requires a gauge transformation of the functional's energy density. The resulting SCAN-sdSIC, evaluated on SCAN-SIC total and localized orbital densities, leads to an acceptable description of many equilibrium properties including the dissociation energies of weak bonds.

Interpretations of ground-state symmetry breaking and strong correlation in wavefunction and density functional theories.

Strong correlations within a symmetry-unbroken ground-state wavefunction can show up in approximate density functional theory as symmetry-broken spin densities or total densities, which are sometimes observable. They can arise from soft modes of fluctuations (sometimes collective excitations) such as spin-density or charge-density waves at nonzero wavevector. In this sense, an approximate density functional for exchange and correlation that breaks symmetry can be more revealing (albeit less accurate) than an exact functional that does not. The examples discussed here include the stretched H2 molecule, antiferromagnetic solids, and the static charge-density wave/Wigner crystal phase of a low-density jellium. Time-dependent density functional theory is used to show quantitatively that the static charge-density wave is a soft plasmon. More precisely, the frequency of a related density fluctuation drops to zero, as found from the frequency moments of the spectral function, calculated from a recent constraint-based wavevector- and frequency-dependent jellium exchange-correlation kernel.

The Fermi-Löwdin self-interaction correction for ionization energies of organic molecules.

(Semi)-local density functional approximations (DFAs) suffer from self-interaction error (SIE). When the first ionization energy (IE) is computed as the negative of the highest-occupied orbital (HO) eigenvalue, DFAs notoriously underestimate them compared to quasi-particle calculations. The inaccuracy for the HO is attributed to SIE inherent in DFAs. We assessed the IE based on Perdew-Zunger self-interaction correction on 14 small to moderate-sized organic molecules relevant in organic electronics and polymer donor materials. Although self-interaction corrected DFAs were found to significantly improve the IE relative to the uncorrected DFAs, they overestimate. However, when the self-interaction correction is interiorly scaled using a function of the iso-orbital indicator zσ, only the regions where SIE is significant get a correction. We discuss these approaches and show how these methods significantly improve the description of the HO eigenvalue for the organic molecules.

Examining the order-of-limits problem and lattice constant performance of the Tao-Mo functional.

In their recent communication, Tao and Mo [Phys. Rev. Lett. 117, 073001 (2016)] presented a semi-local density functional derived from the density matrix expansion of the exchange hole localized by a general coordinate transformation. We show that the order-of-limits problem present in the functional, dismissed as harmless in the original publication, causes severe errors in predicted phase transition pressures. We also show that the claim that lattice volume prediction accuracy exceeds that of existing similar functionals was based on comparison to reference data that miss anharmonic zero-point expansion and consequently overestimates accuracy. By highlighting these omissions, we give a more accurate assessment of the Tao-Mo functional and show a possible direction for resolving the order-of-limits problem.

Chemisorption Can Reverse Defect-Defect Interaction on Heterogeneous Catalyst Surfaces.

Atomic-level understanding of roles of defect-defect interaction in the bonding of adsorbates on surfaces is critical for tailoring catalysts atom-by-atom and designing new catalysts. Here, from first-principles calculations, we propose a microscopic mechanism for the role of sulfur vacancy-vacancy interaction in hydrogen bonding on surfaces of MoS2, a nonprecious two-dimensional catalyst for hydrogen evolution reaction. We find that before hydrogen adsorption the interaction of a sulfur vacancy with others is repulsive, originating from the antibonding-like coupling of occupied in-gap vacancy states. When the sulfur vacancy is adsorbed by a hydrogen atom, its interaction with other unadsorbed sulfur vacancies becomes attractive, which can be attributed to the decoupling of repulsive vacancy-vacancy interactions and the occupying of bonding-like coupling states between the in-gap vacancy states that are unoccupied before hydrogen adsorption. This repulsive-to-attractive reverse of vacancy-vacancy interaction reduces the hydrogen adsorption energy and explains why the hydrogen adsorption energy decreases with increasing sulfur vacancy concentration. The emerging picture enables a more general discussion of local defect effects on the adsorption of various adsorbates at different surfaces, providing guidance to improve catalytic performance through defect engineering.

Reducing the Many-Electron Self-Interaction Error in the Second-Order Screened Exchange Method.

Preserving the beneficial properties of the second-order screened exchange (SOSEX) method, such as its freedom from one-body self-correlation error, and its seamless treatment of long-range dispersion interaction, we construct new nonlocal functionals by down-scaling the higher-order terms in the SOSEX series to reduce the many-body self-correlation error in molecular systems. Our down-scaled SOSEX (dsSOSEX) and scaled equation SOSEX (seSOSEX) approaches deliver considerably more accurate noncovalent interaction energies, reaction energies, and barrier heights than the original SOSEX method. The dsSOSEX approach improves on the description of medium- and long-range correlation, for example, in isogyric processes, while the seSOSEX approach improves on the description of processes with short- and medium-range rearrangement in the electronic structure, such as atomization. The He2+ potential energy curve shows that the many-body self-correlation error is slightly smaller in the dsSOSEX method than in the seSOSEX approach. Furthermore, the H2 potential energy curve reveals that the static correlation error can also be reduced at medium range by the dsSOSEX and seSOSEX schemes. As our dsSOSEX method provides a better description of medium- and long-range correlation, it generally leads to more accurate energetics than the seSOSEX method; hence it should be preferred over the latter. We compare our results to other empirical and nonempirical direct random phase approximation (dRPA) and beyond-dRPA methods and also discuss the possibilities for further development.

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.

Adiabatic Connection without Coupling Constant Integration.

Using a second-order approximation to Random Phase Approximation renormalized (RPAr) many-body perturbation theory for the interacting density-density response function, we have developed a so-called higher-order terms (HOT) approximation for the correlation energy. In combination with the first-order RPAr correction, our new method faithfully captures the infinite-order correlation for a given exchange-correlation kernel, yielding errors of the total correlation energy on the order of 1% or less for most systems. For exchange-like kernels, our new method has the further benefit that the coupling-strength integration can be completely eliminated resulting in a modest reduction in computational cost compared to the traditional approach. When the correlation energy is accurately reproduced by the HOT approximation, structural properties and energy differences are also accurately reproduced, as we demonstrate for several periodic solids and some molecular systems. Energy differences involving fragmentation are challenging for the HOT method, however, due to errors that may not cancel between a composite system and its constituent pieces.

Negative Poisson's ratio in 1T-type crystalline two-dimensional transition metal dichalcogenides.

Materials with a negative Poisson's ratio, also known as auxetic materials, exhibit unusual and counterintuitive mechanical behaviour-becoming fatter in cross-section when stretched. Such behaviour is mostly attributed to some special re-entrant or hinged geometric structures regardless of the chemical composition and electronic structure of a material. Here, using first-principles calculations, we report a class of auxetic single-layer two-dimensional materials, namely, the 1T-type monolayer crystals of groups 6-7 transition-metal dichalcogenides, MX2 (M=Mo, W, Tc, Re; X=S, Se, Te). These materials have a crystal structure distinct from all other known auxetic materials. They exhibit an intrinsic in-plane negative Poisson's ratio, which is dominated by electronic effects. We attribute the occurrence of such auxetic behaviour to the strong coupling between the chalcogen p orbitals and the intermetal t2g-bonding orbitals within the basic triangular pyramid structure unit. The unusual auxetic behaviour in combination with other remarkable properties of monolayer two-dimensional materials could lead to novel multi-functionalities.

Understanding band gaps of solids in generalized Kohn-Sham theory.

The fundamental energy gap of a periodic solid distinguishes insulators from metals and characterizes low-energy single-electron excitations. However, the gap in the band structure of the exact multiplicative Kohn-Sham (KS) potential substantially underestimates the fundamental gap, a major limitation of KS density-functional theory. Here, we give a simple proof of a theorem: In generalized KS theory (GKS), the band gap of an extended system equals the fundamental gap for the approximate functional if the GKS potential operator is continuous and the density change is delocalized when an electron or hole is added. Our theorem explains how GKS band gaps from metageneralized gradient approximations (meta-GGAs) and hybrid functionals can be more realistic than those from GGAs or even from the exact KS potential. The theorem also follows from earlier work. The band edges in the GKS one-electron spectrum are also related to measurable energies. A linear chain of hydrogen molecules, solid aluminum arsenide, and solid argon provide numerical illustrations.

Construction of a Spin-Component Scaled Dual-Hybrid Random Phase Approximation.

Recently, we have constructed a dual-hybrid direct random phase approximation method, called dRPA75, and demonstrated its good performance on reaction energies, barrier heights, and noncovalent interactions of main-group elements. However, this method has also shown significant but quite systematic errors in the computed atomization energies. In this paper, we suggest a constrained spin-component scaling formalism for the dRPA75 method (SCS-dRPA75) in order to overcome the large error in the computed atomization energies, preserving the good performance of this method on spin-unpolarized systems at the same time. The SCS-dRPA75 method with the aug-cc-pVTZ basis set results in an average error lower than 1.5 kcal mol-1 for the entire n-homodesmotic hierarchy of hydrocarbon reactions (RC0-RC5 test sets). The overall performance of this method is better than the related direct random phase approximation-based double-hybrid PWRB95 method on open-shell systems of main-group elements (from the GMTKN30 database) and comparable to the best O(N4)-scaling opposite-spin second-order perturbation theory-based double-hybrid methods like PWPB95-D3 and to the O(N5)-scaling RPAX2@PBEx method, which also includes exchange interactions. Furthermore, it gives well-balanced performance on many types of barrier heights similarly to the best O(N5)-scaling second-order perturbation theory-based or spin-component scaled second-order perturbation theory-based double-hybrid methods such as XYG3 or DSD-PBEhB95. Finally, we show that the SCS-dRPA75 method has reduced self-interaction and delocalization errors compared to the parent dRPA75 method and a slightly smaller static correlation error than the related PWRB95 method.

Application of a Dual-Hybrid Direct Random Phase Approximation to Water Clusters.

In water clusters, there is a delicate balance of van der Waals interactions and hydrogen bonds. Although semilocal and nonlocal density functional approximations have been recently routinely applied to water in various phases, the accurate description of hydrogen bonds remains a challenge. The most popular density functional approaches fail to predict the correct ordering of the energies of water clusters. To illustrate the required accuracy, the CCSD(T) complete basis set extrapolated dissociation energy difference between the two lowest energy hexamer structures is 0.06 kcal mol(-1) per monomer. In this work, we assessed interaction energies in neutral and ionic water clusters with various density functionals with or without van der Waals correction. Generally, van der Waals approximations play a significant role in clusters with increasing size, while hybrid functionals improve the description of hydrogen bonds. Despite these general trends, none of the tested density functional approximations with or without van der Waals correction and exact exchange mixing can lead to a uniform performance for neutral and ionic water clusters. The recently constructed dual-hybrid dRPA75 approximation is a successful combination of exact and semilocal exchange, and nonlocal correlation in its energy, while utilizing a high fraction of exact exchange. We have shown that the dRPA75 method has a systematic error, which can be efficiently compensated for by the aug-cc-pVTZ basis set for small- and medium-sized water clusters.

Accurate first-principles structures and energies of diversely bonded systems from an efficient density functional.

One atom or molecule binds to another through various types of bond, the strengths of which range from several meV to several eV. Although some computational methods can provide accurate descriptions of all bond types, those methods are not efficient enough for many studies (for example, large systems, ab initio molecular dynamics and high-throughput searches for functional materials). Here, we show that the recently developed non-empirical strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation (meta-GGA) within the density functional theory framework predicts accurate geometries and energies of diversely bonded molecules and materials (including covalent, metallic, ionic, hydrogen and van der Waals bonds). This represents a significant improvement at comparable efficiency over its predecessors, the GGAs that currently dominate materials computation. Often, SCAN matches or improves on the accuracy of a computationally expensive hybrid functional, at almost-GGA cost. SCAN is therefore expected to have a broad impact on chemistry and materials science.