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Accurate and efficient calculation of optical response properties of solid materials is still challenging. We present a meta-generalized gradient approximation (metaGGA) density functional based time-dependent and dielectric function dependent method for calculating optical absorption, exciton binding energy and intrinsic exciton lifetime for bulk solids and two-dimensional (2D) monolayer materials. This method uses advanced metaGGA functionals to describe the band structures, and a dielectric function mBSE (model Bethe-Salpeter equation) to capture the screening effect accurately and efficiently and the interaction between electrons and holes. The calculated optical absorption spectra of bulk Si, diamond, SiC, MgO, and monolayer MoS2 qualitatively agree with experimental results. The exciton binding energies of the first prominent peak in the optical absorption spectra of the direct band gap solids Ar, NaCl and MgO from mBSE qualitatively agree with those from standard GW-BSE. For monolayer MoS2, mBSE predicts quantitatively accurate binding energy for the first prominent peak, better than GW-BSE does. The calculated intrinsic exciton lifetimes for materials considered here show magnitudes of several nanoseconds for most bright excitons. The presented mtaGGA-mBSE method is established as a computationally efficient alternative for optical properties of materials with an overall qualitative accuracy., Comment: 20 pages

The layered transition metal dichalcogenide 1T-TiSe$_2$ is of great research interest, having intriguing properties of charge density waves (CDW) and superconductivity under doping or pressurizing. The monolayer form of 1T-TiSe$_2$ also shows a CDW with a higher transition temperature T_c than the bulk, indicating a stronger CDW interaction. By using the meta-generalized gradient approximation (metaGGA)-based model Bethe-Salpeter Equation (BSE) and many-body perturbation GW+BSE methods, we calculate the exciton binding energies and electron energy loss spectrum (EELS) for the 1T-TiSe$_2$ monolayer under different in-plane biaxial strains. We find that even without strain the 1T-TiSe$_2$ monolayer can have negative exciton energies at the Brillouin zone boundary point M, with a binding energy larger than the gap. The calculated EELS reinforces this picture, indicating EI (exciton insulator) states in 1T-TiSe$_2$ monolayer even without strain. The Wannier-Mott formula calculations of exciton binding energy corroborate results from GW+BSE. Small compressive strains enhance the EI state, and for tensile strains slightly less than 3%, the EI state in this monolayer persists. At large tensile strains, the material makes a transition to a normal semiconductor. Our results provide important information for understanding the quantum nature of this two-dimensional (2D) material. Our results from the standard G0W0@PBE+SOC+U+BSE approach are not qualitatively different from those of a more computationally efficient metaGGA-based SCAN+SOC+U+mBSE+$f_{xc}^{loc}$ approach that employs a model BSE.

Quantum spin Hall (QSH) insulators have attracted intensive experimental and theoretical studies due to their beneficial applications in spintronic devices. Density functional theory (DFT) meets challenges when describing the electronic structure of QSH materials. Only the Heyd-Scuseria-Ernzerhof (HSE06) with spin-orbit coupling (SOC) is effective in revealing the band opening in the typical QSH 1T`-WTe2, but with increased computational demands. Here, using DFT, Wannier function simulations, the screened hybrid HSE06 functional, and first-principles-based many body perturbation theory GW, we investigate the sensitive electronic structure in monolayer 1T`-WTe2, with advanced meta-generalized gradient (meta-GGA) density functional approximations. The success of the recent SCAN and r2SCAN meta-GGAs left their predecessor meta-GGA made very simple (MVS) ignored by the scientific community. Largely unnoticed were the increased band gaps of MVS compared to any semilocal approximation including SCAN. We find that the non-empirical MVS approximation yields a positive fundamental band gap, without any help from exact exchange, Hubbard U, or SOC correction. We explain the success of the meta-GGA MVS for the band gap in 1T`-WTe2 by presenting two working mechanisms in meta-GGA approximations. Besides, we point out the difficulty of using G0W0 for 1T`-WTe2. Although the single shot GW correction with an MVS reference yields a smaller band gap than GW with PBE, the G0W0@MVS is still not suitable for simulating 1T`-WTe2, due to its negative band gap. These DFT and beyond DFT results highlight the importance of meta-GGAs and novel construction schemes with enhanced kinetic energy density dependence. The MVS approximation re-appears as an appealing alternative for accurately describing 1T`-WTe2, paving an efficient way for exploring other two-dimensional QSH materials in high-throughput calculations., Comment: 15 pages, 5 figures, and Supplementary Materials

Monolayer molybdenum disulfide ($\mathrm{MoS_2}$) under strain has many interesting properties and possible applications in technology. A recent experimental study examined the effect of strain on the bandgap of monolayer $\mathrm{MoS_2}$ on a mildly curved graphite surface, reporting that under biaxial strain with a Poisson's ratio of 0.44, the bandgap decreases at a rate of 400 meV/\% strain. In this work, we performed density functional theory (DFT) calculations for a free-standing $\mathrm{MoS_2}$ monolayer, using the generalized gradient approximation (GGA) PBE, the hybrid functional HSE06, and many-body perturbation theory with the GW approximation using PBE wavefunctions (G0W0@PBE). For the unstrained monolayer, we found a standard level of agreement for the bandgap between theory and experiment. For biaxial strain at the experimental Poisson's ratio, we found that the bandgap decreases at rates of 63 meV/\% strain (PBE), 73 meV/\% strain (HSE06), and 43 meV/\% strain (G0W0@PBE), which are significantly smaller than the experimental rate. We also found that PBE predicts a similarly smaller rate (90 meV/\% strain) for a different Poisson's ratio of 0.25. Spin-orbit correction (SOC) has little effect on the gap or its strain dependence. The strong disagreement between theory and experiment may reflect an unexpectedly strong effect of the substrate on the strain dependence of the gap. Additionally, we observed a transition from a direct to an indirect bandgap under strain, and (under an equal biaxial strain of 10\%) a semiconductor-to-metal transition, consistent with previous theoretical work.

Charge density waves (CDWs) in transition metal dichalcogenides are the subject of growing scientific interest due to their rich interplay with exotic phases of matter and their potential technological applications. Here, using density functional theory with advanced meta-generalized gradient approximations (meta-GGAs) and linear response time-dependent density functional theory (TDDFT) with state-of-the-art exchange-correlation kernels, we investigate the electronic, vibrational, and optical properties in 1T-TiSe2 with and without CDW. In both bulk and monolayer TiSe2, the electronic bands and phonon dispersions in either normal (semi-metallic) or CDW (semiconducting) phase are described well via meta-GGAs, which separate the valence and conduction bands just as HSE06 does but with significantly more computational feasibility. Instead of the underestimated gap with standard exchange-correlation approximations and the overestimated gap with screened hybrid functional HSE06, the band gap of the monolayer TiSe2 CDW phase calculated by the meta-GGA MVS (151 meV) is consistent with the angle-resolved photoemission spectroscopy (ARPES) gap of 153 meV measured at 10 K. In addition, the gap of bulk TiSe2 CDW phase reaches 67 meV within the TASK approximation, close to the ARPES gap of 82 meV. Regarding excitations of many-body nature, for bulk TiSe2 in normal and CDW phases, the experimentally observed humps of electron energy loss spectroscopy and plasmon peak are successfully reproduced in TDDFT, without an obvious kernel dependence. To unleash the full scientific and technological potential of CDWs in transition metal dichalcogenides, the chemical doping, heterostructure engineering, and pump-probe techniques are needed. Our study opens the door to simulating these complexities in CDW compounds from first principles by revealing meta-GGAs as an accurate low-cost alternative to HSE06., Comment: 22 pages, 4 figures, Supplementary Materials

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-GGA functional, we were able to achieve accurate phonon spectra of an insulating cuprate YBa$_2$Cu$_3$O$_6$, 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 PBE 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 YBa2 Cu3 O6 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 SCAN/r2SCAN, are also compared and discussed., Comment: arXiv admin note: text overlap with arXiv:2210.06569

Time-dependent density functional theory (TDDFT) 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 ($\omega=0$) 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.'' Beside collective excitons, the physics in the low-density regime is rich, as exemplified by a static charge-density wave that was recently found for $r_\mathrm{s} > 69$, and was shown to be associated with softening of the plasmon mode. These excitations are seen to be present in much higher density 2D HEGs, of $r_\mathrm{s} \geq 4$. 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 of our analysis. We highlight the relevance of exact constraints as we display and explain screening and excitations in the low-density region., Comment: Updated in response to reviewer report - see especially new figures in App. A, and new Apps. B and C

Two-dimensional (2D) transition metal dichalcogenide (TMD) materials have versatile electronic and optical properties. TMD nanoribbons show interesting properties due to reduced dimensionality, quantum confinement, and edge states. Tang et al. showed that the edge bands evolved with bending can tune the optical properties for various widths of TMD nanoribbons. Defects are commonly present in 2D TMD materials, and can dramatically change the material properties. In this following work, we investigate the interaction between the edge and the defect states in WS2 nanoribbons with line defects under different bending conditions, using density functional theory (DFT). We reveal interesting semiconducting-to-metallic phase transitions, suggesting potential applications in nano-electronics or molecular electronics. We also calculate the optical absorption of the nanoribbons with different defect positions with the many-body GW-BSE (Bethe-Salpeter equation) approach, revealing a tunable optical spectrum and diverse exciton states in the defected TMD nanoribbons.

A WSe2 monolayer of 1T' phase is a large band gap quantum spin Hall insulator, supporting dissipationless charge and spin transports through the topologically protected edge states. In this work, we explore the nanoribbon forms of 1T' phase WSe2 by first-principles density functional calculations and the many-body perturbation GW and Bethe-Salpeter equation method. We found that the 1T' WSe2 nanoribbon can show topological edge states with a ribbon width of ~4-6 nm. Those edge bands show crossing through the Fermi level an odd number of times, with one kind of spin-polarization connecting the valence band continuum and conduction band continuum. The topological features of the edge bands hold even under small and medium bending in the nanoribbon, while large bending induces large band splitting, resulting in a topological switch-off in the edge bands. The semiconducting 1T' WSe2 nanoribbon shows a large tunability with bending in optical absorption spectra and exciton states. The lowest-energy exciton is changed from optically dark in the flat nanoribbon to bright in the bent nanoribbons. These properties in the 1T' WSe2 nanoribbons suggest potential applications in controllable quantum electronics and exciton-based quantum information processes., Comment: 15pages

A WSe$_2$ monolayer shows many interesting properties due to its spin-orbit coupling induced spin splitting in bands around the Fermi level and the spin-valley configuration. The orientation of the spin polarization in the relevant bands is crucial for the nature of exciton states and the optical valley selectivity. In this work, we studied the WSe$_2$ nanoribbons under different mechanical bending curvatures and electron/hole doping with density functional theory and their optical absorption and excitonic states with many-body perturbation GW and BSE (Bethe-Salpeter equation) methods. We found that the WSe$_2$ nanoribbons can exhibit an enhanced SOC effect and a spatially varying spin polarization in bands around the Fermi level under bending. The spin-polarization can show an anisotropy (or asymmetry) in those nearly degenerate bands, leading to a controllable magnetism via bending and electron/hole doping to the nanoribbons, suggesting a potential application in compact and controllable magnetic nanodevices and spintronics. The optical absorption spectrum of the nanoribbon presents a large tunability with bending within the near infrared region of about 0.4 to 1.5 eV, showing an enhanced absorption at a large bending condition. The exciton states generally show mixed or various spin configuration in the electron and hole pairs that are controlled by bending, potentially useful for applications in spin-based quantum information processes.

A monolayer of CrI3 has an amazing ferromagnetic ground-state. In this work, we calculate band structures and magnetic moments of tensile-strained and bent zigzag CrI3 nanoribbons with density functional theory. The edge iodine atoms form flat low-lying conduction bands and couple with chromium atoms ferromagnetically, while the non-edge iodine atoms weakly couple antiferromagnetically. CrI3 nanoribbons have a nearly equal preference for the out-of-plane and in-plane magnetic moment configurations, slightly favoring the in-plane one. We also calculate optical absorption with many-body perturbation GW-BSE (Bethe-Salpeter equation) and investigate magneto-optical properties, including magnetic dichroism, Faraday and magneto-optical Kerr effects. The low-energy dark excitons are mainly from transitions between electrons and holes with unlike spins and are non-Frenkel-like, while the bright excitons have mixed spin configurations. Tensile strains and bending manifestly modulate the absorption spectra and magneto-optical properties of CrI3 nanoribbons within a technologically important photon energy-range of ~1.0-2.0 eV, suggesting a potential application in tunable magnetic optoelectronics., Comment: 17 pages, 5 figures

We have assessed mechanical bending as a powerful controlling tool for the electronic structure and optical properties of phosphorene nanoribbons. We use state-of-the-art density functional approximations in our work. The overall performance of the recently developed meta-generalized gradient approximation (meta-GGA) mTASK [Phys. Rev. Mater. \textbf{5}, 063803 (2021)] functional establishes the method as a useful alternative to the screened hybrid HSE06 for better band gaps of phosphorene nanoribbons. We present a detailed and novel analysis to interpret the optical absorption of bent phosphorene nanoribbons using the GW-Bethe-Salpeter approximation (GW-BSE). We demonstrate the important role of the unoccupied in-gap state and conclude that this in-gap state in armchair nanoribbons introduced by bending can significantly affect the properties of low-energy excitons, and add some useful opportunities for applications as optoelectronic devices.

The large tunability of band gaps and optical absorptions of armchair MoS$_2$ 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 two 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 delta_n=3, 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 MoS$_2$ nanoribbons is promising and will find applications in tunable optoelectronic nanodevices.

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(DCEP) method of Kohut, Ryabinkin, and Staroverov to obtain SI corrected local effective potentials from the SI corrected Fermi-L\"owdin orbitals and density in the FLOSIC 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., Comment: 8 pages, 3 figures

We propose a spatially and temporally nonlocal exchange-correlation (xc) kernel for the spin-unpolarized fluid phase of ground-state jellium, for use in time-dependent density functional and linear response calculations. The kernel is constructed to satisfy known properties of the exact xc kernel, to accurately describe the correlation energies of bulk jellium, and to satisfy frequency-moment sum rules at a wide range of bulk jellium densities, including those low densities that display strong correlation and symmetry breaking. These effects are easier to understand in the simple jellium model than in real systems. All exact constraints satisfied by the recent MCP07 kernel [A. Ruzsinszky, et al., Phys. Rev. B 101, 245135 (2020)] are maintained in the new revised MCP07 (rMCP07) kernel, while others are added. The revision $f_\mathrm{xc}^\mathrm{rMCP07}(q,\omega)$ differs from MCP07 only for non-zero frequencies $\omega$. Only at densities much lower than those of real bulk metals is the frequency dependence of the kernel important for the correlation energy of jellium. As the wavevector $q$ tends to zero, the kernel has a $-4\pi \alpha(\omega)/q^2$ divergence whose frequency-dependent ultranonlocality coefficient $\alpha(\omega)$ vanishes in jellium, and is predicted by rMCP07 to be extremely small for the real metals Al and Na.}, Comment: (1st revision) Changes to the TC21 model, new App. F discussing numerical methods. (2nd revision) Revisions in response to peer comments. Refocused discussion around building a kernel for jellium, rather than for metals/materials. (3rd revision) Name change of kernel, TC21 --> rMCP07; added details of QMC calculations; added CP07 and Richardson-Ashcroft correlation energies

In the framework of time-dependent density functional theory (TDDFT), the exact exchange-correlation (xc) kernel $f_{xc}(n,q,\omega)$ determines the ground-state energy, excited-state energies, lifetimes, and the time-dependent linear density response of any many-electron system. The recently developed MCP07 xc kernel $f_{xc}(n,q,\omega)$ of A. Ruzsinszky et al. [Phys. Rev. B 101, 245135 (2020)] yields excellent uniform electron gas (UEG) ground-state energies and plausible plasmon lifetimes. As MCP07 is constructed to describe $f_{xc}$ of the UEG, it cannot capture optical properties of real materials. To verify this claim, we follow Nazarov et al. [Phys. Rev. Lett. 102, 113001 (2009)] to construct the long-range, dynamic xc kernel, $\lim_{q\to 0}f_{xc}(n,q,\omega) = -\alpha(\omega)e^2/q^2$, of a weakly inhomogeneous electron gas, using MCP07 and other common xc kernels. The strong wavevector and frequency dependence of the "ultranonlocality" coefficient $\alpha(\omega)$ is demonstrated for a variety of simple metals and semiconductors. We examine how imposing exact constraints on an approximate kernel shapes $\alpha(\omega)$. Comparisons to kernels derived from correlated-wavefunction calculations are drawn., Comment: Includes new kernels: a novel QV-MCP07 hybrid kernel that better estimates ultranonlocality, and the LRC and 2p2h kernels as better references for ultranonlocality. Miscellaneous typographical/syntactic changes

The recent TASK meta-GGA density functional [Phys. Rev. Research, 1, 033082 (2019)] is constructed with an enhanced nonlocality in the generalized Kohn-Sham scheme, and therefore harbors great opportunities for band gap prediction. Although this approximation was found to yield excellent band gaps of bulk solids, this accuracy cannot be straightforwardly transferred to low-dimensional materials. The reduced screening of these materials results in larger band gaps compared to their bulk counterparts, as an additional barrier to overcome. In this work, we demonstrate how the alteration of exact physical constraints in this functional affects the band gaps of monolayers and nanoribbons, and present accurate band gaps competing with the HSE06 approximation. In order to achieve this goal, we have modified the TASK functional (a) by changing the tight upper-bound for one or two-electron systems ($h_X^0$) from 1.174 to 1.29 (b) by changing the limit of interpolation function $f_X (\alpha \rightarrow \infty$) of the TASK functional that interpolates the exchange enhancement factor $F_X (s,\alpha)$ from $\alpha=$ 0 to 1. The resulting modified TASK (mTASK) was tested for various materials from 3D to 2D to 1D (nanoribbons), and was compared with the results of the higher-level hybrid functional HSE06 or with the G$_0$W$_0$ approximation within many-body perturbation theory. We find that mTASK greatly improves the band gaps and band structures of 2D and 1D systems, without significantly affecting the accuracy of the original TASK for the bulk 3D materials, when compared to the PBE-GGA and SCAN meta-GGA. We further demonstrate the applicability of mTASK by assessing the band structures of TMD nanoribbons with respect to various bending curvatures.

The Perdew-Zunger self-interaction correction(PZ-SIC) improves the performance of density functional approximations(DFAs) 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 LSIC, local scaling 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 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 z{\sigma}, which distinguishes one-electron regions from many-electron regions. LSIC+ applied to LSDA works better for many equilibrium properties than LSDA-LSIC and the Perdew, Burke, and Ernzerhof(PBE) generalized gradient approximation(GGA), and almost as well as the strongly constrained and appropriately normed(SCAN) meta-GGA. LSDA-LSIC and LSDA-LSIC+, however, both 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 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., Comment: 12 pages, 8 figures

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, rVV10) or empirical methods (DFT+D, DFT+vdW, 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 like benzene (C6H6) and thiophene (C4H4S) respectively, with reasonable accuracy. In this work, we present an alternative scheme based on Zaremba-Kohn's theory, called DFT+vdW-dZK. We show that, unlike other popular methods, DFT+vdW-dZK and particularly SCAN+vdW-dZK gives an accurate description of the physisorption of a rare-gas atom (Xe) and two small albeit diverse prototype organic molecules on the (111) surfaces of the coinage metals.

(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 corrections on 14 small to moderate-sized organic molecules relevant in organic electronics and polymer donor materials. Though 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 z{\sigma}, 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.

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 non-zero 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 H$_2$ molecule, antiferromagnetic solids, and the static charge-density wave/Wigner crystal phase of a low-density jellium. It is shown that (and in what sense) the static charge density wave is a soft plasmon.

We performed density functional calculations to estimate the formation energies of intermetallic alloys. We used two semilocal approximations, the generalized gradient approximation (GGA) by Perdew-Burke-Ernzerhof (PBE) and the strongly constrained and appropriately normed (SCAN) meta-GGA. In addition, we utilized two nonlocal DFT functionals, the hybrid HSE06, and the state-of-the-art random phase approximation (RPA). The nonlocal functionals such as HSE06 and RPA yield accurate formation energies of binary alloys with completely-filled d-band metals, where semilocal functionals underperform. The accuracy at the nonlocal functionals is greatly reduced when a partially-filled d-band metal is present in an alloy, while PBE-GGA outperforms in these cases. We show that the accurate prediction of formation energies by any DFT method depends on its ability to predict the accurate electronic properties, e.g., valence d-band contribution to the density of states (DOS). The SCAN meta-GGA often corrects the PBE-DOS, however, it does not provide accurate formation energies compared to PBE. This is assumed to be due to the lack of proper error cancellation that should be expected due to the similar bulk nature of both alloys and their constituents, which may improve with the modification of meta-GGA ingredients. RPA yields too negative formation energies of alloys with partially-filled d-band metals. RPA results can be corrected by restoring the exchange-correlation kernel, thereby improving the short-range electron-electron correlation in metallic densities.

According to time-dependent density functional theory, the exact exchange-correlation kernel f$_{xc}$(n, q, $\omega$) determines not only the ground-state energy but also the excited-state energies/lifetimes and time-dependent linear density response of an electron gas of uniform density n $=$ 3/(4$\pi$r$^3_s$). Here we propose a parametrization of this function based upon the satisfaction of exact constraints. For the static ($\omega$ = 0) limit, we modify the model of Constantin and Pitarke at small wavevector q to recover the known second-order gradient expansion, plus other changes. For all frequencies $\omega$ at q $=$ 0, we use the model of Gross, Kohn, and Iwamoto. A Cauchy integral extends this model to complex $\omega$ and implies the standard Kramers-Kronig relations. A scaling relation permits closed forms for not only the imaginary but also the real part of f$_{xc}$ for real $\omega$. We then combine these ingredients by damping out the $\omega$ dependence at large q in the same way that the q dependence is damped. Away from q $=$ 0 and $\omega$ $=$ 0, the correlation contribution to the kernel becomes dominant over exchange, even at r$_s$ $=$ 4, the valence electron density of metallic sodium. The resulting correlation energy from integration over imaginary $\omega$ is essentially exact. The plasmon pole of the density response function is found by analytic continuation of f$_{xc}$ to $\omega$ just below the real axis, and the resulting plasmon lifetime first decreases from infinity and then increases as q grows from 0 toward the electron-hole continuum. A static charge-density wave is found for r$_s$ $>$ 69, and shown to be associated with softening of the plasmon mode. The exchange-only version of our static kernel confirms Overhauser's 1968 prediction that correlation enhances the charge-density wave., Comment: 20 pages including 11 figures

In their recent communication [Phys. Rev. Lett., 117, 073001 (2016)] Tao and Mo presented a semi-local density functional derived from the density matrix expansion of the exchange hole localised 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 misses 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 simple route to resolving the problems.

Small-wavevector excitations in Coulomb-interacting systems can be decomposed into the high-energy collective longitudinal plasmon and the low-energy single-electron excitations. At the critical wavevector and corresponding frequency where the plasmon branch merges with the single-electron excitation region, the collective energy of the plasmon dissipates into single electron-hole excitations. The jellium model provides a reasonable description of the electron-energy-loss spectrum (EELS) of metals close to the free-electron limit. The random phase approximation (RPA) is exact in the high-density limit but can capture the plasmonic dispersion reasonably even for densities with rs > 1. RPA and all beyond-RPA methods investigated here, result in a wrong infinite plasmon lifetime for a wavevector smaller than the critical one where the plasmon dispersion curve runs into particle-hole excitations. Exchange-correlation kernel corrections to RPA modify the plasmon dispersion curve. There is however a large difference in the construction and form of the kernels investigated earlier. Our current work introduces recent model exchange-only and exchange-correlation kernels and discusses the relevance of some exact constraints in the construction of the kernel. We show that, because the plasmon dispersion samples a range of wavevectors smaller than the range sampled by the correlation energy, different kernels can make a strong difference for the correlation energy and a weak difference for the plasmon dispersion. This work completes our understanding about the plasmon dispersion in realistic metals, such as Cs, where a negative plasmon dispersion has been observed. We find only positive plasmon dispersion in jellium at the density for Cs.

Accurate modeling of electronic and structural properties of organic molecule-metal interfaces are challenging problems because of the complicated electronic distribution of molecule and screening of charges at the metallic surface. This is also the reason why the organic/inorganic system can be engineered for several applications by fine-tuning the metallic work function. Here, we use density-functional theory (DFT) calculations with different level of functional approximations for a systematic study of thiophene interacting with Copper surfaces. In particular, we considered adsorbed structures with the thiophene molecule seated on the top site, with the S atom of the molecule located on the top of a Cu atom. In this work, we find that the weak chemisorption hypothesis of thiophene binding on the copper surface is well justified by the two meta-GGAs-based approximations, SCAN and SCAN+rVV10. PBE-GGA and TM meta-GGA describe it as a physisorption phenomenon by significantly underestimating the adsorption energies. Calculated adsorption energy curves reveal that non-local dispersion interaction between the molecule and metallic surface predominantly controls the bonding mechanism and thus, modifies the copper's work function. Our results imply that semi-local functionals without any kind of van der Waals (vdW) correction can often misinterpret this as physisorption, while, a fortuitous error cancellation can give a right description of this adsorption picture for a wrong reason as in the case of SCAN. The calculated density of states of the adsorbed molecule shows that the long-range vdW correction of SCAN+rVV10 causes more than enough hybridization between the \textit{p} orbitals of S atom and the copper \textit{d}-bands and therefore overestimates the adsorption energies by an average of 16\%.

We review the theory and application of adiabatic exchange-correlation (xc-) kernels for ab initio calculations of ground state energies and quasiparticle excitations within the frameworks of the adiabatic connection fluctuation dissipation theorem and Hedin's equations, respectively. Various different xc-kernels, which are all rooted in the homogeneous electron gas, are introduced but hereafter we focus on the specific class of renormalized adiabatic kernels, in particular the rALDA and rAPBE. The kernels drastically improve the description of short-range correlations as compared to the random phase approximation (RPA), resulting in significantly better correlation energies. This effect greatly reduces the reliance on error cancellations, which is essential in RPA, and systematically improves covalent bond energies while preserving the good performance of the RPA for dispersive interactions. For quasiparticle energies, the xc-kernels account for vertex corrections that are missing in the GW self-energy. In this context, we show that the short-range correlations mainly correct the absolute band positions while the band gap is less affected in agreement with the known good performance of GW for the latter. The renormalized xc-kernels offer a rigorous extension of the RPA and GW methods with clear improvements in terms of accuracy at little extra computational cost., Comment: Review article. 53 pages-

Semi-local density functional approximations are widely used. None of them can capture the long-range van der Waals (vdW) attraction between separated subsystems, but they differ remarkably in the extent to which they capture intermediate-range vdW effects responsible for equilibrium bonds between neighboring small closed-shell subsystems. The local density approximation (LDA) often overestimates this effect, while the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) underestimates it. The strongly-constrained and appropriately normed (SCAN) meta-GGA often estimates it well. All of these semi-local functionals require an additive non-local correction such as the revised Vydrov-Van Voorhis 2010 (rVV10) to capture the long-range part. This work reports adsorption energies and the corresponding geometry of the aromatic thiophene (C$_4$H$_4$S) bound to transition metal surfaces. The adsorption process requires a genuine interplay of covalent and weak binding and requires a simultaneously accurate description of surface and adsorption energies with the correct prediction of the adsorption site. All these quantities must come from well balanced short and long-range correlation effects for a universally applicable method for weak interactions with chemical accuracy.

The ground state equilibrium properties of copper-gold alloys have been explored with the state of art random phase approximation (RPA). Our estimated lattice constants agree with the experiment within a mean absolute percentage error (MAPE) of 1.4 percent. Semi-local functionals such as the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE) and strongly constrained and appropriately normed (SCAN) fail to provide accurate bulk moduli, which indicate their inability to describe the system in a stretched or compressed state with respect to the equilibrium geometry. We find that the non-locality present in RPA is able to describe the transition between two delocalized electron densities (bulk elemental constituents to crystallized alloys), as required to provide accurate formation energies. Based on our results, we conclude that it is difficult to find a universal density functional which can give accurate results for a wide range of properties of intermetallic alloys. However, RPA can capture different bonding situations, often better than other density functionals. It gives accurate results for a wide range of ground state properties for the alloys, generated from metals with completely filled d-shells.

The random phase approximation (RPA) is exact for the exchange energy of a many-electron ground state, but RPA makes the correlation energy too negative by about 0.5 eV/electron. That large short-range error, which tends to cancel out of iso-electronic energy differences, is largely corrected by an exchange-correlation kernel, or (as in RPA+) by an additive local or semilocal correction. RPA+ is by construction exact for the homogeneous electron gas, and it is also accurate for the jellium surface. RPA+ often gives realistic total energies for atoms or solids in which spin-polarization corrections are absent or small. RPA and RPA+ also yield realistic singlet binding energy curves for H2 and N2, and thus RPA+ yields correct total energies even for spin-unpolarized atoms with fractional spins and strong correlation, as in stretched H2 or N2. However, RPA and RPA+ can be very wrong for spin-polarized one-electron systems (especially for stretched H2+), and also for the spin-polarization energies of atoms. The spin-polarization energy is often a small part of the total energy of an atom, but important for ionization energies, electron affinities, and the atomization energies of molecules. Here we propose a computationally efficient generalized RPA+ (gRPA+) that changes RPA+ only for spin-polarized systems by making gRPA+ exact for all one-electron densities, in the same simple semilocal way that the correlation energy densities of many meta-generalized gradent approximations are made self-correlation free. By construction, gRPA+ does not degrade the exact RPA+ description of jellium. gRPA+ is found to greatly improve upon RPA and RPA+ for the ionization energies and electron affinities of light atoms. Many versions of RPA with an approximate exchange-correlation kernel fail to be exact for all one-electron densities, and they can also be self-interaction corrected in this way.

The mechanical and electronic properties of transition metal dichalcogenide (TMD) monolayers corresponding to transition groups IV, VI, and X are explored under mechanical bending from first principles calculations using the strongly constrained and appropriately normed (SCAN) meta-GGA (MGGA). SCAN provides an accurate description of the phase stability of the TMD monolayers. Our calculated lattice parameters and other structural parameters agree well with experiment. We find that bending stiffness (or flexural rigidity) increases as the transition metal group goes from IV to X to VI, with the exception of PdTe$_2$. Variation in mechanical properties (local strain, physical thickness) and electronic properties (local charge density, band structure) with bending curvature is discussed. The local strain profile of these TMD monolayers under mechanical bending is highly non-uniform. The mechanical bending tunes not only the thickness of the TMD monolayers but also the local charge distribution as well as the band structures, adding more functionalization options to these materials.

Semi-local 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 semi-local 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 semi-local approximations satisfy, and 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 (GGA's) and meta-GGA's, 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 SCAN meta-GGA, for which the correlation part is already self-interaction-free. That property makes SCAN a natural first candidate for a generalized SIC.

The description of the chemical bond between a solid surface and an atom or a molecule is the fundamental basis for understanding a broad range of scientific problems in heterogeneous catalysis, semiconductor device fabrication, and fuel cells. Widespread understandings are based on the molecular orbital theory and focused on the degree of filling of antibonding surface-adsorbate states that weaken bonding on surfaces. The unoccupied antibonding surface-adsorbate states are often tacitly assumed to be irrelevant. Here, we show that most antibonding states become unoccupied because the electrons that would occupy these antibonding states are transferred to the lower-energy Fermi level. Such antibonding electron transfer goes beyond molecular orbital theory. It leads to an energy gain that largely controls the trends of surface adsorption strength and can serve as a primary descriptor for bonding on surfaces. This finding is illustrated from the first-principles study of hydrogen adsorption on MoS$_2$ surfaces. A clear linear relationship between the energies of antibonding electron transfer and hydrogen adsorption is identified. The hydrogen evolution reaction on MoS$_2$ is found to originate from the in-gap states induced by sulfur vacancies or edges. The effects of surface inhomogeneity (e.g., defects, step edges) on surface catalysis can be understood from the corresponding different energies gained from antibonding electron transfer. The emerging picture also offers a physically different explanation for the well-known $d$-band theory for hydrogen adsorption on transition metal surfaces., Comment: 12 pages, 3 figures, and 1 table

Materials with a negative Poisson's ratio, also known as auxetic materials, exhibit unusual and counterintuitive mechanical behavior - becoming fatter in cross-section when stretched. Such behavior is mostly attributed to some special reentrant or hinged geometric structures regardless the chemical composition and electronic structure of a material. Here, using first principles calculations, we report a new class of auxetic single-layer two-dimensional (2D) materials, i.e., the 1T-type monolayer crystals of groups 6-7 transition-metal dichalcogenides, MX$_2$ (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 the electronic effects. We attribute the occurrence of such auxetic behavior to the strong coupling between the chalcogen p orbitals and the intermetal t$_{2g}$-bonding orbitals within the basic triangular pyramid structure unit. The unusual auxetic behavior in combination with other remarkable properties of monolayer 2D materials could lead to novel multi-functionalities., Comment: 21 pages, 4 figures

The fundamental energy gap of a periodic solid distinguishes insulators from metals and characterizes low-energy single-electron excitations. But 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 new 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 meta-generalized 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.

Kohn-Sham density functional theory (DFT) is a widely-used electronic structure theory for materials as well as molecules. DFT is needed especially for large systems, ab initio molecular dynamics, and high-throughput searches for functional materials. DFT's accuracy and computational efficiency are limited by the approximation to its exchange-correlation energy. Currently, the local density approximation (LDA) and generalized gradient approximations (GGAs) dominate materials computation mainly due to their efficiency. We show here that the recently developed non-empirical strongly constrained and appropriately normed (SCAN) meta-GGA improves significantly over LDA and the standard Perdew-Burke-Ernzerhof GGA for geometries and energies of diversely-bonded materials (including covalent, metallic, ionic, hydrogen, and van der Waals bonds) at comparable efficiency. Thus SCAN may be useful even for soft matter. Often SCAN matches or improves upon the accuracy of a computationally expensive hybrid functional, at almost-GGA cost. SCAN is therefore expected to have a broad impact on materials science.

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.

Approximations to the exact density functional for the exchange-correlation energy of a many-electron ground state can be constructed by satisfying constraints that are universal, i.e., valid for all electron densities. Gedanken densities are designed for the purpose of this construction, but need not be realistic. The uniform electron gas is an old gedanken density. Here, we propose a spherical two-electron gedanken density in which the dimensionless density gradient can be an arbitrary positive constant wherever the density is non-zero. The Lieb-Oxford lower bound on the exchange energy can be satisfied within a generalized gradient approximation (GGA) by bounding its enhancement factor or simplest GGA exchange-energy density. This enhancement-factor bound is well known to be sufficient, but our gedanken density shows that it is also necessary. The conventional exact exchange-energy density satisfies no such local bound, but energy densities are not unique, and the simplest GGA exchange-energy density is not an approximation to it. We further derive a strongly and optimally tightened bound on the exchange enhancement factor of a two-electron density, which is satisfied by the local density approximation but is violated by all published GGA's or meta-GGA's. Finally, some consequences of the non-uniform density-scaling behavior for the asymptotics of the exchange enhancement factor of a GGA or meta-GGA are given., Comment: 26 pages and 6 figures