Nonlocal Exchange-correlation Research Articles

Taming Negative Ion Resonances Using Nonlocal Exchange-Correlation Functionals.

The characterization of negative ion resonances poses a fundamental challenge to density functional methods due to the unbound nature of resonances. To overcome this challenge, we propose one-particle nonlocal exchange-correlation (xc) potentials combining the exact-exchange (EXX) and the random phase approximation (RPA) correlation potentials. The negative ion resonances are identified by perturbing the real Hermitian nonlocal xc potentials using complex absorbing local potentials. Our studies show that the nonlocal EXX+RPA potential significantly enhances the description of positions and widths of negative ion resonance states compared to potentials that exclude dynamic polarization in RPA or include only EXX. The use of low-scaling algorithms simplifies the computation of the RPA potential, thereby providing a practical solution for resonance-state characterization within the density functional framework. A theoretical framework and the underlying assumptions required for combining real Hermitian nonlocal xc potentials with complex local potentials are discussed.

Superconductivity in transition metal carbides, TaC and HfC: A density functional theory study with local, semilocal, and nonlocal exchange–correlation functionals

We studied electronic, dynamical, and superconducting properties of TaC and HfC using local, semilocal, and nonlocal exchange–correlation functionals in the density functional theory. It turns out that there is a slight shift of Fermi energy and the corresponding density of states with different functionals. However, the phonon frequencies of, especially, the optical modes for both TaC and HfC shift by moderately larger values. The most important differences are observed for the electron–phonon interactions where the electron–phonon coupling constant, λ≈0.9, calculated using the nonlocal correlation functionals, vdW-DF2 and vdW-DF3 for TaC, are in the closest agreement with the experimental results. Although the Kohn anomalies and Fermi surface nesting are critical for the electron–phonon coupling, a significant contribution to λ, for TaC, comes from the regions of the Brillouin zone where the matrix elements have a predominant role. Moreover, the optical modes give 20%–23% of λ for TaC and 50%–57% for HfC.

Assessing the dynamics of CO adsorption on Cu(110) using the vdW-DF2 functional and artificial neural networks

In this work, we revisit the dynamics of carbon monoxide molecular chemisorption on Cu(110) by using quasi-classical trajectory calculations. The molecule–surface interaction is described through an atomistic neural network approach based on Density Functional Theory calculations using a nonlocal exchange–correlation (XC) functional that includes the effect of long-range dispersion forces: vdW-DF2 [Lee et al. Phys. Rev. B, 82, 081101 (2010)]. With this approach, we significantly improve the agreement with experiments with respect to a similar previous study based on a semi-local XC functional. In particular, we obtain excellent agreement with molecular beam experimental data concerning the dependence of the initial sticking probability on surface temperature and impact energy at normal incidence. For off-normal incidence, our results also reproduce two trends observed experimentally: (i) the preferential sticking for molecules impinging parallel to the [1̄10] direction compared to [001] and (ii) the change from positive to negative scaling as the impact energy increases. Nevertheless, understanding the origin of some remaining quantitative discrepancies with experiments requires further investigations.

The electronic, optical, and vibrational properties of Ag3X (X = S, Se) with density functional theory

Using ab initio first-principles calculations, we investigate the structural, electronic, optical, and vibrational properties of Silver Sulphide Ag3S and Selenide Ag3Se with nonlocal hybrids exchange-correlation functional. With our computational predictions, we manage to classify the material to be Fermi-Dirac semi-metal, rather than Weyl metal. Our calculated results show that the electronic band in between the Fermi-Dirac cone shifts downward when we replace the element Sulphide S with Selenide Se. The obtained optical results such as absorption coefficients and dielectric functions (conductivity, reflectivity, etc.) are similar for both Ag3S and Ag3Se. A high absorption coefficient of [Formula: see text] cm[Formula: see text] has been reported, and about 50% of light is reflected. In Raman spectra, the A[Formula: see text] managed to shift downward when replacing the element X, sulphide S with selenide Se, while the A[Formula: see text] shifts upward (to higher wavelength). The rotation and vibration of the bonding between atoms have also been explained. The calculated results of Silver-VI compounds provide useful information in the exploitation of more complicated structures.

Note: Reproducibility of potential energy surfaces of organic/metal interfaces on the example of PTCDA on Ag(111).

We recently published a benchmark study of common local, semi-local, and non-local exchange correlation functionals in combination with various van der Waals (vdW) corrections, where we investigated the reproducibility of the potential energy surface of perylenetetracarboxylic dianhydride on Ag(111). This Note presents an additional benchmark of the recently developed non-local many body dispersion (MBD-NL) vdW correction, coupled with the Perdew-Burke-Ernzerhof (PBE) functional. We find that this computation method shows similar performance as the established approaches. Notably, it yields very similar results as PBE + MBD.

First-principles wave-vector- and frequency-dependent exchange-correlation kernel for jellium at all densities

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.}

Heisenberg Spin Hamiltonian Derived from a Multiple Grand Canonical Spin Density Functional Theory with a Principal Nonlocal Exchange–Correlation Energy Functional

Heisenberg Spin Hamiltonian Derived from a Multiple Grand Canonical Spin Density Functional Theory with a Principal Nonlocal Exchange–Correlation Energy Functional

EQE 2.0: Subsystem DFT beyond GGA functionals

By adopting a divide-and-conquer strategy, subsystem-DFT (sDFT) can dramatically reduce the computational cost of large-scale electronic structure calculations. The key ingredients of sDFT are the nonadditive kinetic energy and exchange-correlation functionals which dominate it's accuracy. Even though, available semilocal nonadditive functionals find a broad range of applications, their accuracy is somewhat limited especially for those systems where achieving balance between exchange-correlation interactions on one side and nonadditive kinetic energy on the other is crucial. In eQE 2.0, we improve dramatically the accuracy of sDFT simulations by (1) implementing nonlocal nonadditive kinetic energy functionals based on the LMGP family of functionals; (2) adapting Quantum ESPRESSO's implementation of rVV10 and vdW-DF nonlocal exchange-correlation functionals to be employed in sDFT simulations; (3) implementing “deorbitalized” meta GGA functionals (e.g., SCAN-L). We carefully assess the performance of the newly implemented tools on the S22-5 test set. eQE 2.0 delivers excellent interaction energies compared to conventional Kohn-Sham DFT and CCSD(T). The improved performance does not come at a loss of computational efficiency. We show that eQE 2.0 with nonlocal nonadditive functionals retains the same linear scaling behavior achieved previously in eQE 1.0 with semilocal nonadditive functionals. Program summaryProgram title: eQECPC Library link to program files:https://doi.org/10.17632/g55n9xmnt2.1Developer's repository link:https://gitlab.com/Pavanello/eqeLicensing provisions: GPLv2Programming language: Fortran 90External routines/libraries: BLACS, MPINature of problem: Solving the electronic structure of molecules and materials with subsystem density functional theorySolution method: This version of eQE uses subsystem Density-Functional Theory (DFT) to compute the electronic structure of molecules and materials. Subsystem DFT is a divide-and-conquer version of DFT that can be massively parallelized and is linear scaling in work and data. However, it requires the use of density functionals for kinetic and exchange-correlation energies. eQE can now employ nonlocal functionals as well as meta-GGA functionals for these energy terms.Additional comments: Url of stable release http://eqe.rutgers.edu

Self-consistent assessment of Li+ ion cathodes: Theory vs. experiments

A self-consistent DFT framework without fitting parameters has been carried out to make assessments for the well-recognized cathode materials for lithium ion batteries. It offers a dependable framework for theoretical assessment of cathode materials. Transition metal oxide cathodes such as layered LiCoO 2 , spinel LiMn 2 O 4 and olivine LiFePO 4 have been commercialized for several decades and widely used in the rechargeable Li-ion batteries (LIBs). While great theoretical efforts have been made using the density functional theory (DFT) method, leading to insightful understanding covering materials stability and functional properties, the lack of consistency in choices of functionals and/or convergence criteria makes it somewhat difficult to compare results. It is therefore highly useful to assess these established systems towards self-consistency, thus offering a reliable working basis for theoretical formulation of novel cathodes. Here in this work, we have carried out systematic DFT calculations on the basis of recently established framework covering both thermodynamic stability, functional properties and associated mechanisms. Efforts have been made in self-consistent selection of exchange–correlation (XC) functionals in terms of dependable accuracy with affordable computational cost, which is essential for high-throughput first-principles calculations. The outcome of the current work on three established cathode systems is in very good agreement with experimental data, and the methodology is to provide a solid basis for designing novel cathode materials without using costing non-local exchange–correlation functionals for structure-energy calculations.

Next-Generation Nonlocal van der Waals Density Functional.

The fundamental ideas for a nonlocal density functional theory-capable of reliably capturing van der Waals interactions-were already conceived in the 1990s. In 2004, a seminal paper introduced the first practical nonlocal exchange-correlation functional called vdW-DF, which has become widely successful and laid the foundation for much further research. However, since then, the functional form of vdW-DF has remained unchanged. Several successful modifications paired the original functional with different (local) exchange functionals to improve performance, and the successor vdW-DF2 also updated one internal parameter. Bringing together different insights from almost 2 decades of development and testing, we present the next-generation nonlocal correlation functional called vdW-DF3, in which we change the functional form while staying true to the original design philosophy. Although many popular functionals show good performance around the binding separation of van der Waals complexes, they often result in significant errors at larger separations. With vdW-DF3, we address this problem by taking advantage of a recently uncovered and largely unconstrained degree of freedom within the vdW-DF framework that can be constrained through empirical input, making our functional semiempirical. For two different parameterizations, we benchmark vdW-DF3 against a large set of well-studied test cases and compare our results with the most popular functionals, finding good performance in general for a wide array of systems and a significant improvement in accuracy at larger separations. Finally, we discuss the achievable performance within the current vdW-DF framework, the flexibility in functional design offered by vdW-DF3, as well as possible future directions for nonlocal van der Waals density functional theory.

Role of nonlocality in exchange correlation for magnetic two-dimensional van der Waals materials

To obtain accurate independent-particle descriptions for ferromagnetic two-dimensional van der Waals materials, we apply the quasiparticle self-consistent $GW$ (QSGW) method to ${\mathrm{VI}}_{3}, {\mathrm{CrI}}_{3}, {\mathrm{CrGeTe}}_{3}$, and ${\mathrm{Fe}}_{3}{\mathrm{GeTe}}_{2}$. QSGW provides a description of the nonlocal exchange-correlation term in the one-particle Hamiltonian. The nonlocal term is important not only as the $U$ of density functional theory $(\mathrm{DFT})+U$ but also for differentiating occupied and unoccupied states in semiconductors. We show the limitations of $\mathrm{DFT}+U$ in mimicking QSGW.

First-Principles Study of Van Der Waals Interactions between Halogen Molecules (Cl2 and I2)

Density Functional Theory (DFT) based first-principles calculations have been performed to investigate vander Waals (vdW) interactions in between halogen atoms/molecules —Cl-Cl, I-I, Cl2-Cl2, Cl2-I2, I2-I2—via with and without a non-local exchange-correlation (XC) functional (vdW-DF) using Quantum ESPRESSO codes. The non-polar covalent bond length between atomic halogens (Cl-Cl and I-I) is not observed to be affected by vdW interactions and agrees well with experimental values. The binding energy between theatomic halogens, on the other hand, is slightly corrected by vdW interactions. However, the role of vdW interactions is observed to be crucial to bind molecular halogens. The molecules are weakly bound in the presence of vdW interactions and not correlated (bound) in the absence of them.

Machine Learning the Physical Nonlocal Exchange-Correlation Functional of Density-Functional Theory.

We train a neural network as the universal exchange-correlation functional of density-functional theory that simultaneously reproduces both the exact exchange-correlation energy and the potential. This functional is extremely nonlocal but retains the computational scaling of traditional local or semilocal approximations. It therefore holds the promise of solving some of the delocalization problems that plague density-functional theory, while maintaining the computational efficiency that characterizes the Kohn-Sham equations. Furthermore, by using automatic differentiation, a capability present in modern machine-learning frameworks, we impose the exact mathematical relation between the exchange-correlation energy and the potential, leading to a fully consistent method. We demonstrate the feasibility of our approach by looking at one-dimensional systems with two strongly correlated electrons, where density-functional methods are known to fail, and investigate the behavior and performance of our functional by varying the degree of nonlocality.

Deep learning and density-functional theory

We show that deep neural networks can be integrated into, or fully replace, the Kohn-Sham density functional theory (DFT) scheme for multielectron systems in simple harmonic oscillator and random external potentials with no feature engineering. We first show that self-consistent charge densities calculated with different exchange-correlation functionals can be used as input to an extensive deep neural network to make predictions for correlation, exchange, external, kinetic, and total energies simultaneously. Additionally, we show that one can make all of the same predictions with the external potential rather than the self-consistent charge density, which allows one to circumvent the Kohn-Sham DFT scheme altogether. We then show that a self-consistent charge density found from a nonlocal exchange-correlation functional can be used to make energy predictions for a semilocal exchange-correlation functional. Lastly, we use a deep convolutional inverse graphics network to predict the charge density given an external potential for different exchange-correlation functionals and assess the viability of the predicted charge densities. This work shows that extensive deep neural networks are generalizable and transferable given the variability of the potentials (maximum total energy range $\ensuremath{\approx}100$ Ha) because they require no feature engineering and because they can scale to an arbitrary system size with an $O(N)$ computational cost.

Quantum Monte Carlo Studies of CO Adsorption on Transition Metal Surfaces

The adsorptions of CO molecule on various fcc(111) surfaces (Rh, Ir, Pt, and Cu) have been studied by diffusion quantum Monte Carlo (DMC) calculations, and the results show that the top site is the most stable adsorption site on all the four surfaces, in agreement with experiments. In particular, the site preference including the bridge site for CO/Pt(111) is predicted, i.e., the top site is most preferred followed by the bridge site while the hollow sites are much less favorable, in accordance with the existing experimental observations of the bridge-site adsorption, yet never on the hollow sites. Compared to the DMC results, density functional theory (DFT) calculations with the generalized-gradient approximation (GGA) predict very similar adsorption energies on the top site, but they overestimate those on the bridge and hollow sites. That is, although the nonlocal exchange-correlation contribution is small for the single-coordinated top-site adsorption, it is essential and required to be properly included for a correct description of the higher coordinated bridge- and hollow-sites adsorptions. These altogether explain why the top site adsorption for CO on Rh, Pt, and Cu(111) surfaces was not predicted correctly by the previous standard local or semilocal DFT calculations.

Plasmonic performance of AuxAgyCu1−x−y alloys from many-body perturbation theory

We present a detailed appraisal of the optical and plasmonic properties of ordered alloys of the form AuxAgyCu1-x-y, as predicted by means of first-principles many-body perturbation theory augmented by a semi-empirical Drude–Lorentz model. In benchmark simulations on elemental Au, Ag, and Cu, we find that the random-phase approximation (RPA) fails to accurately describe inter-band transitions when it is built upon semi-local approximate Kohn–Sham density-functional theory band-structures. We show that non-local electronic exchange-correlation interactions sufficient to correct this, particularly for the fully-filled, relatively narrow d-bands which contribute strongly throughout the low-energy spectral range (0–6 eV), may be modeled very expediently using band-stretching operators that imitate the effect of a perturbative self-energy correction incorporating quasiparticle (QP) mass renormalization. We thereby establish a convenient work-flow for carrying out approximated spectroscopic calculations on alloys and, in particular here, we have considered alloy concentrations down to 12.5% in , including all possible crystallographic orderings of face-centred cubic type. We develop a pragmatic procedure for calculating the Drude plasmon frequency from first principles, including self-energy effects, as well as a semi-empirical scheme for interpolating the plasmon inverse lifetimes between stoichiometries. A distinctive M-shaped profile is observed in both quantities for binary alloys, in qualitative agreement with previous experimental findings. A range of optical and plasmonic figures of merit are discussed, and plotted for ordered at three representative solid-state laser wavelengths. On this basis, we predict that certain compositions may offer improved performance over elemental Au for particular application types. We predict that while the loss functions for both bulk and surface plasmons are typically diminished in strength through binary alloying, certain stoichiometric ratios may exhibit higher-quality (longer-lived) localized surface-plasmons and surface-plasmon polaritons, at technologically-relevant wavelengths, than those in elemental Au.

Shock induced phase transition in SiC polytypes

The effect of shock on 3C and 6H phases of silicon carbide was investigated within our earlier developed scaled binding energy based Debye–Gru¨neisen model. Required input parameters for the equation of state (EOS) model were obtained from density functional theory calculations using PBE-GGA functional as well as a nonlocal exchange-correlation functional B3LYP. In our earlier calculations using PBE-GGA functional, we predicted the phase transition from 3C to B1 phase at about 68 GPa, which deviated significantly from the experimental value of about 100 GPa. An empirical energy correction was applied in that case to obtain the experimental transition pressure. However, in the present work, we observed that if hybrid B3LYP functional is employed to calculate EOS parameters, shock induced phase transitions from 3C to B1 and 6H to B1 phases occur at about 102 GPa and 105 GPa, respectively, in close agreement with experiments without invoking any empirical correction. We obtained good agreement of our predictions with experimental shock data using a simple model of metastability and the hybrid B3LYP functional, which accounts for exchange-correlation effects better than the PBE-GGA functional in the case of SiC.

First-principles study of electronic structure, magnetic and optical properties of laminated molybdenum oxides

According to the pseudopotential plane-wave method of first-principles calculation based on the spin density functional theory, the electronic structure, magnetic and optical properties of laminated molybdenum oxides (orthonormal and monoclinic MoO<sub>3</sub>) are studied theoretically. The interlaminar dissociation energy, band-structure, spin polarization, dielectric function, and the optical absorption/reflectivity in a charged state are systematically calculated to explore the potential technology applications of laminated MoO<sub>3</sub> as electrochromic or electromagnetic materials in optoelectronic devices. The semilocal GGA-PW91 and nonlocal HSE06 exchange-correlation functional are employed to obtain the more accurate crystal structure and band gap respectively. The cleavage energy results indicate that the single layers can easily flake off from the bulk material of these molybdenum oxides. The band structure and atomic-projected density of states prove that the conduction band minimum and valence band maximum are mainly derived from the atom-orbitals bonding oriented in layer-plane, representing characteristic two-dimensional electronic structure. The spin polarized calculations imply that the evident magnetic-moment will engender in MoO<sub>6</sub> octahedron layers of the perfect MoO<sub>3</sub> due to the substantial spin polarization of Mo and vertex O atoms which are ferromagnetic-coupling to produce significant net magnetic moments, essentially accounting for the magnetic source of bulk MoO<sub>3</sub>. The Mo vacancy reduces the electronic density of states derived from the spin polarized d-orbitals, leading the net magnetic moment to decrease, while the O<sub>I</sub> vacancy can reduce the density of spin-down states in the MoO<sub>3</sub>, resulting in the significant improvement of net magnetic moment. The existence of O<sub>II</sub> vacancy leads to the energetic spin-splitting of O-2p and Mo-4d orbital states, and thus increasing net magnetic moment by raising the electronic density of polarized spin-up states. The electron spin polarization of Mo-4d orbital component dominantly contributes to the bulk magnetism. The laminated MoO<sub>3</sub> presents a significant optical response in the visible region with obvious anisotropy of optical absorption spectra, which will represent a considerable blue shift or new low-frequency absorption peaks for visible light when loading charges. The calculation results demonstrate that the laminated molybdenum oxides have evident electrochromic property with controllable magnetic moment, which provides theoretical basis and technical data for developing novel functional materials with high performance to be used in electromagnetic or optoelectronic devices.

Pressure dependence on electronic structures, charge distribution and bond orders of solid nitromethane using nonlocal DFT functional

ABSTRACTThe electronic properties of solid nitromethane are studied using nonlocal exchange-correlation functional (optPBE–vdW) under hydrostatic compression up to 40 GPa. We found that the optPBE–vdW functional can reproduce well the crystalline structures compared with the experiments, and an isomorphic phase transition has been verified by their P–V curve. Bader’s charge analysis shows the electron flows from CH3 group to NO2 group with the pressure. Moreover, the calculated bond orders show that the pressure only strengthens the intermolecular C–N bond and intermolecular C–H···O hydrogen bonds though it shortens all bond lengths. Furthermore, the electronic structure and its pressure dependence have also been discussed in detail.

Combining Density Functional Theory and Green's Function Theory: Range-Separated, Nonlocal, Dynamic, and Orbital-Dependent Hybrid Functional.

We present a rigorous framework which combines single-particle Green's function theory with density functional theory based on a separation of electron-electron interactions into short- and long-range components. Short-range contribution to the total energy and exchange-correlation potential is provided by a density functional approximation, while the long-range contribution is calculated using an explicit many-body Green's function method. Such a hybrid results in a nonlocal, dynamic, and orbital-dependent exchange-correlation functional of a single-particle Green's function. In particular, we present a range-separated hybrid functional called srSVWN5-lrGF2 which combines the local-density approximation and the second-order Green's function theory. We illustrate that similarly to density functional approximations, the new functional is weakly basis-set dependent. Furthermore, it offers an improved description of the short-range dynamic correlation. The many-body contribution to the functional mitigates the many-electron self-interaction error present in many density functional approximations and provides a better description of molecular properties. Additionally, we illustrate that the new functional can be used to scale down the self-energy and, therefore, introduce an additional sparsity to the self-energy matrix that in the future can be exploited in calculations for large molecules or periodic systems.