Correlation Energy Functionals Research Articles

Quantum Monte Carlo study of correlation energy and pair correlation function at various electron-positron density ratios: Accurate calculation of positron annihilation lifetimes in solids

Quantum Monte Carlo study of correlation energy and pair correlation function at various electron-positron density ratios: Accurate calculation of positron annihilation lifetimes in solids

Semilocal Meta-GGA Exchange-Correlation Approximation from Adiabatic Connection Formalism: Extent and Limitations.

The incorporation of a strong-interaction regime within the approximate semilocal exchange-correlation functionals still remains a very challenging task for density functional theory. One of the promising attempts in this direction is the recently proposed adiabatic connection semilocal correlation (ACSC) approach [Constantin, L. A.; Phys. Rev. B 2019, 99, 085117] allowing one to construct the correlation energy functionals by interpolation of the high and low-density limits for the given semilocal approximation. The current study extends the ACSC method to the meta-generalized gradient approximations (meta-GGA) level of theory, providing some new insights in this context. As an example, we construct the correlation energy functional on the basis of the high- and low-density limits of the Tao-Perdew-Staroverov-Scuseria (TPSS) functional. Arose in this way, the TPSS-ACSC functional is one-electron self-interaction free and accurate for the strictly correlated and quasi-two-dimensional regimes. Based on simple examples, we show the advantages and disadvantages of ACSC semilocal functionals and provide some new guidelines for future developments in this context.

Exact Sum-Rule Approach to Polarizability and Asymptotic van der Waals Functionals─Derivation of Exact Single-Particle Benchmarks

Using a sum-rule approach, we develop an exact theoretical framework for polarizability and asymptotic van der Waals correlation energy functionals of small isolated objects. The functionals require only monomer ground-state properties as input. Functional evaluation proceeds via solution of a single position-space differential equation, without the usual summations over excited states or frequency integrations. Explicit functional forms are reported for reference physical systems, including atomic hydrogen and single electrons subject to harmonic confinement, and immersed in a spherical-well potential. A direct comparison to the popular Vydrov-van Voorhis density functional shows that the best performance is obtained when density decay occurs at atomic scales. The adopted sum-rule approach implies general validity of our theory, enabling exact benchmarking of van der Waals density functionals and direct inspection of the subtle long-range correlation effects that constitute a major challenge for approximate (semi)local density functionals.

N2v: A density‐to‐potential inversion suite. A sandbox for creating, testing, and benchmarking density functional theory inversion methods

AbstractFrom the most fundamental to the most practical side of density functional theory (DFT), Kohn–Sham inversions (iKS) can contribute to the development of functional approximations and shed light on their performance and limitations. On the one hand, iKS allows for the direct exploration of the Hohenberg–Kohn and Runge–Gross density‐to‐potential mappings that provide the foundations for DFT and time‐dependent DFT. On the other hand, iKS can guide the analysis and development of approximate exchange–correlation and noninteracting kinetic energy functionals, and diagnose their errors. iKS can also play a similar role in the development of nonadditive functionals for modern density‐based embedding methods. Various strategies to perform iKS calculations have been explored since the inception of DFT. We introduce n2v, a density‐to‐potential inversion Python module that is capable of performing the most useful and state‐of‐the‐art inversion calculations. Currently based on NumPy, n2v was developed to be easy to learn by newcomers to the field. Its structure allows for other inversion methods to be easily added. The code offers a general interface that gives the freedom to use different software packages in the computational molecular sciences (CMS) community, and the current release supports the Psi4 and PySCF packages. Six inversion methods have been implemented into n2v and are reviewed here along with detailed numerical illustrations on molecules with numbers of electrons ranging from ~10 to ~100.This article is categorized under: Software > Quantum Chemistry Electronic Structure Theory > Density Functional Theory

Organic Emitters Showing Excited-States Energy Inversion: An Assessment of MC-PDFT and Correlation Energy Functionals Beyond TD-DFT

The lowest-energy singlet (S1) and triplet (T1) excited states of organic conjugated chromophores are known to be accurately calculated by modern wavefunction and Time-Dependent Density Functional Theory (TD-DFT) methods, with the accuracy of the latter heavily relying on the exchange-correlation functional employed. However, there are challenging cases for which this cannot be the case, due to the fact that those excited states are not exclusively formed by single excitations and/or are affected by marked correlation effects, and thus TD-DFT might fall short. We will tackle here a set of molecules belonging to the azaphenalene family, for which research recently documented an inversion of the relative energy of S1 and T1 excited states giving rise to a negative energy difference (ΔEST) between them and, thereby, contrary to most of the systems thus far treated by TD-DFT. Since methods going beyond standard TD-DFT are not extensively applied to excited-state calculations and considering how challenging this case is for the molecules investigated, we will prospectively employ here a set of non-standard methods (Multi-Configurational Pair Density Functional Theory or MC-PDFT) and correlation functionals (i.e., Lie–Clementi and Colle–Salvetti) relying not only on the electronic density but also on some modifications considering the intricate electronic structure of these systems.

Nonlocal exchange and correlation energy functionals using the Yukawa potential as ingredient: Application to the linear response of the uniform electron gas

We show that the reduced, dimensionless Yukawa potential ${y}_{\ensuremath{\alpha}}$ can be employed as an important ingredient in the construction of the exchange and correlation energy functionals. A functional based on ${y}_{\ensuremath{\alpha}}$ provides a better description of the exchange and correlation linear response functions of the homogeneous electron gas, not only at small wave vectors, where gradient expansions are correct, but also at large wave vectors, where semilocal exchange and correlation functionals fail badly. Moreover, the ${y}_{\ensuremath{\alpha}}$ ingredient gives a realistic description of the exchange energy and potential at the nuclear cusp and the inner atomic core, where the semilocal ingredients (i.e., the reduced gradient and Laplacian of the density) are not suitable, causing divergence of the potential. Thus, the ${y}_{\ensuremath{\alpha}}$ ingredient can be attractive for the development of various exchange-correlation functionals.

Hybrid exchange–correlation energy functionals for accurate prediction of the electronic and optical properties of alkaline-earth metal oxides

An essential issue in electro-optical applications is to design materials with appropriate band gaps. In the framework of density functional theory (DFT), the generalized gradient approximation (GGA) and local density approximation (LDA) generally underestimate band gaps for semiconductors. Hybrid functionals that include some exact Hartree–Fock exchange are known to be better. In this research, we applied hybrid functionals, which has the main factor of providing almost accurate exchange potential, for calculating structural, electronic and optical properties of alkaline earth metal oxides. Results show that the hybrid functionals have a tendency to improve the description of structural and electronic parameters with respect to LDA and GGA. We find that the PBE0 and B3PW91 are the best functional for estimating lattice constant. LDA-HF gives the better results for calculating the energy band gaps with respect to the experimental values, and B3PW91 and PBE0 improved the amount of dielectric constant. The calculated imaginary part of dielectric function and reflectivity spectra shows that B3PW91 and LDA-Fock α give the best accordance with experimental results. The present work has shown that applying hybrid functionals can lead to very accurate results, describing correctly the structural, electronic and optical properties of the alkaline earth metal oxides.

Impact of replacement of Re by W on dislocation slip mediated creeps of γ′-Ni3Al phases

The anomalous flow behavior of γ′-Ni3Al phases at high temperature is closely related to the cross-slip of 1/2〈110〉{111} super-partial dislocations. Generalized stacking fault energy curves (i.e., Γ-surfaces) along the lowest energy path can provide a great deal of information on the nucleation and movement of dislocations. With the first-principles calculation, the interplay between Re and W, Mo, Ta, Ti doped at preferential sites and their synergetic influence on Γ-surfaces and ideal shear strength (τmax) in γ′-Ni3Al phases are investigated. Similar to single Re-addition, the Suzuki segregation of W at stacking faults is demonstrated to enable to impede the movement of 1/6〈112〉{111} Shockley partial dislocations and promote the cross-slip of 1/2〈110〉{111} super-partial dislocations. With the replacement of a part of Re by W, a decreased indicates that the anomalous flow behavior of γ′ phases at high temperature is not as excellent as the double Re-addition, but an increased τmax means that the creep rupture strength of Ni-based single crystal superalloys can be benefited from this replacement to some extent, especially in the co-segregation of Re and W at Al−Al sites. As the interaction between X1Al and X2Al point defects is characterized by an correlation energy function , it is found that both strong attraction and strong repulsion are unfavarable for the improvement of yield strengths of γ′ phase.

Improving the applicability of the Pauli kinetic energy density based semilocal functional for solids

The Pauli kinetic energy enhancement factor α = (τ − τ W )/τ unif is an important density ingredient, used to construct many meta-generalized gradient approximations (meta-GGA) exchange–correlation (XC) energy functionals, including the very successful strongly constrained and appropriately normed (SCAN) semilocal functional. Another meta-GGA functional, known as MGGAC (2019 Phys. Rev. B 100 155140), is also proposed in recent time depending only on the α ingredient and based on the generalization of the Becke–Roussel approach with the cuspless hydrogen exchange hole density. The MGGAC functional is proved to be a very useful and competitive meta-GGA semilocal functional for electronic structure properties of solids and molecules. Based on the successful implication of the ingredient α, which is also useful to construct the one-electron self-interaction free correlation energy functional, here we propose revised correlation energy for MGGAC exchange functional which is more accurate and robust, especially for the high and low-density limits of the uniform density scaling. The present XC functional, named as revised MGGAC (rMGGAC), shows an impressive improvement for the structural and energetic properties of solids compared to its previous version. Moreover, the assessment of the present constructed functional shows to be quite useful in solid-state physics in terms of addressing several current challenging solid-state problems.

Efficient Band Structure Calculation of Two-Dimensional Materials from Semilocal Density Functionals.

The experimental and theoretical realization of two-dimensional (2D) materials is of utmost importance in semiconducting applications. Computational modeling of these systems with satisfactory accuracy and computational efficiency is only feasible with semilocal density functional theory methods. In the search for the most useful method in predicting the band gap of 2D materials, we assess the accuracy of recently developed semilocal exchange–correlation (XC) energy functionals and potentials. Though the explicit forms of exchange–correlation (XC) potentials are very effective against XC energy functionals for the band gap of bulk solids, their performance needs to be investigated for 2D materials. In particular, the LMBJ [J. Chem. Theory Comput.2020, 16, 265432097004] and GLLB-SC [Phys. Rev. B82, 2010, 115106] potentials are considered for their dominance in bulk band gap calculation. The performance of recently developed meta generalized gradient approximations, like TASK [Phys. Rev. Res.1, 2019, 033082] and MGGAC [Phys. Rev. B. 100, 2019, 155140], is also assessed. We find that the LMBJ potential constructed for 2D materials is not as successful as its parent functional, i.e., MBJ [Phys. Rev. Lett.102, 2009, 22640119658882] in bulk solids. Due to a contribution from the derivative discontinuity, the band gaps obtained with GLLB-SC are in a certain number of cases, albeit not systematically, larger than those obtained with other methods, which leads to better agreement with the quasi-particle band gap obtained from the GW method. The band gaps obtained with TASK and MGGAC can also be quite accurate.

Density functional study of atoms spatially confined inside a hard sphere

AbstractAn atom placed inside a cavity of finite dimension offers many interesting features, and thus has been a topic of great current activity. This work proposes a density functional approach to pursue both ground and excited states of a multi‐electron atom under a spherically impenetrable enclosure. The radial Kohn‐Sham (KS) equation has been solved by invoking a physically motivated work‐function‐based exchange potential, which offers near‐Hartree‐Fock‐quality results. Accurate numerical eigenfunctions and eigenvalues are obtained through a generalized pseudospectral method (GPS) fulfilling the Dirichlet boundary condition. Two correlation functionals, viz., (i) simple, parametrized local Wigner‐type, and (ii) gradient‐ and Laplacian‐dependent non‐local Lee‐Yang‐Parr (LYP) functionals are adopted to analyze the electron correlation effects. Preliminary exploratory results are offered for ground states of He‐isoelectronic series (Z = 2 − 4), as well as Li and Be atom. Several low‐lying singly excited states of He atom are also reported. These are compared with available literature results–which offers excellent agreement. Radial densities as well as expectation values are also provided. The performance of correlation energy functionals are discussed critically. In essence, this presents a simple, accurate scheme for studying atomic systems inside a hard spherical box within the rubric of KS density functional theory.

Adiabatic connection in density functional theory in two-dimensions: A semi-analytic wavefunction based study for two-electron atomic systems.

This work focuses on studying the adiabatic-connection in density functional theory in two dimensions. It employs a recently developed accurate form of wavefunction for two-electron systems. The explicit semianalytic form of the wavefunction makes it possible to calculate ground state wavefunctions, energies, densities, and the resulting properties for the scaled Coulomb interaction between the electrons at fixed density accurately. The results so obtained for the correlation energies are then used as the reference values for studying the performance of two-dimensional correlation energy functionals.

Impact of Re-clustering on resistances to dislocation slip mediated plastic deformations in γ matrix phases

Generalized planar fault energy curves (i.e., Γ-surfaces) along the lowest energy path can provide a great deal of information on the nucleation and movement of dislocations. Using the first-principles calculation, the influence of Re-clustering on Γ-surfaces and ideal shear strengths σmax in the 112-111 slip direction in the γ phase of Ni-based single crystal (SC) superalloys is investigated. An isolated substitution of Re for Ni atoms (i.e.,ReNi), which can reduce intrinsic stacking fault energy γisf, raise unstable stacking fault energy γusf and enhance σmax, is demonstrated to be beneficial to reinforce the resistance to dislocation slip mediated plastic deformations. With the increase of Re-additions, Re atoms tend to separate apart from each other, but a clustering phenomena is likely to occurs in γ matrixes at some special stages of creep of Ni-based SC superalloys. A careful analysis for the Γ-surface and σmax in γ-Ni(Re) phases shows the geometrical configuration and spatial arrangement of ReNi defects has a significant impact on the nucleation and movement of a0/6112-111 Shockley partials, and the distance between ReNi defects is dominant compared with their position orientation. σmax is revealed to be very sensitive to the clustering degree of Re atoms, while Γ-surfacemainly depend on the size of Re-clusters. As the interaction between ReNi defects being characterized by a correlation energy function ΔEi, it is found that a strong repulsion caused by Re-clustering is unfavorable for the strengthening of Ni-based SC superalloys, although the resistance to dislocation slip mediated plastic deformations in γ-Ni(Re) phases can benefit from more Re-additions.

A synergistic reinforcement of Re and W for ideal shear strengths of γ′-Ni3Al phases

Using first-principles calculations, we investigate the ideal shear strengths σmax of L12-Ni3Al crystals with various multiple additions of Re and W. A correlation energy function ΔEReA+WB(d) is adopted to evaluate the interaction between point defects (i.e., ReA and WB). The results indicate extra addition of Re or W does not change the site preference of Re and W at Al sites, and W in preference to Re occupies Al sites. In this preferred site, σmax of L12-Ni3Al crystals with single Re addition is larger than that with single W addition, but the strengthening effect of double Re addition is weak compared with multiple addition of Re and W. Strong repulsion is found to be disadvantageous for the reinforcement of γ′-Ni3Al phases, and σmax in ReA+WB complexes decreases with increasing ΔEReA+WB(d). The analysis of electronic and geometric structures reveals Re/W-addition-induced strengthening mainly originates from stronger Re/WNi bonding than AlNi bonding, but a significant increase of σmax in γ′-Ni3Al-ReW systems is attributed to a cooperative effect of electronic interaction and local elastic strain energy, and the local elastic strain energy is dominant.

Correlation energy functionals from adiabatic connection formalism

We propose a modified interaction strength interpolation method that is more robust in the quasi-two-dimensional density regime and more accurate than the original method [M. Seidl et al., Phys. Rev. Lett. 84, 5070 (2000)] for the correlation energy and adiabatic integrand of small atoms. This method also allows us to construct correlation energy densities as simple local interpolations along the adiabatic connection. As an example, we develop a generalized gradient approximation correlation functional that performs in line with, and often better than, popular semilocal correlation functionals.

Structural, elastic, thermodynamic and electronic properties of covellite, CuS

Covellite, the CuS, is a unique compound owing to both superconducting and metallic behavior at different temperatures. We model and characterize the elastic, electronic and associated properties of the CuS launching the state-of-art first-principles calculations taking the exchange and correlation energy functionals based on the gradient generalized approximation and hybrid functionals. After settling the crystal structure, we find elastic constants and related mechanical constants. As the crystal satisfies the stability criterion, so we compute the sound velocity, Debye temperature and lower bound of the thermal conductivity also. The electronic bands dispersion and the density of states exhibit the metallic behavior of the compound. The isotropic and the anisotropic parts of the electron momentum density are calculated by means of the Compton profiles. The isotropic Compton profile is compared with our measurement deploying the 5Ci 241Am spectrometer based on the 59.54 keV gamma-rays and a good agreement is found. The anisotropies in the directional Compton profiles are also presented. The Mulliken population analysis is performed to see nature of bonding and occupied charges on the crystallographically distinct Cu and S atoms in CuS.

Inhomogeneity induced and appropriately parameterized semilocal exchange and correlation energy functionals in two-dimensions.

The construction of meta generalized gradient approximations based on the density matrix expansion (DME) is considered as one of the most accurate techniques to design semilocal exchange energy functionals in two-dimensional density functional formalism. The exchange holes modeled using DME possess unique features that make it a superior entity. Parameterized semilocal exchange energy functionals based on the DME are proposed. The use of different forms of the momentum and flexible parameters is to subsume the non-uniform effects of the density in the newly constructed semilocal functionals. In addition to the exchange functionals, a suitable correlation functional is also constructed by working upon the local correlation functional developed for 2D homogeneous electron gas. The non-local effects are induced into the correlation functional by a parametric form of one of the newly constructed exchange energy functionals. The proposed functionals are applied to the parabolic quantum dots with a varying number of confined electrons and the confinement strength. The results obtained with the aforementioned functionals are quite satisfactory, which indicates why these are suitable for two-dimensional quantum systems.

Extended screened exchange functional derived from transcorrelated density functional theory.

We propose a new formulation of the correlation energy functional derived from the transcorrelated method in use in density functional theory (TC-DFT). An effective Hamiltonian, HTC, is introduced by a similarity transformation of a many-body Hamiltonian, H, with respect to a complex function F: HTC=1FHF. It is proved that an expectation value of HTC for a normalized single Slater determinant, Dn, corresponds to the total energy: E[n] = ⟨Ψn|H|Ψn⟩/⟨Ψn|Ψn⟩ = ⟨Dn|HTC|Dn⟩ under the two assumptions: (1) The electron density nr associated with a trial wave function Ψn = DnF is v-representable and (2) Ψn and Dn give rise to the same electron density nr. This formulation, therefore, provides an alternative expression of the total energy that is useful for the development of novel correlation energy functionals. By substituting a specific function for F, we successfully derived a model correlation energy functional, which resembles the functional form of the screened exchange method. The proposed functional, named the extended screened exchange (ESX) functional, is described within two-body integrals and is parametrized for a numerically exact correlation energy of the homogeneous electron gas. The ESX functional does not contain any ingredients of (semi-)local functionals and thus is totally free from self-interactions. The computational cost for solving the self-consistent-field equation is comparable to that of the Hartree-Fock method. We apply the ESX functional to electronic structure calculations for a solid silicon, H- ion, and small atoms. The results demonstrate that the TC-DFT formulation is promising for the systematic improvement of the correlation energy functional.

Effect of exchange-correlation functionals on the density functional theory simulation of phase transformation of fast-ion conductors: A case study in the Li garnet oxide Li7La3Zr2O12

The phase transformation of a fast-ion conductor Li7La3Zr2O12 (LLZ) upon heating was investigated using first-principle molecular dynamics by applying the local density approximation (LDA) and thirteen generalized gradient approximations (GGA) of the electron exchange and correlation (XC) energy functionals within the density-functional theory (DFT) framework. It was found that some functionals in the selected group failed to predict the phase transformation behavior while others predicted too large or small lattice volumes. Of the fourteen, three functional types, PBEsol, SOGGA, and PBE2, exhibited behaviors consistent with the tetragonal to cubic phase transformation upon heating and they were able to reproduce crystallite volumes within 1.5% of the experimental values. The correlation of XC functional forms and their accuracy in predicting materials properties was discussed.

First-principles calculation on electronic properties of zinc oxide by zinc–air system

First-principles calculations are performed to study the electronic properties of zinc oxide (ZnO) formed on an anode after discharging a Zn–air system. Prior to calculation, the ZnO is characterised by X-ray diffraction using Rietveld refinement. Diffracted patterns proved the formation of single phase ZnO, while Rietveld analysis shows that the ZnO has a hexagonal wurtzite structure with lattice parameters, a=3.244 and c=5.199Å. Geometry optimisation of the hexagonal wurtzite structure of the ZnO is performed using various exchange–correlation energy functionals. The local density approximation functional method is used to explain the structure, electronic band structure and density of state properties of hexagonal ZnO. The calculated energy band gap was 0.75eV while the density of states reveals that the O 2p (the top valence band) and Zn 4s (the bottom conduction band) states domination.