Kinetic energy (KE) approximations are key elements in orbital-free density functional theory. To date, the use of non-local functionals, possibly employing system dependent parameters, has been considered mandatory in order to obtain satisfactory accuracy for different solid-state systems, whereas semilocal approximations are generally regarded as unfit to this aim. Here, we show that instead properly constructed semilocal approximations, the Pauli-Gaussian (PG) KE functionals, especially at the Laplacian-level of theory, can indeed achieve similar accuracy as non-local functionals and can be accurate for both metals and semiconductors, without the need of system-dependent parameters.
The correct treatment of d electrons is of prime importance in order to predict the electronic properties of the prototype chalcopyrite semiconductors. The effect of d states is linked with the anion displacement parameter u, which in turn influences the bandgap of these systems. Semilocal exchange-correlation functionals which yield good structural properties of semiconductors and insulators often fail to predict reasonable u because of the underestimation of the bandgaps arising from the strong interplay between d electrons. In the present study, we show that the meta-generalized gradient ap…
We assess the performance of Tao-Mo semilocal exchange correlation (TM) functional [J. Tao and Y. Mo, Phys. Rev. Lett. 117, 073001 (2016)] using projector-augmented-wave method with the plane wave basis set in Vienna ab initio simulation package (VASP). The meta-GGA level semilocal functional TM is an all purpose exchange-correlation functional which performs accurately for the wide range of molecular and solid state properties. The exchange functional part of TM is designed from the density matrix expansion (DME) technique together with the slowly varying fourth order gradient expansion. The …
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 [Phys. Rev. B 100, 155140 (2019)], 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 fun…
Kohn-Sham (KS) density functional theory (DFT) is a very efficient method for calculating various properties of solids as, for instance, the total energy, the electron density, or the electronic band structure. The KS-DFT method leads to rather fast calculations, however the accuracy depends crucially on the chosen approximation for the exchange and correlation (xc) functional $E_{\text{xc}}$ and/or potential $v_{\text{xc}}$. Here, an overview of xc methods to calculate the electronic band structure is given, with the focus on the so-called semilocal methods that are the fastest in KS-DFT and …
Range separated hybrid density functionals are very successful in describing a wide range of molecular and solid state properties accurately. Range separated hybrid functionals are designed from spherically averaged or system averaged reversed engineered exchange hole. In the present attempt, we employ screened range separated hybrid functional scheme to the meta-GGA rung by using Tao-Mo semilocal exchange hole (or functional). The hybrid functional proposed here utilizes the spherically averaged density matrix expansion based exchange hole in range separation scheme. For slowly varying densit…
The relative energetic stability of the structural phases of common antiferromagnetic transition-metal oxides (MnO, FeO, CoO, and NiO) within the semilocal and hybrid density functionals are fraught with difficulties. In particular, MnO is known to be the most difficult case for almost all common semilocal and hybrid density approximations. Here, we show that the meta-generalized gradient approximation (meta-GGA) constructed from the cuspless hydrogen model and Pauli kinetic energy density (MGGAC) can lead to the correct ground state of MnO. The relative energy differences of zinc-blende (zb) …
It is highlighted recently that the Tao-Mo (TM) [Phys. Rev. Lett. 117, 073001 (2016)] semilocal exchange-correlation energy functional suffers from the order-of-limit problem, which affects the functional performance for phase transition pressures [J. Chem. Phys. 152, 244112 (2020)]. The root of the order-of-limit problem of the TM functional inherent within the interpolation function, which switches between the compact density and the slowly varying density. In this paper, we propose a different switch function that avoids the order-of-limit problem and interpolates correctly between the comp…
The bulk properties (lattice constants, bulk moduli, and cohesive energies) of alkali, alkaline-earth, and transition metals are studied within the framework of the recently developed meta-GGA (meta-Generalized Gradient Approximation) semilocal exchange-correlation functionals. To establish the applicability, broadness and accuracy of meta-GGA functionals we also put the results of PBE (Perdew-Burke-Ernzerhof) and PBEsol (PBE reparametrized for solids) functionals. The interesting feature of the present paper is that it measures the accuracy of the recently developed TM (Tao-Mo) and TMTPSS (TM…
Accurate theoretical prediction of the band offsets at interfaces of semiconductor heterostructures can often be quite challenging. Although density functional theory has been reasonably successful to carry out such calculations and efficient and accurate semilocal functionals are desirable to reduce the computational cost. In general, the semilocal functionals based on the generalized gradient approximation (GGA) significantly underestimate the bulk band gaps. This, in turn, results in inaccurate estimates of the band offsets at the heterointerfaces. In this paper, we investigate the performa…
Ultrafast light-matter interaction is a powerful tool for the study of solids. Upon laser excitation, carrier multiplication and lattice acceleration beyond thermal velocity can occur, as a result of far-from-equilibrium carrier relaxation. The roles of electron-electron and electron-phonon scatterings are identified by first-principles dynamic simulations, from which a unified phase diagram emerges. It not only explains the experimentally-observed "inertial" melting but also predicts abnormal damping by Pauli Exclusion Principle with a new perspective on ultrahigh-intensity laser applications…
The nonlocal van der Waals (NL-vdW) functionals [Dion et al., Phys. Rev. Lett. 92, 246401 (2004)] are being applied more and more frequently in solid-state physics, since they have shown to be much more reliable than the traditional semilocal functionals for systems where weak interactions play a major role. However, a certain number of NL-vdW functionals have been proposed during the last few years, such that it is not always clear which one should be used. In this work, an assessment of NL-vdW functionals is presented. Our test set consists of weakly bound solids, namely rare gases, layered …
A meta generalized gradient level screened range-separated hybrid functional is developed for solid-state electronic structure theory. Assessment of the present range-separated hybrid functional for solid-state lattice constants and band gaps indicate that the present functional can be used for describing those properties efficiently in meta-GGA level. Specifically, the performance of the present functional for band gap of solids indicates that the present meta-GGA level screened hybrids functional is quite productive beyond the GGA level. The most appealing feature of the present formalism is…
The description of the molecular solid phase of O$_2$, especially its ground-state antiferromagnetic insulating phase, is known to be quite unsatisfactory within the conventional local and semilocal density functional approximations used in the Kohn-Sham formalism of density functional theory. The recently-developed van der Waals functionals that take into account nonlocal correlations have also shown subpar performance in this regard. The difficulty lies in the subtle balance between the van der Waals interactions and the exchange coupling between the antiferromagnetic and ferromagnetic molec…
Influence of Exchange-Correlation Functionals and Neural Network Architectures on Li$^+$-Ion Conductivity in Solid-State Electrolyte from Molecular Dynamics Simulations with Machine-Learning Force Fields
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理国家实验室）；University of Chinese Academy of Sciences（中国科学院大学）
Hybrid density functional (HDF) approximations usually deliver higher accuracy than local and semilocal approximations to the exchange-correlation functional, but this comes with drastically increased computational cost. Practical implementations of HDFs inevitably involve numerical approximations -- even more so than their local and semilocal counterparts due to the additional numerical complexity arising from treating the exact-exchange component. This raises the question regarding the reproducibility of the HDF results yielded by different implementations. In this work, we benchmark the num…
Constructed to satisfy all known exact constraints and appropriate norms for a semilocal density functional, the strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation functional has shown early promise for accurately describing the electronic structure of molecules and solids. One open question is how well SCAN predicts the formation energy, a key quantity for describing the thermodynamic stability of solid-state compounds. To answer this question, we perform an extensive benchmark of SCAN by computing the formation energies for a diverse group of nearly …
A revised version of the semilocal exchange-correlation functional [Phys. Rev. Lett. 117, 073001 (2016)] (TM) is proposed by incorporating the modifications to its correlation content obtained from the full high-density second-order gradient expansion as proposed in the case of revised Tao-Perdew-Staroverov-Scuseria (revTPSS) [Phys. Rev. Lett. 103, 026403 (2009)] functional. The present construction improves the performance of TM functional over a wide range of quantum chemical and solid-state properties (thermochemistry and structural). More specifically, the cohesive energies, jellium surfac…
Machine-learned exchange-correlation functionals for molecules, solids, and reactive surfaces
Harvard University（哈佛大学）；Massachusetts Institute of Technology（麻省理工学院）；Robert Bosch LLC Research and Technology Center（罗伯特博世有限责任公司研究与技术中心）；Initiative for Computational Catalysis, Flatiron Institute（计算催化倡议，平顿研究所）
RS-CIDER: A non-local machine learning model for approximating screened hybrid functionals
Center for Computational Science and Engineering, Massachusetts Institute of Technology（麻省理工学院计算科学与工程中心）；Department of Materials Science and Engineering, Massachusetts Institute of Technology（麻省理工学院材料科学与工程系）；John A. Paulson School of Engineering and Applied Sciences, Harvard University（哈佛大学约翰·A·保尔森工程与应用科学学院）；Robert Bosch LLC Research and Technology Center, Watertown（罗伯特博世有限责任公司研究和技术中心）；Initiative for Computational Catalysis, Flatiron Institute（平顿研究所计算催化倡议）
Functionals of the meta-generalized gradient approximation (MGGA) are nowadays widely used in chemistry and solid-state physics for the simulation of electronic systems like molecules, solids, or surfaces. Due to their dependency on the kinetic energy density, they are in principle more accurate than GGA functionals for various properties (geometry, binding energy, electronic structure, etc.), while being nearly as fast since they are still of the semilocal form. Thus, when an accuracy better than GGA is required, one may consider using a MGGA instead of the much more costly hybrid functionals…
Density functional theory within the local or semilocal density approximations (DFT-LDA/GGA) has become a workhorse in electronic structure theory of solids, being extremely fast and reliable for energetics and structural properties, yet remaining highly inaccurate for predicting band gaps of semiconductors and insulators. Accurate prediction of band gaps using firstprinciples methods is time consuming, requiring hybrid functionals, quasi-particle GW, or quantum Monte Carlo methods. Efficiently correcting DFT-LDA/GGA band gaps and unveiling the main chemical and structural factors involved in …
Frequency-dependent dielectric function of semiconductors with application to physisorption
The dielectric function is one of the most important quantities that describes the electrical and optical properties of solids. Accurate modeling of the frequency-dependent dielectric function has great significance in the study of the long-range van der Waals (vdW) interaction for solids and adsorption. In this work, we calculate the frequency-dependent dielectric functions of semiconductors and insulators using the $GW$ method with and without exciton effects, as well as efficient semilocal density functional theory (DFT), and compare these calculations with a model frequency-dependent diele…
Analytical Forces from the Bethe-Salpeter Equation for Large-Scale Excited-State Relaxation
Pritzker School of Molecular Engineering, University of Chicago（芝加哥大学普里茨克分子工程学院）；Initiative for Computational Catalysis, Flatiron Institute（平顿研究所计算催化倡议）；Materials Science Division, Argonne National Laboratory（阿贡国家实验室材料科学部）；Department of Physics, Computer Science, and Mathematics, University of Modena and Reggio Emilia（摩德纳和雷焦艾米利亚大学物理、计算机和数学系）；Department of Chemistry, University of Chicago（芝加哥大学化学系）
Recent investigations have found that the strongly constrained and appropriately normed (SCAN) meta-GGA exchange-correlation functional significantly over-magnetizes elemental Fe, Co, and Ni solids. For the paradigmatic case, bcc Fe, the error relative to experiment is $\gtrsim 20 \%$. Comparative analysis of magnetization results from SCAN and its \textit{deorbitalized} counterpart, SCAN-L, leads to identification of the source of the discrepancy. It is not from the difference between Kohn-Sham (SCAN-L) and generalized Kohn-Sham (SCAN) procedures. The key is the iso-orbital indicator $α$ (the…
Kinetic energy functional constructed from exact gradient expansion of second order in uniform gas limit
School of Physical Sciences, National Institute of Science Education and Research, An OCC of Homi Bhabha National Institute（国家科学教育研究中心物理科学学院）；Faculty of Industrial Engineering, Mechanical Engineering and Computer Science, University of Iceland（冰岛大学工业工程、机械工程和计算机科学学院）；Department of Physics, Indian Institute of Technology Kanpur（坎普尔印度理工学院物理系）
Optically and magnetically active point defects in semiconductors are interesting platforms for the development of solid-state quantum technologies. Their optical properties are usually probed by measuring photoluminescence spectra, which provide information on excitation energies and on the interaction of electrons with lattice vibrations. We present a combined computational and experimental study of photoluminescence spectra of defects in diamond and SiC, aimed at assessing the validity of theoretical and numerical approximations used in first principles calculations, including the use of th…
Finite-temperature adiabatic-connection reduced density-matrix functional theory: a unified framework for i-DMFT and TAO-DFT
Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Department of Applied Physics, Nanjing University of Science and Technology（南京理工大学应用物理系）
