One of the standard generalized-gradient approximations (GGAs) in use in modern electronic-structure theory, PBE, and a recently proposed modification designed specifically for solids, PBEsol, are identified as particular members of a family of functionals taking their parameters from different properties of homogeneous or inhomogeneous electron liquids. Three further members of this family are constructed and tested, together with the original PBE and PBEsol, for atoms, molecules and solids. We find that PBE, in spite of its popularity in solid-state physics and quantum chemistry, is not always the best performing member of the family, and that PBEsol, in spite of having been constructed specifically for solids, is not the best for solids. The performance of GGAs for finite systems is found to sensitively depend on the choice of constraints steaming from infinite systems. Guidelines both for users and for developers of density functionals emerge from this work.
Structural geometries, formation enthalpies, and dissociation energies of all diatomic and triatomic molecules consisting of the four basic elements C, H, N, and/or O are calculated from the projector augmented wave (PAW) density functional theory (DFT) method with the PBE and optB88-vdW exchange-correlation functionals. The calculations are also extended to two larger molecules NO3 and HNO3, which consist of 4 and 5 atoms, respectively. In total, 82 molecules or isomers are considered in the calculations. The geometric parameters including 42 bond lengths and 15 bond angles of these molecules…
Data science and machine learning in materials science require large datasets of technologically relevant molecules or materials. Currently, publicly available molecular datasets with realistic molecular geometries and spectral properties are rare. We here supply a diverse benchmark spectroscopy dataset of 61,489 molecules extracted from organic crystals in the Cambridge Structural Database (CSD), denoted OE62. Molecular equilibrium geometries are reported at the Perdew-Burke-Ernzerhof (PBE) level of density functional theory (DFT) including van der Waals corrections for all 62k molecules. For…
An alternative type of approximation for the exchange and correlation functional in density functional theory is proposed. This approximation depends on a variable $u$ that is able to detect inhomogeneities in the electron density $ρ$ without using derivatives of $ρ$. Instead, $u$ depends on the orbital energies which can also be used to measure how a system differs from the homogeneous electron gas. Starting from the functional of Perdew, Burke, and Ernzerhof (PBE) [Phys. Rev. Lett. 77, 3865 (1996)], a functional depending on $u$ is constructed. Tests on the lattice constant, bulk modulus, an…
Adsorption of the molecule CO on metallic surfaces is an important unsolved problem in Kohn-Sham density functional theory (KS-DFT). We present a detailed study of carbon monoxide adsorption on fcc (111) surfaces of 3d, 4d and 5d metals using nonempirical semilocal density functionals for the exchange-correlation energy: the local-density approximation (LDA), two generalized gradient approximations or GGAs (PBE and PBEsol), and a meta-GGA (SCAN). The typical error pattern (as found earlier for free molecules and for free transition metal surfaces), in which results improve from LDA to PBE or P…
Uncertainty of DFT calculated mechanical and structural properties of solids due to incompatibility of pseudopotentials and exchange-correlation functionals
The $GW$ approximation to many-body perturbation theory is a reliable tool for describing charged electronic excitations, and it has been successfully applied to a wide range of extended systems for several decades using a plane-wave basis. However, the $GW$ approximation has been used to test limited spectral properties of a limited set of finite systems (e.g. frontier orbital energies of closed-shell $sp$ molecules) only for about a decade using a local-orbital basis. Here, we calculate the quasiparticle spectra of closed- and open-shell molecular anions with partially and completely filled …
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 …
Functional and Density-Driven Errors in Density Functional Theory: Quantum Monte Carlo Benchmarks for Solids
Ruhr University Bochum（波鸿鲁尔大学）；Research Center Future Energy Materials and Systems of the University Alliance Ruhr（鲁尔大学联盟未来能源材料与系统研究中心）；Interdisciplinary Centre for Advanced Materials Simulation（先进材料模拟跨学科中心）
The performance of density functional theory (DFT) approximations for predicting materials thermodynamics is typically assessed by comparing calculated and experimentally determined enthalpies of formation from elemental phases, ΔHf. However, a compound competes thermodynamically with both other compounds and their constituent elemental forms, and thus, the enthalpies of the decomposition reactions to these competing phases, ΔHd, determines thermodynamic stability. We evaluated the phase diagrams for 56,791 compounds to classify decomposition reactions into three types: 1. those that produce e…
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…
Quantum Monte Carlo Calculations of Dihydrogen Binding Energetics on Ca Cations: an Assessment of Errors in Density Functionals for Weakly Bonded Systems
We revisit the two derivations of the PBE correlation functional: The real-space cut-off of the exchange-correlation hole and the imposition of exact conditions. These differ in the Lieb-Simon limit, exemplified by the scaling of neutral atoms to large $N$ and $Z$, in which LDA becomes relatively exact. We use the leading correction to this limit for neutral atoms to design an asymptotically corrected correlation GGA as a compromise between these two constructions which becomes relatively more accurate for atoms with increasing atomic number. When paired with a similar correction for exchange,…
Comparative study of unscreened and screened molecular static linear polarizability in the Hartree-Fock, hybrid-density functional, and density functional models
The aim of this study is to clarify the physics which governs the transition from epsilon phase to zeta phase of solid oxygen observed experimentally at 96 GPa using density functional theory (DFT). The transition was predicted at 40 GPa with PBE functional. Then the Hubbard correction was added to enhance the localization of p-orbital of oxygen. The epsilon-zeta transition pressure was significantly improved to 70 GPa. Finally, we included the non-local van der Waals correction. The transition pressure slightly increases to 80 GPa. These results demonstrate that the contribution from Hubbard …
Open-shell systems such as magnetic molecules or defects with a triplet ground state are challenging to describe in electronic structure methods, but are of great interest for quantum information applications. We demonstrate a spin-flip approach within the Bethe-Salpeter equation to calculate ground and excited states of open-shell molecules and defected solids. The approach works in periodic boundary conditions without any need for embedding or selection of a subspace. Our benchmark results for the torsion potential-energy surface of ethylene and the optical excitations of the diamond NV$^{-}…
Configurations of the molecules on the wall of a vacancy, formed by removing a central and its first and second nearest-neighbor (NN) molecules in solid CO2 with the Pa3 structure, were calculated by the Monte Carlo simulation technique at T = 0, 100, and 200 K and a nominal pressure of P = 1 bar. It was found that the deviations of both the center-of-mass and the orientational coordinates of the molecules from the unperturbed coordinates had a three-fold symmetry about a body diagonal axis of the crystal. It was also found that a single CO2 molecule, initially placed in the center of the vaca…
In this work we investigate the electronic properties of mercaptocarboxylic acids with several carbon chain lengths adsorbed on ZnO-(10-10) surfaces via density functional theory calculations using semi-local and hybrid exchange-correlation functionals. Amongst the investigated structures, we identify the monodentate adsorption mode to be stable. Moreover, this mode introduces optically active states in the ZnO gap, is further confirmed by the calculation of the dielectric function at PBE0 and TD-PBE0 levels. One interesting finding is that adsorption mode and the dielectric properties of the …
The interaction between electronic and nuclear spins in the presence of external magnetic fields can be described by a spin Hamiltonian, with parameters obtained from first principles, electronic structure calculations. We describe an approach to compute these parameters, applicable to both molecules and solids, which is based on Density Functional Theory (DFT) and real-space, all-electron calculations using finite elements (FE). We report results for hyperfine tensors, zero field splitting tensors (spin-spin component) and nuclear quadrupole tensors of a series of molecules and of the nitroge…
Post density functional theoretical studies of highly polar semiconductive Pb(Ti$_{1-x}$Ni$_{x}$)O$_{3-x}$ solid solutions: The effects of cation arrangement on band gap
Energetically minimum configurations of the first- and second-nearest neighbor (NN) CO2 molecules surrounding a vacancy, created by removing a single molecule from the Pa3 structure, were calculated by use of the Monte Carlo simulation technique at zero temperature. It was found that among the 1st NN molecules, only six NN molecules, closest to the oxygen atoms of the removed CO2 molecule, significantly changed the positions and orientations, while the other six molecules were not influenced by the creation of the vacancy. The configurations of the molecules no longer had the three-fold symmet…
Accurately predicting the formation energy of a compound, which describes its thermodynamic stability, is a key challenge in materials physics. Here, we employ many-body quantum Monte Carlo (QMC) with single-reference trial functions to compute the formation energy of two electronically disparate compounds, the intermetallic VPt$_2$ and the semiconductor CuI, for which standard density functional theory (DFT) predictions using both the Perdew-Burke Ernzerhof (PBE) and the strongly constrained and appropriately normed (SCAN) density functional approximations deviate markedly from available expe…
Dispersion Corrected DFT Study of Pentacene Thin Films on Flat and Vicinal Au Surfaces
本文采用密度泛函理论研究了并五苯超薄膜在平面[（111）]和邻位[（455）] Au表面上的性质。我们已经进行了晶体和电子结构的计算，通过使用PBE和optB 86 b-vdW泛函和研究的影响，从一个单一的孤立分子的覆盖范围从4单层的覆盖范围不同的覆盖范围的长程范德华相互作用。对于一个孤立的分子，这两个功能产生的中空网站作为最稳定的一个与桥60网站是非常接近的能量的情况下optB 86 b-vdW。并五苯在台阶边缘的结合强度远大于在阶地上的结合强度。比较了不同的实验报道的单层结构，发现（6 x 3）晶胞比（2 x 2 $\sqrt{7}$）和（2 x $\sqrt{31}$）晶胞在能量上更稳定。对于一个单层膜，虽然分散校正的计算有利于平台上的平坦并五苯分子，但标准（PBE）计算发现倾斜和平坦构型在能量上相似（在（111）表面上）或有利于倾斜构型（在（455）表面上）。用optB 86 b-vdW泛函进行的PDOS计算表明，与（111）表面相比，（455）表面的Au态上分子轨道的分散度更大，表明并五苯-金界面处的载流子传输增强，有利于邻位表面。从第二个单层开始，两个泛函都有利于两个表面的倾斜配置。我们的研究结果强调了分散校正的重要性，松散的结合系统，如并五苯在金和步骤的边缘在确定多层膜结构和电荷转移在有机分子-金属界面所发挥的作用。
