描述甲烷在Pt(110)-(21)表面的化学吸附解离的密度泛函评估

本文探讨了几种梯度近似(GGA)密度泛函及元梯度近似(meta-GGA)密度泛函在描述甲烷在重构的Pt(110)-(2×1)上的解离化学吸附作用的适用性. 金属的体相和表面结构、甲烷的吸附能量和解离能垒等被用来评估泛函的可靠性. 另外,在从头算分子动力学计算中,采用范德瓦尔斯矫正的GGA函数(optPBE-vdW)和范德瓦尔斯矫正的meta-GGA函数(MS-PBEl-rVV10）计算粘附概率. 计算结果表明,使用这两种泛函能更好地与现有的实验结果吻合,从而为发展甲烷在Pt(110)-(2×1)表面解离的可靠机器学习势能面打下重要基础.     

Quantum Monte Carlo assessment of density functionals for π-electron molecules: ethylene and bifuran

ABSTRACT

We perform all-electron, pure-sampling quantum Monte Carlo (QMC) calculations on ethylene and bifuran molecules. The orbitals used for importance sampling with a single Slater determinant are generated from Hartree-Fock and density functional theory (DFT). Their fixed-node energy provides an upper bound to the exact energy. The best performing density functionals for ethylene are BP86 and M06, which account for 99% of the electron correlation energy. Sampling from the π-electron distribution with these orbitals yields a quadrupole moment comparable to coupled cluster CCSD(T) calculations. However, these, and all other density functionals, fail to agree with CCSD(T) while sampling from electron density in the plane of the molecule. For bifuran, as well as ethylene, a correlation is seen between the fixed-node energy and deviance of the QMC quadrupole moment estimates from those calculated by DFT. This suggests that proximity of DFT and QMC densities correlates with the quality of the exchange nodes of the DFT wave function for both systems.     

Van der Waals interactions in DFT made easy by Wannier functions

Ubiquitous van der Waals interactions between atoms and molecules are important for many molecular and solid structures. These systems are often studied from first principles using the density functional theory (DFT). However, the commonly used DFT functionals fail to capture the essence of van der Waals effects. Most attempts to correct for this problem have a basic semiempirical character, although computationally more expensive first principles schemes have been recently developed. We here describe a novel approach, based on the use of the maximally localized Wannier functions, that appears to be promising, being simple, efficient, accurate, and transferable (charge polarization effects are naturally included). The results of test applications to small molecules and bulk graphite are presented.     

Density functional theory study on the magnetic properties of Co3O4 with normal spinel structure

The magnetic properties of Co₃O₄ with a normal spinel structure were investigated via the full potential linearized augmented plane wave (FP-LAPW) method based on density functional theory (DFT). The exchange and correlation effects between electrons were treated with a standard generalized gradient approximation (GGA) from Perdew–Burke–Ernzerhof (PBE), as a function of the on-site Coulomb U term, the GGA−PBE+U method, and a B3PW91 hybrid functional with different Hartree–Fock exchange admixtures. Were calculated all of these exchange–correlation (XC) functionals both with and without spin–orbit coupling (SOC). The objective for these calculations was to predict the ground-state magnetic structure of Co₃O₄ crystal using different XC functionals and to investigate the influence that SOC had on these results. All of our calculations confirmed that the collinear antiferromagnetic (AFM) order was energetically more favorable than the ferromagnetic (FM) one, which agrees with experimental findings. This conclusion was not influenced by the XC functional type employed or whether the spin–orbit effect was used. Thus, the present work does not confirm the recent DFT plane wave pseudopotential results that when including spin–orbit effects, the calculations determined that the collinear FM state had lower energy than the AFM one.     

Fractional-charge and fractional-spin errors in range-separated density-functional theory

ABSTRACT

We investigate fractional-charge and fractional-spin errors in range-separated density-functional theory (DFT). Specifically, we consider the range-separated hybrid (RSH) method which combines long-range Hartree-Fock (HF) exchange with a short-range semilocal exchange-correlation density functional, and the RSH+MP2 method which adds long-range, second-order Møller-Plesset (MP2) correlation. Results on atoms and molecules show that the fractional-charge errors obtained in RSH are much smaller than in the standard Kohn-Sham (KS) scheme applied with semilocal or hybrid approximations, and also generally smaller than in the standard HF method. The RSH+MP2 method tends to have smaller fractional-charge errors than standard MP2 for the most diffuse systems, but larger fractional-charge errors for the more compact systems. Even though the individual contributions to the fractional-spin errors in the H atom coming from the short-range exchange and correlation density-functional approximations are smaller than the corresponding contributions for the full-range exchange and correlation density-functional approximations, RSH gives fractional-spin errors that are larger than in the standard KS scheme and only slightly smaller than in standard HF. Adding long-range MP2 correlation only leads to infinite fractional-spin errors. This work clarifies the successes and limitations of range-separated DFT approaches for eliminating self-interaction and static-correlation errors.     

The importance of the asymptotic exchange-correlation potential in density functional theory

The importance to density functional theory (DFT) of the integer discontinuity in the exchange-correlation potential is reiterated and further examined. It follows that if generalized gradient approximation (GGA) functional are used, then the asymptotic value of the exchange-correlation potential must be a positive system-dependent constant. Our previously introduced asymptotic correction (AC), which forces the correct behaviour of the potential in the asymptotic region, is further discussed. Three examples are given that demonstrate the importance of the analysis; (i) HOMO eigenvalues lie well above the negative of the ionization energy when GGA functionals are used—this is not detrimental to GGA DFT; (ii) an independent calculation of the GGA asymptotic potentials for some molecules is presented, based on the determination of parametrized GGA functionals; (iii) Rydberg states of He⁺ and H⁺ ₂ are studied, demonstrating that essentially exact Rydberg potential energy curves can be determined if the AC is used, even though the valence curves may be incorrect.     

Electronic Structure of RCo2 (R = Y, Nd, Ho, Er)

The results of electronic structure studies of the YCo₂ performed in the framework of the density functional theory (DFT) are reported. We have applied both local spin density approximation (LSDA) and generalized gradient approximation (GGA) for the treatment of exchange and correlation effects. We have found the stable paramagnetic ground state (a _min/a _exp = 0.962) using LSDA. In addition, we have investigated the influence of the local R-4f moments in RCo₂ (R = Nd, Ho, Er) on the ferrimagnetic solution using a self-interaction corrected LSDA method.     

Density functional theory of transition metal phthalocyanines,I: electronic structure of NiPc and CoPc—self-interaction effects

We present a two-part systematic density functional theory study of the electronic structure of selected transition metal phthalocyanines. We use a semi-local generalized gradient approximation (GGA) functional, as well as several hybrid exchange-correlation functionals, and compare the results to experimental photoemission data. Here, we study the low-spin systems NiPc and CoPc. We show that hybrid functionals provide computed photoemission spectra in excellent agreement with experimental data, whereas the GGA functional fails qualitatively. This failure is primarily because of under-binding of localized orbitals due to self-interaction errors.     

An efficient implementation of two-component relativistic density functional theory with torque-free auxiliary variables

An integration and assembly strategy for efficient evaluation of the exchange correlation term in relativistic density functional theory within two-component Kohn–Sham framework is presented. Working equations that both take into account all the components of the spin magnetization and can exploit parallelism, optimized cache utilization, and micro-architecture specific-floating point operations are discussed in detail in this work. The presented assembly of the exchange correlation potential, suitable for both open and closed shell systems, uses spinor density and a set of auxiliary variables, ensuring easy retrofitting of existing density functionals designed for collinear density. The used auxiliary variables in this paper, based on the scalar and non-collinear density, can preserve non-zero exchange correlation magnetic field local torque, without violating the required overall zero torque, even for GGA functionals. This is mandatory to obtain accurate spin dynamics and proper time evolution of the magnetization. Spin frustrated hydrogen rings are used to validate the current implementation and phenoxy radicals of different sizes are used to monitor the performance. This approach is a step towards extending the applicability of relativistic two-component DFT to systems of large size (>100 atoms).     

Accurate non-relativistic density functional theory predictions for 77Se NMR shielding parameters

A reoptimized density functional theory (DFT) hybrid functional gives orbitals and energies which when substituted into the uncoupled generalized gradient approximation (GGA) sum-over-states expressions gives NMR shielding constants of high accuracy for first- and second-row nuclei. This procedure is validated further and its performance compared against well established exchange-correlation (XC) functionals for the prediction of the third-row ⁷⁷Se NMR shielding constants, in a series of challenging molecules where both accurate theoretical and experimental data are available. The shielding parameters obtained from this new mixed hybrid GGA scheme provide a significant improvement over conventional XC functionals. and are competitive with the benchmark coupled-cluster singles and doubles (CCSD) methods. From these results together with previous studies it is now apparent that this new GGA shielding scheme provides high accuracy NMR shielding constants for first-, second-and third-row atoms (excluding transition-metal atoms) even in molecules exhibiting large correlation effects.     

Chlorination of ammonia and aliphatic amines by Cl2: DFT study of medium and substituent effects

The mechanism of chlorination of ammonia and aliphatic amines by Cl₂ was studied by quantum‐chemical calculations using a series of DFT functionals. Three different reaction pathways were considered for the reaction between Cl₂ and NH₃ in the gas phase. Several intermediates and transition state structures, not described earlier, were located on the corresponding potential energy surface. It is calculated that the reaction field effects (SCIPCM) on the chlorination is much less pronounced than the effect of a specific solvent interaction which was modeled by an explicit water molecule. It is also found that the calculated energy barrier and the reaction free energy of the chlorination of different amines are dependent on the alkyl‐substituent effects. With increase in the basicity of amine, the chlorination reaction becomes more feasible. Calculated geometries of intermediates and overall reaction energetics are significantly influenced by the method for a treatment of electron correlation (DFT vs. MP2), and by the fraction of HF exchange (χ) in DFT functionals. With increase in the χ in the corresponding functional, the DFT results approach those obtained at the MP2 level, and are closer to experimental values, as well. Copyright © 2008 John Wiley & Sons, Ltd.     

Eigenvalues,integer discontinuities and NMR shielding constants in Kohn—Sham theory

Kohn—Sham eigenvalues are determined from coupled cluster electron densities. The calculated HOMO—LUMO eigenvalue differences are compared with those from conventional generalized gradient approximation (GGA) exchange-correlation functionals for a range of small molecules. In all cases, GGA HOMO—LUMO differences are smaller than those calculated from the coupled cluster densities. When the GGA HOMO—LUMO differences are explicitly corrected—such that they equal those calculated from electron densities—significant improvements in NMR shielding constants are obtained. The eigenvalues calculated from electron densities are also used to approximate the magnitude of the integer discontinuity in the exact exchange-correlation potential. The value of the Kohn—Sham HOMO eigenvalue is then considered. Although HOMO eigenvalues from high quality, asymptotically vanishing, exchange-correlation potentials are close to the negative of the ionization potential, HOMO eigenvalues from the GGA functionals are shifted upwards by approximately 50% of the calculated integer discontinuity. An alternative approach for correcting NMR shielding constants is investigated.     

Attracted by long-range electron correlation: adenine on graphite

The adsorption of adenine on graphite is analyzed from first-principles calculations as a model case for the interaction between organic molecules and chemically inert surfaces. Within density-functional theory we find no chemical bonding due to ionic or covalent interactions, only a very weak attraction at distances beyond the equilibrium position due to the lowering of the kinetic energy of the valence electrons. Electron exchange and correlation effects are much more important for the stabilization of the adsystem. They are modeled by the local density or generalized gradient approximation supplemented by the London dispersion formula for the van der Waals interaction.     

Role of electron correlation in the polydeprotonation of benzene to form trianions

Computations for anion, dianions, and trianions of benzene are carried out to study the role of electron correlation in the polydeprotonation of benzene leading to benzene trianions both in the singlet and triplet states. The computations, while assessing the use of polarization and diffuse functions, are performed with Møller–Plesset second‐order (MP2) perturbation theory and coupled‐cluster theory up to the level of CCSD(T)/6‐311++G(d,p)//MP2/6‐311++G(d,p), and with density functional theory (DFT) employing a hybrid, B3LYP, and a meta‐hybrid, M05‐2X, exchange‐correlation functionals with Gaussian basis set 6‐311++G(d,p) and correlation consistent basis set aug‐cc‐pVDZ. The deprotonation energies, including zero‐point energy correction, of benzene anion and dianions are found to be highly sensitive to the quantum mechanical method and the basis set used. The formation of dianions and trianions, where the anionic centers lie adjacent to each other, is observed with unusual behavior in the deprotonation energy and the geometrical parameters obtained from the different level of the theories. The two exchange‐correlation functionals compared show contrasting and unusual results for the trianionic species particularly for the triplet states, even if the diffuse functions are included in the basis set. Besides this, the ortho‐dianion and 1,3,5‐trianion are predicted to be ground‐state triplet at CCSD(T)/6‐311++G(d,p)//MP2/6‐311++G(d,p) and DFT/M05‐2X/6‐311++G(d,p) levels, whereas DFT/B3LYP/6‐311++G(d,p) predicts meta‐dianion and 1,2,3‐trianion to be ground‐state triplet where all the anionic centers lie adjacent to each other. Copyright © 2014 John Wiley & Sons, Ltd.     

Climbing the density functional ladder: nonempirical meta-generalized gradient approximation designed for molecules and solids

The electron density, its gradient, and the Kohn-Sham orbital kinetic energy density are the local ingredients of a meta-generalized gradient approximation (meta-GGA). We construct a meta-GGA density functional for the exchange-correlation energy that satisfies exact constraints without empirical parameters. The exchange and correlation terms respect two paradigms: one- or two-electron densities and slowly varying densities, and so describe both molecules and solids with high accuracy, as shown by extensive numerical tests. This functional completes the third rung of "Jacob's ladder" of approximations, above the local spin density and GGA rungs.     

van der Waals interactions between thin metallic wires and layers

Quantum Monte Carlo (QMC) methods have been used to obtain accurate binding-energy data for pairs of parallel thin metallic wires and layers modeled by 1D and 2D homogeneous electron gases. We compare our QMC binding energies with results obtained within the random phase approximation, finding significant quantitative differences and disagreement over the asymptotic behavior for bilayers at low densities. We have calculated pair-correlation functions for metallic biwire and bilayer systems. Our QMC data could be used to investigate van der Waals energy functionals.     

CO2在金属有机骨架材料有机链上的吸附机理研究

金属有机骨架是一种新型的温室气体CO₂吸附材料。本文采用密度泛函理论（DFT）方法研究CO₂在MOF-5有机链上的6种不同吸附位置及其3种不同构型下的吸附行为。考虑GGA水平下三种不同泛函对计算结果的影响,对比发现GGA/PW91泛函能够较好地计算CO₂分子与有机链原子之间的弱范德华力;发现CO₂分子与苯环边相交以及与苯环上的碳原子平行是两种吸附能最大的构型;利用Br原子替代苯环上的H原子可以显著增强对CO₂分子的吸附能力,为设计具有较高CO₂吸附能力的MOFs材料提供理论依据。