Semiempirical GGA-type density functional constructed with a long-range dispersion correction.
TL;DR: A new density functional of the generalized gradient approximation (GGA) type for general chemistry applications termed B97‐D is proposed, based on Becke's power‐series ansatz from 1997, and is explicitly parameterized by including damped atom‐pairwise dispersion corrections of the form C6 · R−6.
Abstract: A new density functional (DF) of the generalized gradient approximation (GGA) type for general chemistry applications termed B97-D is proposed. It is based on Becke's power-series ansatz from 1997 and is explicitly parameterized by including damped atom-pairwise dispersion corrections of the form C(6) x R(-6). A general computational scheme for the parameters used in this correction has been established and parameters for elements up to xenon and a scaling factor for the dispersion part for several common density functionals (BLYP, PBE, TPSS, B3LYP) are reported. The new functional is tested in comparison with other GGAs and the B3LYP hybrid functional on standard thermochemical benchmark sets, for 40 noncovalently bound complexes, including large stacked aromatic molecules and group II element clusters, and for the computation of molecular geometries. Further cross-validation tests were performed for organometallic reactions and other difficult problems for standard functionals. In summary, it is found that B97-D belongs to one of the most accurate general purpose GGAs, reaching, for example for the G97/2 set of heat of formations, a mean absolute deviation of only 3.8 kcal mol(-1). The performance for noncovalently bound systems including many pure van der Waals complexes is exceptionally good, reaching on the average CCSD(T) accuracy. The basic strategy in the development to restrict the density functional description to shorter electron correlation lengths scales and to describe situations with medium to large interatomic distances by damped C(6) x R(-6) terms seems to be very successful, as demonstrated for some notoriously difficult reactions. As an example, for the isomerization of larger branched to linear alkanes, B97-D is the only DF available that yields the right sign for the energy difference. From a practical point of view, the new functional seems to be quite robust and it is thus suggested as an efficient and accurate quantum chemical method for large systems where dispersion forces are of general importance.
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TL;DR: In this paper, the authors used ab initio density functional theory calculations to understand the electronic, dynamical, and thermoelectric behavior of layered crystalline phase-change materials.
Abstract: We use ab initio density functional theory calculations to understand the electronic, dynamical, and thermoelectric behavior of layered crystalline phase-change materials. We perform calculations on the pseudobinary compounds ${(\mathrm{GeTe})}_{x}/({\mathrm{Sb}}_{2}{\mathrm{Te}}_{3})$ (GST) with $x=1$, 2, and 3. Since the stable configuration of these compounds remains somehow unsettled, we study one stacking configuration for GST124 ($x=1$), three for GST225 ($x=2$), and two for GST326 ($x=3$). A supercell approach is used to check the dynamical stability of the systems while thermoelectric properties are obtained by solving the Boltzmann transport equation. We report that the most accepted stacking configuration of GST124, GST225, and GST326 have metallic character and for the case of $x=2$ and 3, those are the ones with the lowest energy. However, we find the metallic of GST326 configuration to be dynamically unstable. In general, our values of the Seebeck coefficient and thermal conductivity for compounds with $x=1$ and 2 agree very well with the available experimental data. The small differences that we observe with respect to experimental data are attributed to the disorder that is present experimentally and that we have not taken into account. We do not find a Dirac cone in the electronic band structure of GST225, contrarily to previous reports. We attribute this due to the theoretical strain induced by the choice of the pseudopotential.
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TL;DR: In this paper, the authors investigated whether the inclusion of an empirical dispersion correction leads to qualitatively different predictions in comparison with dispersion-uncorrected DFT, taking CO adsorbed in sodium-exchanged chabazite having two different Si/Al ratios (Si/Al = 11:1 and Si/A = 2:1) as a model system.
Abstract: Density functional theory (DFT) calculations have played a pivotal role in identifying and understanding different coordination modes of carbon monoxide adsorbed in zeolites: Previous studies combining IR spectroscopic measurements and DFT have firmly established that an adsorbed CO molecule can interact either with a single cation (single-site interaction), or with two or more cations simultaneously (dual-site or multiple-site interaction). However, one aspect that has been scarcely addressed so far is the dependence of the DFT equilibrium structures on the choice of the functional. With the ongoing development of DFT, exemplified by the more widespread use of dispersion-corrected DFT, this question becomes increasingly relevant. The present study investigates whether the inclusion of an empirical dispersion correction leads to qualitatively different predictions in comparison with dispersion-uncorrected DFT, taking CO adsorbed in sodium-exchanged chabazite having two different Si/Al ratios (Si/Al = 11:1 and Si/Al = 2:1) as a model system. Equilibrium structures obtained with the PBE functional and with the dispersion-corrected PBE-D functional are compared, revealing a tendency of dispersion-corrected DFT to favour a stronger interaction of CO with dual sites. This is indicated by a short contact between the oxygen atom of the CO molecule (already coordinated through its carbon atom to a primary Na+ cation) and a secondary Na+ cation. In addition to these qualitative findings, the quantitative agreement of calculated adsorption enthalpies and C–O stretching frequencies with experimental values obtained from variable-temperature IR spectroscopy is evaluated. While neither functional is particularly successful in predicting accurate adsorption enthalpies, the range of C–O stretching frequency values delivered by the PBE-D functional shows a better agreement with the experimental measurements.
15 citations
Cites methods from "Semiempirical GGA-type density func..."
...As one central aim of this study was to assess the influence of the dispersion correction term, separate calculations were carried out using the PBE functional without dispersion correction [45] and the PBE-D functional, which includes an empirical dispersion correction proposed by Grimme [46] (this particular parameterisation of the Grimme-type dispersion correction is often referred to as “D2”)....
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TL;DR: In this article, the accuracy of dispersion-corrected calculations (DFT-D2, DFT-D3 and DFTNL) with large basis sets (def2-QZVP) to avoid incompleteness effects, for the most stable structure of a real-world polyphenol dimer chosen as an appropriate model was assessed.
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TL;DR: The modelling shows that the distribution of libration amplitudes and phases for different water molecules in the RbBr unit cell varies greatly between the different modes, and the necessity of obtaining low-temperature data to observe all the calculated modes is confirmed.
Abstract: Terahertz spectroscopy of RbBr reveals four prominent absorption lines at room temperature and a further 15 lines at 10 K. Via density-functional-theory (DFT) numerical modelling using the PBE0 hybrid GGA functional, all the absorptions are identified as correlated librations of water molecules in the RbBr lattice. Each libration mode is a combination of rocking, wagging and twisting motions of the water molecules. The number of libration lines and numerical modelling show that the C2v symmetry of water in RbBr is broken. Our modelling shows that the distribution of libration amplitudes and phases for different water molecules in the RbBr unit cell varies greatly between the different modes. All librational lines red-shift with increasing temperature. The rate of change for most lines is in the range 60-90 MHz K(-1) (or (2-3) × 10(-3) cm(-1) K(-1)). Two lines shift more rapidly with temperature, at rates of 240 and 300 MHz K(-1) (or (8 and 10) × 10(-3) cm(-1) K(-1)), respectively. Furthermore, the temperature dependence of the linewidth distinguishes two groups of lines. For one group, with weak linear temperature dependence of linewidth, cubic anharmonic terms in the RbBr crystal field are significant. This group is mainly associated with fully symmetric correlated librations. For the second group, with strong non-linear temperature dependence of the linewidth, quartic anharmonic terms in the RbBr crystal field are significant. However, the distribution of libration amplitudes, as well as the type of libration modes, influence the temperature dependence of the red shift, the linewidth, and the intensity, as well. Our combined experimental and theoretical investigation confirms the necessity of obtaining low-temperature data to observe all the calculated modes; moreover, the richness of detail in the temperature dependence of the data invites further modelling spanning a range of temperatures.
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TL;DR: In this article, the authors revisited the problem of acetylene adsorption on silicon and extended previous theoretical work and including van der Waals forces explicitly in the simulations to remove existing ambiguities about the adsorbing sites.
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TL;DR: A simple derivation of a simple GGA is presented, in which all parameters (other than those in LSD) are fundamental constants, and only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked.
Abstract: Generalized gradient approximations (GGA’s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. [S0031-9007(96)01479-2] PACS numbers: 71.15.Mb, 71.45.Gm Kohn-Sham density functional theory [1,2] is widely used for self-consistent-field electronic structure calculations of the ground-state properties of atoms, molecules, and solids. In this theory, only the exchange-correlation energy EXC › EX 1 EC as a functional of the electron spin densities n"srd and n#srd must be approximated. The most popular functionals have a form appropriate for slowly varying densities: the local spin density (LSD) approximation Z d 3 rn e unif
146,533 citations
TL;DR: In this article, a semi-empirical exchange correlation functional with local spin density, gradient, and exact exchange terms was proposed. But this functional performed significantly better than previous functionals with gradient corrections only, and fits experimental atomization energies with an impressively small average absolute deviation of 2.4 kcal/mol.
Abstract: Despite the remarkable thermochemical accuracy of Kohn–Sham density‐functional theories with gradient corrections for exchange‐correlation [see, for example, A. D. Becke, J. Chem. Phys. 96, 2155 (1992)], we believe that further improvements are unlikely unless exact‐exchange information is considered. Arguments to support this view are presented, and a semiempirical exchange‐correlation functional containing local‐spin‐density, gradient, and exact‐exchange terms is tested on 56 atomization energies, 42 ionization potentials, 8 proton affinities, and 10 total atomic energies of first‐ and second‐row systems. This functional performs significantly better than previous functionals with gradient corrections only, and fits experimental atomization energies with an impressively small average absolute deviation of 2.4 kcal/mol.
87,732 citations
TL;DR: Numerical calculations on a number of atoms, positive ions, and molecules, of both open- and closed-shell type, show that density-functional formulas for the correlation energy and correlation potential give correlation energies within a few percent.
Abstract: A correlation-energy formula due to Colle and Salvetti [Theor. Chim. Acta 37, 329 (1975)], in which the correlation energy density is expressed in terms of the electron density and a Laplacian of the second-order Hartree-Fock density matrix, is restated as a formula involving the density and local kinetic-energy density. On insertion of gradient expansions for the local kinetic-energy density, density-functional formulas for the correlation energy and correlation potential are then obtained. Through numerical calculations on a number of atoms, positive ions, and molecules, of both open- and closed-shell type, it is demonstrated that these formulas, like the original Colle-Salvetti formulas, give correlation energies within a few percent.
84,646 citations
TL;DR: In this paper, the Hartree and Hartree-Fock equations are applied to a uniform electron gas, where the exchange and correlation portions of the chemical potential of the gas are used as additional effective potentials.
Abstract: From a theory of Hohenberg and Kohn, approximation methods for treating an inhomogeneous system of interacting electrons are developed. These methods are exact for systems of slowly varying or high density. For the ground state, they lead to self-consistent equations analogous to the Hartree and Hartree-Fock equations, respectively. In these equations the exchange and correlation portions of the chemical potential of a uniform electron gas appear as additional effective potentials. (The exchange portion of our effective potential differs from that due to Slater by a factor of $\frac{2}{3}$.) Electronic systems at finite temperatures and in magnetic fields are also treated by similar methods. An appendix deals with a further correction for systems with short-wavelength density oscillations.
47,477 citations
TL;DR: This work reports a gradient-corrected exchange-energy functional, containing only one parameter, that fits the exact Hartree-Fock exchange energies of a wide variety of atomic systems with remarkable accuracy, surpassing the performance of previous functionals containing two parameters or more.
Abstract: Current gradient-corrected density-functional approximations for the exchange energies of atomic and molecular systems fail to reproduce the correct 1/r asymptotic behavior of the exchange-energy density. Here we report a gradient-corrected exchange-energy functional with the proper asymptotic limit. Our functional, containing only one parameter, fits the exact Hartree-Fock exchange energies of a wide variety of atomic systems with remarkable accuracy, surpassing the performance of previous functionals containing two parameters or more.
45,683 citations