Density-functional thermochemistry. V. Systematic optimization of exchange-correlation functionals

Density functional theory (DFT) is widely used to predict materials properties, but the local density approximation (LDA) and generalized gradient approximation (GGA) exchange-correlation functionals are known to poorly predict the energetics of reactions involving molecular species. In this paper, we obtain corrections for the O${}_{2}$, H${}_{2}$, N${}_{2}$, F${}_{2}$, and Cl${}_{2}$ molecules within the Perdew-Burke-Enzerhof GGA, Perdew-Wang GGA, and Perdew-Zunger LDA exchange-correlation functionals by comparing DFT-calculated formation energies of oxides, hydrides, nitrides, fluorides, and chlorides to experimental values. We also show that the choice of compounds used to obtain the correction is significant, and we use a leave-one-out cross-validation approach to rigorously determine the proper fit set. We report confidence intervals with our correction values, which quantifies the variation caused by the choice of fit set after outlier removal. The remaining variation in the correction values is of the order of 1 kcal/mol, which indicates that chemical accuracy is a realistic goal for these systems.

Density functional theory (DFT) within the generalized gradient approximation (GGA) is known to poorly reproduce the experimental properties of liquid water. The poor description of the dispersion forces in the exchange correlation functionals is one of the possible causes. Recent studies have demonstrated an improvement in the simulated properties when they are taken into account. We present here a study of the effects on liquid water of the recently proposed semi-empirical correction of Grimme et al. [J. Chem. Phys. 132, 154104 (2010)]. The difference between standard and corrected DFT-GGA simulations is rationalized with a detailed analysis upon modifying an accurate parameterised potential. This allows an estimate of the typical range of dispersion forces in water. We also show that the structure and diffusivity of ambient-like liquid water are sensitive to the fifth neighbor position, thus highlighting the key role played by this neighbor. Our study is extended to water at supercritical conditions, where experimental and theoretical results are much more scarce. We show that the semi-empirical correction by Grimme et al. improves significantly, although somewhat counter-intuitively, both the structural and the dynamical description of supercritical water.

First principle calculations using density functional theory (DFT) and full-potential linearized augmented plane waves (FP-LAPW) method are performed to investigate the structural and electronic properties of rutile phase titanium, vanadium, ruthenium, iridium and tin dioxides, TiO2, VO2, RuO2, IrO2, and SnO2, respectively. The exchange correlation function is described using the local density approximation (LDA) and the generalized gradient approximation (GGA). The structural parameters of the dioxides are found to be in a fair agreement with experimental values and previous calculations. TiO2 exhibits the maximum cohesive energy and RuO2 exhibits the minimum, which is opposite to the trend of pure bulk metals. Titanium dioxide in the left of the periodic table exhibits an insulating behavior with an underestimated bandgap of 2 eV. As the d-band filling increases in VO2, the energy bands shift by 3 eV from those of TiO2 to cross the Fermi level and exhibit a metallic behavior with a pseudo gap to the right of the Fermi level. The energy bands coalescence in RuO2 and IrO2 exhibiting metallic behaviors. However, for a complete filled d-band SnO2, the insulating behavior is retrieved. The distortion of the octahedrons in the rutile structure lifts the degeneracy of the eg orbitals causing further splittings.

Pressure induced tunable physical properties of cubic KHgF3 fluoro-perovskite: A first principle study

We examine in this work the potential and the functional to be used in a density functional theory approach in order to describe correctly the formation and migration energies of monovacancies in nickel. As the formation enthalpy is not well-known experimentally at $0\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, we choose in a first step to determine some structural, magnetic, and elastic properties of the bulk, which are well-established experimentally. The comparison between both approaches, i.e., the local spin density approximation (LSDA) and the generalized gradient approximation (GGA) exchange-correlation functionals is analyzed. We conclude that the contribution of nonlocal GGA terms in order to describe correctly the electronic density is necessary to determine the formation and migration enthalpies and activation energy of monovacancy. The calculated formation ${H}_{v}^{f}$ and migration ${H}_{v}^{m}$ enthalpies differ significantly between both approaches. The overestimation of the LSDA approximation is of $0.25\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ for ${H}_{v}^{f}$ and of $0.23\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ for ${H}_{v}^{m}$ with respect to the GGA one, leading to a gap of $0.48\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ between both methods for the activation energy ${Q}_{1}$. We show that the GGA results are comparable with experimental data if the thermal expansion contribution is taken into account through the lattice parameter variation. Finally, it is shown that the activation energy is nearly independent of the thermal expansion effects; thus we can expect that the curvature of the Arrhenius plot of the diffusion factor near the melting point is essentially due to the contribution of divacancies.

Pressure dependence of the structural and elastic properties of perovskite-type cubic SrWO2.05N0.95 was studied using firstprinciples density functional theory (DFT) utilizing the plane wave pseudopotential and the exchange-correlation functionals within the generalized gradient approximation. The estimated bulk modulus and its pressure derivative values from the P − V data fitted to the third-order Birch-Murnaghan equation of state were close to the data obtained from the independent elastic constants. Based on the generalized Born stability criteria, SrWO2.05N0.95 is mechanically stable up to 139 GPa. The influence of hydrostatic pressure (0 to 139 GPa) on the bulk modulus, shear modulus, Young’s modulus, Pugh’s modulus ratio, Poisson’s ratio, Vickers hardness, sound velocities, Debye temperature, Debye-Gruneisen parameter, minimum thermal conductivity and elastic anisotropy of SrWO2.05N0.95 was particularly studied in detail. It was found that SrWO2.05N0.95 is a ductile and hard solid with large bulk, shear and Young’s modulus and displays an extraordinary low thermal conductivity. Since there are not any experimental or theoretical data available for comparison the results of the present study have revealed an important fundamental information about the elastic properties of perovskite-type cubic SrWO2.05N0.95 for future experimental studies.

We benchmark the rSCAN and r2SCAN exchange-correlation functionals by comparing the Nuclear Magnetic Resonance (NMR) magnetic shieldings predicted by Density Functional Theory (DFT) to experimentally observed chemical shifts of halide and oxide inorganic compounds. Significant improvement in accuracy is achieved compared to the Generalised Gradient Approximation (GGA) at a marginally higher computational cost. When using rSCAN or r2SCAN, the correlation coefficient between computationally predicted and experimental values approaches the theoretically expected value of -1 while reducing the deviation, allowing more accurate and reliable spectrum assignments of complex compounds in experimental investigations.

The adsorption and diffusion of hydrogen on the (100) surface of titanium nitride was studied using density-functional theory (DFT) and the generalized gradient approximation (GGA) for the exchange and correlation energy. The adsorption site was found to be on top of the titanium atom with the chemisorption energy of -2.88 eV. The diffusion barrier was determined as 0.73 eV along the path connecting the neighboring titanium atoms. The surface energies and surface relaxations of the three most important surfaces of TiN were studied. The surface energies have the following order: ${S}_{100}<{S}_{110}<{S}_{111}.$ Three different GGA functionals, the Perdew-Wang 1991 (PW91), the Perdew-Burke-Ernzerhof (PBE), and the revised PBE (RPBE) functionals, were tested on crystals, small molecules and TiN surfaces. The RPBE functional when applied to the surface studies of TiN was found to produce slightly lower values of surface energies and of hydrogen adsorption energies than the PW91 functional.

Electronic structure of REFe2 (RE = Dy, Ho and Er) intermetallic compounds: Ab initio spin-density functional theory

The interaction of H2 molecules with a Cu(100) metallic surface has been investigated by DFT approaches using a (H2) n Cu13 cluster model. Nine exchange-correlation functionals, belonging to the generalized gradient approximations (GGA), meta GGA (mGGA), hybrid Kohn–Sham/Hartree–Fock models, either based on GGAs or mGGAs, range-separated hybrids, and double-hybrid families, have been tested on the chemisorption and physisorption processes involving one or two H2 layers. The addition of an empirical correction for dispersion has also been tested for some of these functionals. The calculated energies and structural parameters were compared to sophisticated multi reference configuration interaction including Davidson’s correction for quadruple excitations (MRCI + Q). Our results show that among the nine considered exchange-correlation functionals, none can accurately reproduce all processes involved in the successive layers adsorption. Although an hybrid based on a mGGA such as M06-2X can quantitatively describe both the physisorption step and dissociation barriers involved in the adsorption of the first H2, it fails to reproduce its chemisorption. On the other hand, significant discrepancies with the reference post-HF data are obtained for the description of the second layer interaction, no matter which functional is considered, outlining the need of improvement and/or development of exchange-correlation functionals suitable for complex systems such as H2/H2Cu.

We explore the possibility of the production of Si polytypes via the total energies and free energies obtained in the density-functional theory and the density-functional perturbation theory. We first calculate the total energies of three polytypes of the tetrahedrally coordinated $s{p}^{3}$ Si atoms having the two-layer, three-layer, and four-layer stacking periods in the hexagonal unit cell (``$2H$'', ``$3H$'', and ``$4H$'') as a function of the in-plane lattice constant $a$ using the local-density approximation (LDA) and generalized gradient approximation (GGA) comparatively. In the LDA calculation, the $4H$ phase is energetically the most favorable among three phases in the range of 3.55 \AA{} $\ensuremath{\le}$ $a$ $\ensuremath{\le}$ 3.73 \AA{}. While the $4H$ phase is found to be more stable than the $2H$ phase at a relatively wide range of the $a$ value we studied, the $2H$ phase is found to be more stable than the $3H$ ($3C$) phase in the range of 3.57 \AA{} $\ensuremath{\le}a\ensuremath{\le}$ 3.61 \AA{}. In the GGA calculation, on the other hand, the $4H$ phase becomes the most favorable phase for almost the same range as the LDA case, 3.57 \AA{} $\ensuremath{\le}a\ensuremath{\le}$ 3.73 \AA{}. The $2H$ phase also becomes as stable as the $3H$ phase as in the case of the LDA around the small $a$ value of 3.62 \AA{}, although the $3H$ phase energy is always lower than that of the $2H$ phase in the GGA calculation. Considering the chemical vapor deposition (CVD) growth process, we calculate the biaxial stress values to reduce the lattice constant of the substrate Si crystal to realize the small $a$ values, which can lead to the homoepitaxial growth of the $4H$ phase. The values obtained are 4.69 GPa and 8.14 GPa for the LDA and GGA, respectively. Next, we study the thermal effect on the relative stabilities of the 3 phases. We calculate the phonon dispersion, bulk modulus and thermal expansion including the vibrational and thermal effect. From the comparison with experimental values of the $3C$ phase, it is found that the LDA results show much better agreement with experiment than the GGA, indicating that the LDA calculation is reliable to predict thermal properties of the real systems. Finally, we derive the free energy as a function of $a$ under several designated temperatures. The relative stabilities of the $2H$ and $4H$ phases with respect to the $3H$ phase are found to be enhanced. At around $a=3.65$ \AA{}, stabilities of $2H$ and $4H$ phases relative to the $3H$ phase become most prominent. Although stabilities of the $2H$ and $4H$ phases relative to the $3H$ phase are reduced with increasing temperature at around $a$ = 3.60 \AA{}, $2H$ phase is found to be as stable as $3H$ and $4H$ phases at higher temperatures, indicating the possibility of the production of the $2H$ phase via high-temperature CVD process with the biaxial stress.

The band structure of anatase and rutile titanium dioxide has been calculated by using first-principles plane-wave pseudo-potential with CASTEP code, based on density functional and molecular dynamics theories, as incorporated in Accelrys Material studio. Studies presented in this work were performed using the generalized gradient approximation (GGA) method. For exchange-correlation function, we employed Perdow-Burke-Ernzerhof (PBE) by using both GGA and GGA with LDA+U. Localization of the excess electronic charge is encouraged by using +U term. For energy calculations the system is optimized for all values of U for rutile from 0 eV to 8.0 eV and for anatase from 0 eV to 9.5 eV. The optimum values of U for rutile TiO2 is 7.5 eV and for anatase TiO2 is 9.0 eV respectively. Our investigated results of band structure by using GGA-PBE are 2.140eV (fig. 1(a)) and 1.973eV (fig. 2(a)) for anatase and rutile respectively. The calculated band structures by using GGA-PBE with LDA+U term for both structures are 3.350 eV (anatase, fig.1 (b)) and 2.557 eV (rutile, fig. 2(b)). Obtained band gaps for both polymorphs are characterized as direct band gap for rutile (Figs. 2(a, b)) and indirect band gap for anatase (figs. 1(a, b)) TiO 2 by using both given methods. Our studies show that GGA underestimates the electronic structure but by introducing LDA+U term with GGA predict comparable to experimentally observed the electronic structure for anatase [1] and rutile [2] TiO 2 . In addition, to obtain the zero pressure equilibrium volume, bulk modulus and pressure derivative of bulk modulus, the energy volume equation of state calculations were performed. The calculated values for the parameters of equation of state (anatase (V 0 =141.7 A, B 0 =417.4 GPa and B′ 0 =3.97), rutile (V 0 =65.68 A, B 0 =153.24 GPa and B′ 0 =3.7)) have good agreement with experiment [3–5] and DFT [6] studies. Computed results have been compared with experimental and other theoretical predictions. A good agreement is obtained with the experimental measurements.

The structural, electronic, vibrational, and optical properties of 2D- 2H-WTe2 monolayer are investigated using density functional theory with respect to a plane wave ultrasoft pseudopotentials (PW-USPPs) in a generalized gradient approximation (GGA) and with the Hubbard potential (GGA + U). The equilibrium state properties such as lattice parameters, unit cell volume, bulk modulus, and its derivative are determined. The band gap values of monolayer 2H-WTe2 are investigated for unstrained, 2% biaxial compression, and biaxial tensile stress using GGA, respectively. The obtained band gap values of 2H-WTe2 with respect to GGA are 1.043, 1.1487, and 0.9439 eV for unstrained, biaxial compression, and tensile strain, respectively. Moreover, the band gap values determined using Hubbard correction (GGA + U) are 1.1089 eV (unstrained), 1.2332 eV (2% biaxial compression), and 0.9945 eV (2% biaxial tensile stress), respectively. The band gap value obtained using Hubbard correction predicts the experimental value more precisely. The projected density of state shows W (3d) orbital is more dominant both in the valence band maximum and conduction band minimum. Moreover, a small amount of tensile or compressive strain is used to tune the band gap of the monolayer without affecting its direct band gap nature. In addition to this, the phonon dispersion and optical properties are discussed for tensile strain, unstrained, and compressive strain, respectively.

Suppression of Jahn–Teller distortion by chromium and magnesium doping in spinel LiMn 2O 4: A first-principles study using GGA and GGA+U

Although many transition metal complexes are known to have high multireference character, the multireference character of main-group closed-shell singlet diatomic molecules like BeF, CaO, and MgO has been less studied. However, many group-1 and group-2 diatomic molecules do have multireference character, and they provide informative systems for studying multireference character because they are simpler than transition metal compounds. The goal of the present work is to understand these multireference systems better so that, ultimately, we can apply what we learn to more complicated multireference systems and to the design of new exchange-correlation functionals for treating multireference systems more adequately. Fourteen main-group diatomic molecules and one triatomic molecule (including radicals, cations, and anions, as well as neutral closed-shell species) have been studied for this article. Eight of these molecules contain a group-1 element, and six contain a group-2 element. Seven of these molecules are multireference systems, and eight of them are single-reference systems. Fifty-three exchange-correlation functionals of 11 types [local spin-density approximation (LSDA), generalized gradient approximation (GGA), nonseparable gradient approximation (NGA), global-hybrid GGA, meta-GGA, meta-NGA, global-hybrid meta GGA, range-separated hybrid GGA, range-separated hybrid meta-GGA, range-separated hybrid meta-NGA, and DFT augmented with molecular mechanics damped dispersion (DFT-D)] and the Hartree-Fock method have been applied to calculate the bond distance, bond dissociation energy (BDE), and dipole moment of these molecules. All of the calculations are converged to a stable solution by allowing the symmetry of the Slater determinant to be broken. A reliable functional should not only predict an accurate BDE but also predict accurate components of the BDE, so each bond dissociation energy has been decomposed into ionization potential (IP) of the electropositive element, electron affinity of the electronegative bonding partner (EA), atomic excitation energy (EE) to prepare the valence states of the interacting partners, and interaction energy (IE) of the valence-prepared states. Adding Hartree-Fock exchange helps to obtain better results for atomic excitation energy, and this leads to improvements in getting the right answer for the right reason. The following functionals are singled out for reasonably good performance on all three of bond distance, BDE, and dipole moment: B97-1, B97-3, MPW1B95, M05, M06, M06-2X, M08-SO, N12-SX, O3LYP, TPSS, τ-HCTHhyb, and GAM; all but two (TPSS and GAM) of these functionals are hybrid functionals.