Density functional theory study of CO2 capture with transition metal oxides and hydroxides

We have used density functional theory (DFT) employing several different exchange-correlation functionals (PW91, PBE, PBEsol, TPSS, and revTPSS) coupled with lattice dynamics calculations to compute the thermodynamics of CO(2) absorption/desorption reactions for selected transition metal oxides, (TMO), and hydroxides, TM(OH)(2), where TM = Mn, Ni, Zn, and Cd. The van't Hoff plots, which describe the reaction equilibrium as a function of the partial pressures of CO(2) and H(2)O as well as temperature, were computed from DFT total energies, complemented by the free energy contribution of solids and gases from lattice dynamics and statistical mechanics, respectively. We find that the PBEsol functional calculations are generally in better agreement with experimental phase equilibrium data compared with the other functionals we tested. In contrast, the formation enthalpies of the compounds are better computed with the TPSS and revTPSS functionals. The PBEsol functional gives better equilibrium properties due to a partial cancellation of errors in the enthalpies of formation. We have identified all CO(2) capture reactions that lie on the Gibbs free energy convex hull as a function of temperature and the partial pressures of CO(2) and H(2)O for all TMO and TM(OH)(2) systems studied here.     

Generalized gradient approximation adjusted to transition metals properties: Key roles of exchange and local spin density

Perdew-Burke-Ernzerhof (PBE) and PBE adapted for solids (PBEsol) are exchange-correlation (xc) functionals widely used in density functional theory simulations. Their differences are the exchange, μ, and correlation, β, coefficients, causing PBEsol to lose the Local Spin Density (LSD) response. Here, the μ/β two-dimensional (2D) accuracy landscape is analyzed between PBE and PBEsol xc functional limits for 27 transition metal (TM) bulks, as well as for 81 TM surfaces. Several properties are analyzed, including the shortest interatomic distances, cohesive energies, and bulk moduli for TM bulks, and surface relaxation degree, surface energies, and work functions for TM surfaces. The exploration, comparing the accuracy degree with respect experimental values, reveals that the found xc minimum, called VV, being a PBE variant, represents an improvement of 5% in mean absolute percentage error terms, whereas this improvement reaches ~11% for VVsol, a xc resulting from the restoration of LSD response in PBEsol, and so regarded as its variant.     

Assessment of density functional theory to calculate the phase transition pressure of ice

To assess the accuracy of density functional theory (DFT) methods in describing hydrogen bonding in condensed phases, we benchmarked their performance in describing phase transitions among different phases of ice. We performed DFT calculations of ice for phases Ih, II, III, VI and VII using BLYP, PW91, PBE, PBE-D, PBEsol, B3LYP, PBE0, and PBE0-D, and compared the calculated phase transition pressures between Ih-II, Ih-III, II-VI, and VI-VII with the 0 K experimental values of Whalley [J. Chem. Phys., 1984, 81, 4087]. From the geometry optimization of many different candidates, we found that the most stable proton orientation as well as the phase transition pressure does not show much functional dependence for the generalized gradient approximation and hybrid functionals. Although all these methods overestimated the phase transition pressure, the addition of van der Waals (vdW) correction using PBE-D and PBE0-D reduced the transition pressure and improved the agreement for Ih-II. On the other hand, energy ordering between VI and VII reversed and gave an unphysical negative transition pressure. Binding energy profiles of a few conformations of water dimers were calculated to understand the improvement for certain transitions and failures for others with the vdW correction. We conclude that vdW dispersion forces must be considered to accurately describe the hydrogen bond in many different phases of ice, but the simple addition of the R(-6) term with a small basis set tends to over stabilize certain geometries giving unphysical ordering in the high density phases.     

Transition-metal 13-atom clusters assessed with solid and surface-biased functionals

First-principles density-functional theory studies have reported open structures based on the formation of double simple-cubic (DSC) arrangements for Ru(13), Rh(13), Os(13), and Ir(13), which can be considered an unexpected result as those elements crystallize in compact bulk structures such as the face-centered cubic and hexagonal close-packed lattices. In this work, we investigated with the projected augmented wave method the dependence of the lowest-energy structure on the local and semilocal exchange-correlation (xc) energy functionals employed in density-functional theory. We found that the local-density approximation (LDA) and generalized-gradient formulations with different treatment of the electronic inhomogeneities (PBE, PBEsol, and AM05) confirm the DSC configuration as the lowest-energy structure for the studied TM(13) clusters. A good agreement in the relative total energies are obtained even for structures with small energy differences, e.g., 0.10 eV. The employed xc functionals yield the same total magnetic moment for a given structure, i.e., the differences in the bond lengths do not affect the moments, which can be attributed to the atomic character of those clusters. Thus, at least for those systems, the differences among the LDA, PBE, PBEsol, and AM05 functionals are not large enough to yield qualitatively different results.     

Structural and electronic properties of ZrX2)and HfX2 (X=S and Se) from first principles calculations

Early transition metal dichalcogenides (TMDC), characterized by their quasi-two-dimensional layered structure, have attracted intensive interest due to their versatile chemical and physical properties, but a comprehensive understanding of their structural and electronic properties from a first-principles point of view is still lacking. In this work, four simple TMDC materials, MX(2) (M = Zr and Hf, X = S and Se), are investigated by the Kohn-Sham density functional theory (KS-DFT) with different local or semilocal exchange-correlation (xc) functionals and many-body perturbation theory in the GW approximation. Although the widely used Perdew-Burke-Ernzelhof (PBE) generalized gradient approximation (GGA) xc functional overestimates the interlayer distance dramatically, two newly developed GGA functionals, PBE-for-solids (PBEsol) and Wu-Cohen 2006 (WC06), can reproduce experimental crystal structures of these TMDC materials very well. The GW method, currently the most accurate first-principles approach for electronic band structures of extended systems, gives the fundamental band gaps of all these materials in good agreement with the experimental values obtained from optical absorption. The minimal direct gaps from GW are systematically larger than those measured from thermoreflectance by about 0.1-0.3 eV, implying that excitonic effects may be stronger than previously estimated. The calculated density of states from GW quasi-particle band energies agrees very well with photo-emission spectroscopy data. Ionization potentials of these materials are also computed by combining PBE calculations based on the slab model and GW quasi-particle corrections. The calculated absolute band energies with respect to the vacuum level indicate that that ZrS(2) and HfS(2), although having suitable band gaps for visible light absorption, cannot be used for overall water splitting as a result of mismatch of the conduction band minimum with the redox potential of H(+)/H(2).     

Construction of a generalized gradient approximation by restoring the density-gradient expansion and enforcing a tight Lieb-Oxford bound

Recently, a generalized gradient approximation (GGA) to the density functional, called PBEsol, was optimized (one parameter) against the jellium-surface exchange-correlation energies, and this, in conjunction with changing another parameter to restore the first-principles gradient expansion for exchange, was sufficient to yield accurate lattice constants of solids. Here, we construct a new GGA that has no empirical parameters, that satisfies one more exact constraint than PBEsol, and that performs 20% better for the lattice constants of 18 previously studied solids, although it does not improve on PBEsol for molecular atomization energies (a property that neither functional was designed for). The new GGA is exact through second order, and it is called the second-order generalized gradient approximation (SOGGA). The SOGGA functional also differs from other GGAs in that it enforces a tighter Lieb-Oxford bound. SOGGA and other functionals are compared to a diverse set of lattice constants, bond distances, and energetic quantities for solids and molecules (this includes the first test of the M06-L meta-GGA for solid-state properties). We find that classifying density functionals in terms of the magnitude mu of the second-order coefficient of the density gradient expansion of the exchange functional not only correlates their behavior for predicting lattice constants of solids versus their behavior for predicting small-molecule atomization energies, as pointed out by Perdew and co-workers [Phys. Rev. Lett. 100, 134606 (2008); Perdew ibid. 80, 891 (1998)], but also correlates their behavior for cohesive energies of solids, reaction barriers heights, and nonhydrogenic bond distances in small molecules.     

Performance of the M11-L density functional for bandgaps and lattice constants of unary and binary semiconductors

The recently developed SOGGA11 and M11-L density functionals have been tested for the prediction of bandgaps and lattice constants by comparing to databases containing 31 bandgaps and 34 lattice constants. To make a comparative assessment we also test several other density functionals against the same databases; in particular, we test the local spin density approximation, PBE, PBEsol, SOGGA, TPSS, revTPSS, and M06-L local density functionals and the HSE screened-exchange hybrid nonlocal density functional; and for a subset of 13 lattice constants we also compare the mean errors to those of the AM05 and WC local density functionals and the HISS and HSEsol nonlocal density functionals. The tests show that, of the ten functionals tested against all 65 data, the SOGGA, PBEsol, and HSE functionals are the most accurate for lattice constants, whereas the HSE, M11-L, and M06-L density functionals are the most accurate for bandgaps. However, the SOGGA11 density functional is the most accurate generalized gradient approximation for bandgaps.     

General formulation of spin-flip time-dependent density functional theory using non-collinear kernels: theory, implementation, and benchmarks

We report an implementation of the spin-flip (SF) variant of time-dependent density functional theory (TD-DFT) within the Tamm-Dancoff approximation and non-collinear (NC) formalism for local, generalized gradient approximation, hybrid, and range-separated functionals. The performance of different functionals is evaluated by extensive benchmark calculations of energy gaps in a variety of diradicals and open-shell atoms. The benchmark set consists of 41 energy gaps. A consistently good performance is observed for the Perdew-Burke-Ernzerhof (PBE) family, in particular PBE0 and PBE50, which yield mean average deviations of 0.126 and 0.090 eV, respectively. In most cases, the performance of original (collinear) SF-TDDFT with 50-50 functional is also satisfactory (as compared to non-collinear variants), except for the same-center diradicals where both collinear and non-collinear SF variants that use LYP or B97 exhibit large errors. The accuracy of NC-SF-TDDFT and collinear SF-TDDFT with 50-50 and BHHLYP is very similar. Using PBE50 within collinear formalism does not improve the accuracy.     

Diminished gradient dependence of density functionals: constraint satisfaction and self-interaction correction

The Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation for the exchange-correlation energy functional has two nonempirical constructions, based on satisfaction of universal exact constraints on the hole density or on the energy. We show here that, by identifying one possible free parameter in exchange and a second in correlation, we can continue to satisfy these constraints while diminishing the gradient dependence almost to zero (i.e., almost recovering the local spin density approximation or LSDA). This points out the important role played by the Perdew-Wang 1991 nonempirical hole construction in shaping PBE and later constructions. Only the undiminished PBE is good for atoms and molecules, for reasons we present, but a somewhat diminished PBE could be useful for solids; in particular, the surface energies of solids could be improved. Even for atoms and molecules, a strongly diminished PBE works well when combined with a scaled-down self-interaction correction (although perhaps not significantly better than LSDA). This shows that the undiminished gradient dependence of PBE and related functionals works somewhat like a scaled-down self-interaction correction to LSDA.     

A new parameter-free correlation functional based on an average atomic reduced density gradient analysis

A new parameter-free correlation functional based on the local Ragot-Cortona approach [J. Chem. Phys. 121, 7671 (2004)] is presented. This functional rests on a single ansatz for the gradient correction enhancement factor: it is assumed to be given by a simple analytic expression satisfying some exact conditions and containing two coefficients. These coefficients are determined without implementing the functional and without using a fitting procedure to experimental data. Their values are determined by requiring that the functional gives a correct average reduced density gradient for atoms, which, to some extent, can be considered an intrinsic atomic property. The correlation functional is then coupled with the Perdew-Burke-Erzernhof (PBE) exchange and compared with the original PBE approach as well as with some other pure density or hybrid approaches. Standard tests for atomic and molecular systems show that our new functional significantly improves on PBE, showing very interesting properties.     

Structural properties and phase transformations under pressure of XTe compounds (X = Be,Mg, and Ca): The role of the exchange–correlation potential

We have performed first principles total energy calculations to investigate the structural properties and possible phase transitions under pressure of IIA–VI compounds: BeTe, MgTe and CaTe. We have considered the following possible structures: rock-salt, nickel arsenide, cesium chloride, zinc-blende, and in some cases wurtzite. Calculations are done using the periodic density functional theory. We employ the full potential linearized augmented plane wave method as implemented in the wien2k code. The exchange and correlation potential energies are treated according to the generalized gradient approximation (GGA) using the Perdew, Burke, Ernzerhof (PBE) parameterization, and the local density approximation (LDA). Our results show that the GGA calculations correctly predict the ground state structure of all three binary compounds: zinc-blende for BeTe, wurtzite/zinc-blende for MgTe, and rock-salt for CaTe. Under pressure, BeTe and MgTe transform to the nickel arsenide structure, while CaTe transforms from rock-salt to cesium chloride. Slightly different results are found using the LDA approximation. We discuss the role of the ionicity in the difference between the LDA and GGA results.     

Is the uniform electron gas limit important for small Ag clusters? Assessment of different density functionals for Ag(n) (n < or = 4)

Twenty-three density functional theory (DFT) methods, including the second- and the third-generation functionals, are tested in conjunction with two basis sets (LANL2DZ and SDD) for studying the properties of neutral and ionic silver clusters. We find that DFT methods incorporating the uniform electron gas limit in the correlation functional, namely, those with Perdew's correlation functionals (PW91, PBE, P86, and TPSS), Becke's B95, and the Van Voorhis-Scuseria functional VSXC, generally perform better than the other group of functionals, e.g., those incorporating the LYP correlation functional and variations of the B97 functional. Strikingly, these two groups of functionals can produce qualitatively different results for the Ag3 and Ag4 clusters. The energetic properties and vibrational frequencies of Ag(n) are also evaluated by the different functionals. The present study shows that the choice of DFT methods for heavy metals may be critical. It is found that the exact-exchange-incorporated PBE functional (PBE1PBE) is among the best for predicting the range of properties.     

Reaction energy benchmarks of hydrocarbon combustion by Gaussian basis and plane wave basis approaches

The reaction energies of 275 elementary reactions from the hydrocarbon combustion model GRI-Mech 3.0 were evaluated by electronic structure calculations using both localized Gaussian basis and plane wave basis sets. In the Gaussian basis calculations, the d-polarization function on C, N, and O elements reduces the mean absolute deviation (MAD) from the experimental value by 53%, a significant improvement in computational accuracy. In the plane wave basis calculation using different exchange-correlation (XC) functionals, the MAD values were 0.316–0.426 eV when non-hybrid type XC functionals such as RPBE, PBE, PW91, revPBE, and PBEsol were used. On the other hand, hybrid functionals like B3LYP and HSE06 reduced the MAD values significantly down to 0.182 and 0.233 eV, respectively. The B3LYP results have 49% less MAD compared to the PBE results. These demonstrated the strong advantage of the hybrid functional for calculating gas-phase reaction energies. The present comprehensive benchmarks will be crucial for future microkinetics as well as machine learning studies on the catalytic reactions. © 2019 Wiley Periodicals, Inc.     

Single wall carbon nanotubes density of states: comparison of experiment and theory

We study the electronic structure of a variety of single wall carbon nanotubes and report density of states obtained with the Perdew–Burke–Ernzerhof (PBE) generalized gradient approximation and hybrid PBE0 approximation of density functional theory using Gaussian orbitals and periodic boundary conditions. PBE gives very good results for metallic tubes but the addition of a portion of exact exchange in the hybrid PBE0 functional worsens the agreement between experiment and theory. On the other hand, the PBE0 hybrid significantly improves the theoretical predictions (compared to PBE) for semiconducting tubes.     

Does the gradient-regulated connection improve the description of correlated metal bond properties?

Gradient-regulated connection (GRAC) is a generalized gradient approximation exchange density functional designed by combining the revPBE and PW91 exchange functionals to impose their behaviors in the slowly- and fast-varying density regions, respectively. Such a construction allows one single density functional to accurately estimate both covalent and weak interactions occurring in main-group-based molecular systems. For the first time, the assessment of the performance of the GRAC exchange functional is extended to the modeling of various metal bond energy and structure properties. This assessment shows that when GRAC is coupled with the Perdew, Burke, Ernzerhof (PBE) correlation, the resulting exchange-correlation density functional is an excellent alternative to global hybrids to model bond dissociation energy, atomic electronic excitation energy, and bond length structure properties of single-reference metal bonds. It also shows that coupling with the Tognetti, Cortona, Adamo (TCA) correlation constitutes a robust approach to tackle energy bond properties of organometallic complexes with multi-reference character.     

GGA versus van der Waals density functional results for mixed gold/mercury molecules and pure Au and Hg cluster properties

Dispersion forces, which originate the van der Waals interaction, are indispensable to describe numerous systems and processes, including metallic clusters and surfaces. In this work is used an efficient numerical implementation in the context of density functional theory of a non-local correlation van der Waals density functional (vdW-DF) to self-consistently solve the structure and electronic properties of small molecules (ArAu, AuF, ArAuF, ArCuF, Au(2)Hg, Au(2)Hg(2)), as well as Au(2-15) and Hg(2-6) clusters. Three different flavours of that vdW-DF exchange-correlation (xc) functional are tested. The results for small molecules are compared with those from the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE) against experiments or highly accurate quantum chemical calculations. It is found that, on average, vdw-DF improves PBE binding energies and overestimates bond distances. Our vdW-DF calculations lead to planar structures as lowest energy isomers of Au(14) and Au(15) clusters. The calculated polarizability of Au(2-15) isomers dramatically decreases in passing from two-dimensional (2D) to three-dimensional (3D) equilibrium geometries. A combination of the density of states of two vdw-DF planar isomers of the Au(12)(-) anion is proposed to explain the photoelectron spectroscopy experiments. Contrary to PBE results, the vdW-DF calculations predict that the O(h) isomer of Hg(6) is more stable than the C(2v) one.     

Theoretical study on the molecular structures of X-, α-, and β-types of lithium phthalocyanine dimer

We report here the results from theoretical calculations of the potential energy curves, the geometry optimizations, and the electronic structures for three dimers of lithium phthalocyanine (LiPc) by using three types of functional systems: PBE1PBE, B3LYP, and M06. The results were discussed in comparison with those obtained for the dimers of magnesium phthalocyanine (MgPc). The long-range dispersive interactions were considered in part using these functional systems in the increasing order of PBE1PBE, B3LYP, and M06. The mechanism whereby the dispersive interactions affect the geometric and electronic structures of the LiPc and MgPc dimers is discussed. The calculated results provide insight into the computational methods for both open- and closed-shell metal phthalocyanine (MPc) dimers: Although the PBE1PBE and B3LYP functional systems cannot evaluate a weak dispersion interaction appropriately, the M06 functional can estimate a weak dispersion interaction well in both open- and closed-shell MPc dimers. Basis set superposition error (BSSE) corrections play an important role for the quantitative analysis; however, the calculation results without BSSE corrections may be sufficient for the qualitative discussion on the properties of these dimers such as geometries, stabilities, electronic structures, and so on.