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.     

Scalable properties of metal clusters: a comparative study of modern exchange-correlation functionals

The performance of eight generalized gradient approximation exchange-correlation (xc) functionals is assessed by a series of scalar relativistic all-electron calculations on octahedral palladium model clusters Pd(n) with n = 13, 19, 38, 55, 79, 147 and the analogous clusters Au(n) (for n up through 79). For these model systems, we determined the cohesive energies and average bond lengths of the optimized octahedral structures. We extrapolate these values to the bulk limits and compare with the corresponding experimental values. While the well-established functionals BP, PBE, and PW91 are the most accurate at predicting energies, the more recent forms PBEsol, VMTsol, and VT{84}sol significantly improve the accuracy of geometries. The observed trends are largely similar for both Pd and Au. In the same spirit, we also studied the scalability of the ionization potentials and electron affinities of the Pd clusters, and extrapolated those quantities to estimates of the work function. Overall, the xc functionals can be classified into four distinct groups according to the accuracy of the computed parameters. These results allow a judicious selection of xc approximations for treating transition metal clusters.     

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.     

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).     

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.     

Nonempirical (double-hybrid) density functionals applied to atomic excitation energies: A systematic basis set investigation

We investigate here the lowest-energy (spin-conserving) excitation energies for the set of He-Ne atoms, with the family of nonempirical PBE, PBE0, PBE0-1/3, PBE0-DH, PBE-CIDH, PBE-QIDH, and PBE0-2 functionals, after employing a wide variety of basis sets systematically approaching the basis set limit: def2-nVP(D), cc-pVnZ, aug-cc-pVnZ, and d-aug-cc-pVnZ. We find that an accuracy (ie, mean unsigned error) of 0.3 to 0.4 eV for time-dependent density functional theory (DFT) atomic excitation energies can be robustly achieved with modern double-hybrid methods, which are also stable with respect to the addition of a double set of diffuse functions, contrarily to hybrid versions, in agreement with recent findings employing sophisticated multiconfigurational DFT methods.     

Predicting adsorption enthalpies on silicalite and HZSM‐5: A benchmark study on DFT strategies addressing dispersion interactions

We evaluated the accuracy of periodic density functional calculations for adsorption enthalpies of water, alkanes, and alcohols in silicalite and HZSM‐5 zeolites using a gradient‐corrected density functional with empirical dispersion corrections (PBE‐D) as well as a nonlocal correlation functional (vdW‐DF2). Results of both approaches agree in acceptable fashion with experimental adsorption energies of alcohols in silicalite, but the adsorption energies for n‐alkanes in both zeolite models are overestimated, by 21?46 kJ mol^?1. For PBE‐D calculations, the adsorption of alkanes is exclusively determined by the empirical dispersion term, while the generalized gradient approximation‐DFT part is purely repulsive, preventing the molecule to come too close to the zeolite walls. The vdW‐DF2 results are comparable to those of PBE‐D calculations, but the latter values are slightly closer to the experiment in most cases. Thus, both computational approaches are unable to reproduce available experimental adsorption energies of alkanes in silicalite and HZSM‐5 zeolite with chemical accuracy. © 2014 Wiley Periodicals, Inc.     

Influence of the Delocalization Error and Applicability of Optimal Functional Tuning in Density Functional Calculations of Nonlinear Optical Properties of Organic Donor–Acceptor Chromophores

Nonempirically tuned hybrid density functionals with range‐separated exchange are applied to calculations of the first hyperpolarizability (β_∥) and charge‐transfer (CT) excitations of linear “push–pull” donor–acceptor‐substituted organic molecules with extended π‐conjugated bridges. An unphysical delocalization with increasing chain length in density functional calculations can be reduced significantly by enforcing an asymptotically correct exchange‐correlation potential adjusted to give frontier orbital energies representing ionization potentials. The delocalization error for a number of donor–acceptor systems is quantified by calculations with fractional electron numbers and from orbital localizations. Optimally tuned hybrid variants of the PBE functional incorporating range‐separated exchange can produce similar magnitudes for β_∥ as Møller–Plesset second‐order perturbation (MP2) correlated calculations. Improvements are also found for CT excitation energies, with results similar to an approximate coupled‐cluster model (CC2).     

Excess polarizabilities upon excitation from the ground state to the first dipole‐allowed excited state of diphenylpolyenes

This paper discusses the excess polarizabilities upon excitation from the ground state to the first dipole‐allowed excited state (S₁) of diphenylpolyenes by using the time‐dependent density functional theory. Two hybrid exchange‐correlation (xc) potentials Becke‐3 Lee‐Yang‐Parr (B3LYP) and Perdew‐Burke‐Ernzerhof (PBE1PBE) were employed. Our calculations indicate that the magnitude of the excess polarizability will decrease while the molecule evolves from the unrelaxed S₁ state to the relaxed S₁ state. This decreasing trend is found to be independent of substituents, though substituents can change the value of the excess polarizability. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Density Functional Study on Adsorption of NO on AuSe (010) Surface

NO molecule adsorption on (010) surface of gold selenide (AuSe) has been studied with a periodic slab model by means of the GGA‐PW91 exchange‐correlation functional within the framework of density functional theory (DFT). Four different on‐top adsorption sites Au(1), Au(2), Se(1) and Se(2) were considered for α‐AuSe and three on‐top adsorption sites Au(1), Au(2) and Se(1) for β‐AuSe. N‐end and O‐end adsorptions of NO were investigated for the above sites. The results show that N‐end adsorptions are preferred for α‐ and β‐AuSe and O‐end adsorptions are not feasible and thought as physisorption with the weak adsorption energies from 6.0 to 10.8 kJ/mol. For the N‐end adsorptions on α‐ and β‐AuSe (010) surfaces, Au(2) sites are most favorable with the adsorption energies 89.0 and 78.0 kJ/mol for α‐ and β‐AuSe, respectively. However, the adsorptions at Au1 sites are very weak with the adsorption energies of 27.8 and 7.5 kJ/mol, respectively. In case of the adsorption of N‐down orientations of NO at Se sites for α‐ and β‐AuSe (010) surfaces, the adsorption activities of Se(1) and Se(2) sites on the α‐AuSe (010) surface and Se(1) site on the β‐AuSe (010) surface are almost the same with the adsorption energies 51.2, 52.7 and 49.2 kJ/mol. The geometric optimizations for adsorption configurations were calculated along with accounting for stretching frequency and density of states in our work.     

Which density functional is close to CCSD accuracy to describe geometry and interaction energy of small noncovalent dimers? A benchmark study using Gaussian09

A benchmark study on all possible density functional theory (DFT) methods in Gaussian09 is done to locate functionals that agree well with CCSD/aug‐cc‐pVTZ geometry and Ave‐CCSD(T)/(Q‐T) interaction energy (E_int) for small non‐covalently interacting molecular dimers in “dispersion‐dominated” (class 1), “dipole‐induced dipole” (class 2), and “dipole‐dipole” (class 3) classes. A DFT method is recommended acceptable if the geometry showed close agreement to CCSD result (RMSD < 0.045) and E_int was within 80–120% accuracy. Among 382 tested functionals, 1–46% gave good geometry, 13–44% gave good E_int, while 1–33% satisfied geometry and energy criteria. Further screening to locate the best performing functionals for all the three classes was made by counting the acceptable values of energy and geometry given by each functionals. The meta‐generalized gradient approximation (GGA) functional M06L was the best performer with total 14 hits; seven acceptable energies and seven acceptable geometries. This was the only functional “recommended” for at least two dimers in each class. The functionals M05, B2PLYPD, B971, mPW2PLYPD, PBEB95, and CAM‐B3LYP gave 11 hits while PBEhB95, PW91B95, Wb97x, BRxVP86, BRxP86, HSE2PBE, HSEh1PBE, PBE1PBE, PBEh1PBE, and PW91TPSS gave 10 hits. Among these, M05, B971, mPW2PLYPD, Wb97x, and PW91TPSS were among the “recommended” list of at least one dimer from each class. Long‐range correction (LC) of Hirao and coworkers to exchange‐correlation functionals showed massive improvement in geometry and E_int. The best performing LC‐functionals were LC‐G96KCIS and LC‐PKZBPKZB. Our results predict that M06L is the most trustworthy DFT method in Gaussian09 to study small non‐covalently interacting systems. © 2013 Wiley Periodicals, Inc.     

Improved constraint satisfaction in a simple generalized gradient approximation exchange functional

Though there is fevered effort on orbital-dependent approximate exchange-correlation functionals, generalized gradient approximations, especially the Perdew-Burke-Ernzerhof (PBE) form, remain the overwhelming choice in calculations. A simple generalized gradient approximation (GGA) exchange functional [A. Vela, V. Medel, and S. B. Trickey, J. Chem. Phys. 130, 244103 (2009)] was developed that improves substantially over PBE in energetics (on a typical test set) while being almost as simple in form. The improvement came from constraining the exchange enhancement factor to be below the Lieb-Oxford bound for all but one value of the exchange dimensionless gradient, s, and to go to the uniform electron gas limit at both s = 0 and s → ∞. Here we discuss the issue of asymptotic constraints for GGAs and show that imposition of the large s constraint, lim(s→∞)s(1/2)F(xc)(n,s)<∞, where F(xc)(n, s) is the enhancement factor and n is the electron density, upon the Vela-Medel-Trickey (VMT) exchange functional yields modest further improvement. The resulting exchange functional, denoted VT{8,4}, is only slightly more complicated than VMT and easy to program. Additional improvement is obtained by combining VT{8,4} or VMT exchange with the Lee-Yang-Parr correlation functional. Extensive computational results on several datasets are provided as verification of the overall performance gains of both versions.     

Second‐order elastic constants of hexagonal hydroxylapatite (P63) from ab initio quantum mechanics: Comparison between DFT functionals and basis sets

Three very popular Hamiltonians in the density functional theory framework, PBE, PBEsol, and B3LYP, and different basis sets (Gaussian‐type orbitals and plane waves) were employed to simulate the hydroxylapatite unit cell and its second‐order elastic constants. Dispersive interactions were included in the quantum‐mechanical treatment via the DFT‐D2 and Tkatchenko‐Scheffler schemes. The calculated bulk, shear, and Young's moduli were in the range of 82‐117 GPa, 42‐51 GPa, and 107‐134 GPa, respectively. The axial moduli, K_a and K_b, were instead in the range of 277‐322 GPa and 506‐509 GPa. The theoretical data, especially those from plan waves simulations, are in good agreement with available results in literature and further extend the knowledge of the mechanical and vibrational properties of hydroxylapatite.     

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.     

Analysis of the bond‐valence method for calculating 29Si and 31P magnetic shielding in covalent network solids

²⁹Si and ³¹P magnetic‐shielding tensors in covalent network solids have been evaluated using periodic and cluster‐based calculations. The cluster‐based computational methodology employs pseudoatoms to reduce the net charge (resulting from missing co‐ordination on the terminal atoms) through valence modification of terminal atoms using bond‐valence theory (VMTA/BV). The magnetic‐shielding tensors computed with the VMTA/BV method are compared to magnetic‐shielding tensors determined with the periodic GIPAW approach. The cluster‐based all‐electron calculations agree with experiment better than the GIPAW calculations, particularly for predicting absolute magnetic shielding and for predicting chemical shifts. The performance of the DFT functionals CA‐PZ, PW91, PBE, rPBE, PBEsol, WC, and PBE0 are assessed for the prediction of ²⁹Si and ³¹P magnetic‐shielding constants. Calculations using the hybrid functional PBE0, in combination with the VMTA/BV approach, result in excellent agreement with experiment. © 2016 Wiley Periodicals, Inc.