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.     

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.     

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.     

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).     

Structures and relative stability of medium-sized silicon clusters. V. Low-lying endohedral fullerenelike clusters Si31-Si40 and Si45

We have performed unconstrained search for low-lying structures of medium-sized silicon clusters Si(31)-Si(40) and Si(45), by means of the minimum-hopping global optimization method coupled with a density-functional based tight-binding model of silicon. Subsequent geometric optimization by using density-functional theory with the PBE, BLYP, and B3LYP functionals was carried out to determine the relative stability of various candidate low-lying silicon clusters obtained from the unconstrained search. The low-lying characteristics of these clusters can be affirmed by comparing the binding energies per atom of these clusters with previously determined lowest-energy clusters(Si(n)) in the size range of 21相似文献   

Search for lowest-energy fullerenes: C98 to C110

By combining the semiempirical density-functional based tight-binding optimization with density-functional theory single-point energy calculation at the PBE1PBE/6-311G level, we propose an efficient computational approach to determine lowest-energy structures of large-sized carbon fullerenes. Our studies show that C(92) (D(3): 28) and C(94) (C(2): 43) are the new leading candidates for the lowest-energy structures of C(92) and C(94). Moreover, for the first time, the lowest-energy structures of C(98)-C(110) are identified on the basis of the density-functional theory calculation. The lowest-energy isomers C(102) (C(1): 603) and C(108) (D(2): 1771) are readily isolated experimentally because they are much lower in energy than their other low-lying IPR isomers.     

On the accuracy of density-functional theory exchange-correlation functionals for H bonds in small water clusters: benchmarks approaching the complete basis set limit

The ability of several density-functional theory (DFT) exchange-correlation functionals to describe hydrogen bonds in small water clusters (dimer to pentamer) in their global minimum energy structures is evaluated with reference to second order Moller-Plesset perturbation theory (MP2). Errors from basis set incompleteness have been minimized in both the MP2 reference data and the DFT calculations, thus enabling a consistent systematic evaluation of the true performance of the tested functionals. Among all the functionals considered, the hybrid X3LYP and PBE0 functionals offer the best performance and among the nonhybrid generalized gradient approximation functionals, mPWLYP and PBE1W perform best. The popular BLYP and B3LYP functionals consistently underbind and PBE and PW91 display rather variable performance with cluster size.     

Ab initio calculation of bowl, cage, and ring isomers of C20 and C20-

High-level ab initio calculations have been carried out to reexamine relative stability of bowl, cage, and ring isomers of C(20) and C(20)(-). The total electronic energies of the three isomers show different energy orderings, strongly depending on the hybrid functionals selected. It is found that among three popular hybrid density-functional (DF) methods B3LYP, B3PW91, PBE1PBE, and a new hybrid-meta-DF method TPSSKCIS, only the PBE1PBE method (with cc-pVTZ basis set) gives qualitatively correct energy ordering as that predicted from ab initio CCSD(T)/cc-pVDZ [CCSD(T)-coupled-cluster method including singles, doubles, and noniterative perturbative triples; cc-pVDZ-correlation consistent polarized valence double zeta] as well as from MP4(SDQ)/cc-pVTZ [MP4-fourth-order Moller-Plesset; cc-pVTZ-correlation consistent polarized valence triple zeta] calculations. Both CCSD(T) and MP4 calculations indicate that the bowl is most likely the global minimum of neutral C(20) isomers, followed by the fullerene cage and ring. For the anionic counterparts, the PBE1PBE calculation also agrees with MP4/cc-pVTZ calculation, both predicting that the bowl is still the lowest-energy structure of C(20)(-) at T=0 K, followed by the ring and the cage. In contrast, both B3LYP/cc-pVTZ and B3PW91/cc-pVTZ calculations predict that the ring is the lowest-energy structure of C(20)(-). Apparently, this good reliability in predicting the energy ordering renders the hybrid PBE method a leading choice for predicting relative stability among large-sized carbon clusters and other carbon nanostructures (e.g., finite-size carbon nanotubes, nano-onions, or nanohorns). The relative stabilities derived from total energy with Gibbs free-energy corrections demonstrate a changing ordering in which ring becomes more favorable for both C(20) and C(20)(-) at high temperatures. Finally, photoelectron spectra (PES) for the anionic C(20)(-) isomers have been computed. With binding energies up to 7 eV, the simulated PES show ample spectral features to distinguish the three competitive C(20)(-) isomers.     

Dimers of boroglycine and methylamine boronic acid: a computational comparison of the relative importance of dative versus hydrogen bonding

Boronic acids are widely used in materials science, pharmacology, and the synthesis of biologically active compounds. In this Article, geometrical structures and relative energies of dimers of boroglycine, H2N-CH2-B(OH)2, and its constitutional isomer H3C-NH-B(OH)2, were computed using second-order M?ller-Plesset perturbation theory and density functional theory; Dunning-Woon correlation-consistent cc-pVDZ, aug-cc-pVDZ, cc-pVTZ, and aug-cc-pVTZ basis sets were employed for the MP2 calculations, and the Pople 6-311++G(d,p) basis set was employed for a majority of the DFT calculations. Effects of an aqueous environment were incorporated into the results using PCM and COSMO-RS methodology. The lowest-energy conformer of the H2N-CH2-B(OH)2 dimer was a six-membered ring structure (chair conformation; Ci symmetry) with two intermolecular B:N dative-bonds; it was 14.0 kcal/mol lower in energy at the MP2/aug-cc-pVDZ computational level than a conformer with the classic eight-centered ring structure (Ci symmetry) in which the boroglycine monomers are linked by a pair of H-O...H bonds. Compared to the results of MP2 calculations with correlation-consistent basis sets, DFT calculations using the PBE1PBE and TPSS functionals with the 6-311++G(d,p) basis set were significantly better at predicting relative conformational energies of the H2N-CH2-B(OH)2 and H3C-NH-B(OH)2 dimers than corresponding calculations using the BLYP, B3LYP, OLYP, and O3LYP functionals, particularly with respect to dative-bonded structures.     

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.     

Incremental binding energies of gold(I) and silver(I) thiolate clusters

Density functional theory is used to find incremental fragmentation energy, overall dissociation energy, and average monomer fragmentation energy of cyclic gold(I) thiolate clusters and anionic chain structures of gold(I) and silver(I) thiolate clusters as a measure of the relative stability of these systems. Two different functionals, BP86 and PBE, and two different basis sets, TZP and QZ4P, are employed. Anionic chains are examined with various residue groups including hydrogen, methyl, and phenyl. Hydrogen and methyl are shown to have approximately the same binding energy, which is higher than phenyl. Gold-thiolate clusters are bound more strongly than corresponding silver clusters. Lastly, binding energies are also calculated for pure Au(25)(SR)(18)(-), Ag(25)(SR)(18)(-), and mixed Au(13)(Ag(2)(SH)(3))(6)(-) and Ag(13)(Au(2)(SH)(3))(6)(-) nanoparticles.     

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.     

The AM05 density functional applied to solids

We show that the AM05 functional [Armiento and Mattsson, Phys. Rev. B 72, 085108 (2005)] has the same excellent performance for solids as the hybrid density functionals tested in Paier et al. [J. Chem. Phys. 124, 154709 (2006); 125, 249901 (2006)]. This confirms the original finding that AM05 performs exceptionally well for solids and surfaces. Hartree-Fock hybrid calculations are typically an order of magnitude slower than local or semilocal density functionals such as AM05, which is of a regular semilocal generalized gradient approximation form. The performance of AM05 is on average found to be superior to selecting the best of local density approximation and PBE for each solid. By comparing data from several different electronic-structure codes, we have determined that the numerical errors in this study are equal to or smaller than the corresponding experimental uncertainties.     

Calculation of longitudinal polarizability and second hyperpolarizability of polyacetylene with the coupled perturbed Hartree-Fock/Kohn-Sham scheme: where it is shown how finite oligomer chains tend to the infinite periodic polymer

The longitudinal polarizability, α(xx), and second hyperpolarizability, γ(xxxx), of polyacetylene are evaluated by using the coupled perturbed Hartree-Fock/Kohn-Sham (HF/KS) scheme as implemented in the periodic CRYSTAL code and a split valence type basis set. Four different density functionals, namely local density approximation (LDA) (pure local), Perdew-Becke-Ernzerhof (PBE) (gradient corrected), PBE0, and B3LYP (hybrid), and the Hartree-Fock Hamiltonian are compared. It is shown that very tight computational conditions must be used to obtain well converged results, especially for γ(xxxx), that is, very sensitive to the number of k(->) points in reciprocal space when the band gap is small (as for LDA and PBE), and to the extension of summations of the exact exchange series (HF and hybrids). The band gap in LDA is only 0.01 eV: at least 300 k(->) points are required to obtain well converged total energy and equilibrium geometry, and 1200 for well converged optical properties. Also, the exchange series convergence is related to the band gap. The PBE0 band gap is as small as 1.4 eV and the exchange summation must extend to about 130 A? from the origin cell. Total energy, band gap, equilibrium geometry, polarizability, and second hyperpolarizability of oligomers -(C(2)H(2))(m)-, with m up to 50 (202 atoms), and of the polymer have been compared. It turns out that oligomers of that length provide an extremely poor representation of the infinite chain polarizability and hyperpolarizability when the gap is smaller than 0.2 eV (that is, for LDA and PBE). Huge differences are observed on α(xx) and γ(xxxx) of the polymer when different functionals are used, that is in connection to the well-known density functional theory (DFT) overshoot, reported in the literature about short oligomers: for the infinite model the ratio between LDA (or PBE) and HF becomes even more dramatic (about 500 for α(xx) and 10(10) for γ(xxxx)). On the basis of previous systematic comparisons of results obtained with various approaches including DFT, HF, Moller-Plesset (MP2) and coupled cluster for finite chains, we can argue that, for the infinite chain, the present HF results are the most reliable.     

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.     

Structures and relative stability of medium- and large-sized silicon clusters. VI. Fullerene cage motifs for low-lying clusters Si(39), Si(40), Si(50), Si(60), Si(70), and Si(80)

We performed a constrained search, combined with density-functional theory optimization, of low-energy geometric structures of silicon clusters Si(39), Si(40), Si(50), Si(60), Si(70), and Si(80). We used fullerene cages as structural motifs to construct initial configurations of endohedral fullerene structures. For Si(39), we examined six endohedral fullerene structures using all six homolog C(34) fullerene isomers as cage motifs. We found that the Si(39) constructed based on the C(34)(C(s):2) cage motif results in a new leading candidate for the lowest-energy structure whose energy is appreciably lower than that of the previously reported leading candidate obtained based on unbiased searches (combined with tight-binding optimization). The C(34)(C(s):2) cage motif also leads to a new candidate for the lowest-energy structure of Si(40) whose energy is notably lower than that of the previously reported leading candidate with outer cage homolog to the C(34)(C(1):1). Low-lying structures of larger silicon clusters Si(50) and Si(60) are also obtained on the basis of preconstructed endohedral fullerene structures. For Si(50), Si(60), and Si(80), the obtained low-energy structures are all notably lower in energy than the lowest-energy silicon structures obtained based on an unbiased search with the empirical Stillinger-Weber potential of silicon. Additionally, we found that the binding energy per atom (or cohesive energy) increases typically >10 meV with addition of every ten Si atoms. This result may be used as an empirical criterion (or the minimal requirement) to identify low-lying silicon clusters with size larger than Si(50).     

Performance of six functionals (LDA, PBE, PBESOL, B3LYP, PBE0, and WC1LYP) in the simulation of vibrational and dielectric properties of crystalline compounds. The case of forsterite Mg2SiO4

The performance of six different density functionals (LDA, PBE, PBESOL, B3LYP, PBE0, and WC1LYP) in describing the infrared spectrum of forsterite, a crystalline periodic system with orthorhombic unit cell (28 atoms in the primitive cell, Pbmn space group), is investigated by using the periodic ab initio CRYSTAL09 code and an all‐electron Gaussian‐type basis set. The transverse optical (TO) branches of the 35 IR active modes are evaluated at the equilibrium geometry together with the oscillator strengths and the high‐frequency dielectric tensor ?_∞. These quantities are essential to compute the dielectric function ?(ν), and then the reflectance spectrum R(ν), which is compared with experiment. It turns out that hybrid functionals perform better than LDA and GGA, in general; that B3LYP overperforms WC1LYP and, in turn, PBE0; that PBESOL is better than PBE; that LDA is the worst performing functional among the six under study. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011