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.     

Giant magnetic moment of the core-shell Co13@Mn20 clusters: first-principles calculations

The core-shell clusters Co(13)@TM(20) with TM = Mn, Fe, Co, and Ni are investigated within first-principles simulations in the framework of density-functional theory. Huge magnetic moments have been found in the Co(13)@TM(20) clusters especially for the Co(13)@Mn(20) cluster with a giant magnetic moment of 113 μ(B). The large magnetic moments are mainly due to the special core-shell structure and the weak interaction between the TM and other atoms.     

Structures, spectra, and energies of niobium clusters from Nb13 to Nb20

A comprehensive theoretical investigation on structures and properties of niobium clusters in the range from 13 to 20 atoms, in three different charged states, is performed by using the BPW91 and M06 functionals and the cc-pVDZ-PP basis set. These species are predicted to prefer low spin ground state, i.e., singlet (for even electron) and doublet (for odd electron) systems. In terms of growth mechanism, a compact structure with one Nb encapsulated by a cage formed from five and six triangles is found to be favored over an icosahedral evolution. Unlike many 3d metals, whose volumes are much smaller, 13 and 19 Nb atoms clusters do not exist as icosahedra and double-icosahedra. A distinct case is Nb(15) as it bears a slightly distorted bcc structure. For some systems, several lower lying isomers are computed to be so close in energy that DFT computations cannot clearly establish their ground electronic states. The existence of structural isomers with comparable energy content is established for Nb(n) species with n = 13, 18, 19, and 20 in both neutral and charged states. The vibrational (IR) spectra are also calculated. While the spectra of smaller systems are strongly dependent on addition or removal of an electron from the neutral, the spectra of the larger size clusters are mostly independent of the charged state. The neutrals and their corresponding ions usually have a quite similar IR pattern. Electron affinities (EA), ionization energies (IE), average binding energies, dissociation energies, and frontier orbital energy gaps are evaluated. The computed EAs and IEs are generally in fair agreement with experiment. The Nb(15) system is observed to be stable and it can form a highly symmetric structure in all charged states with both open and closed electron shells.     

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.     

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.     

甲烷晶体的晶格能和弹性性质: 不同方法及泛函的评估

通过对甲烷晶体进行结构、晶格能和弹性特性的研究, 评估了不包含和包含色散能量修正的密度泛函理论的性能. 我们分别利用不包含色散能量修正的密度泛函理论(DFT) (包含不同的标准泛函和杂化泛函)和包含色散能量修正的密度泛函理论(DFT-D)计算了甲烷晶体特性, 并与实验作对比. 尽管DFT-D 与传统密度泛函理论及杂化密度泛函理论相比, 修正了甲烷晶体中的范德华(vdW)相互作用, 但是一些修正方案过分修正了这种相互作用. 因此, 人们在使用DFT-D方法时务必谨慎.     

Quantum-chemical study of intramolecular spin-forbidden rearrangements of the transition metal chelate complexes

An overview of quantum-chemical methods of studying the spin-forbidden reactions is presented. It was shown that HF and MP2 methods overestimate stabilization of the high-spin states whereas DFT methods with the use of LSDA and CGA functionals underestimate these states. Hybrid exchange-correlation density functionals B3P86 and B3LYP give the best agreement with the experimental data. The intramolecular spin-forbidden rearrangement of bis-chelate Ni(II) and Co(II) complexes was studied using the B3LYP/6-311++G (d,p) method.     

Low-lying electronic states of M(3)O(9)(-) and M(3)O(9)(2-) (M = Mo, W)

Multiple low-lying electronic states of M(3)O(9)(-) and M(3)O(9)(2-) (M = Mo, W) arise from the occupation of the near-degenerate low-lying virtual orbitals in the neutral clusters. We used density functional theory (DFT) and coupled cluster theory (CCSD(T)) with correlation consistent basis sets to study the structures and energetics of the electronic states of these anions. The adiabatic and vertical electron detachment energies (ADEs and VDEs) of the anionic clusters were calculated with 27 exchange-correlation functionals including one local spin density approximation functional, 13 generalized gradient approximation (GGA) functionals, and 13 hybrid GGA functionals, as well as the CCSD(T) method. For M(3)O(9)(-), CCSD(T) and nearly all of the DFT exchange-correlation functionals studied predict the (2)A(1) state arising from the Jahn-Teller distortion due to singly occupying the degenerate e' orbital to be lower in energy than the (2)A(1)' state arising from singly occupying the nondegenerate a(1)' orbital. For W(3)O(9)(-), the (2)A(1) state was predicted to have essentially the same energy as the (2)A(1)' state at the CCSD(T) level with core-valence correlation corrections included and to be higher in energy or essentially isoenergetic with most DFT methods. The calculated VDEs from the CCSD(T) method are in reasonable agreement with the experimental values for both electronic states if estimates for the corrections due to basis set incompleteness are included. For M(3)O(9)(2-), the singlet state arising from doubly occupying the nondegenerate a(1)' orbital was predicted to be the most stable state for both M = Mo and W. However, whereas M(3)O(9)(2-) was predicted to be less stable than M(3)O(9)(-), W(3)O(9)(2-) was predicted to be more stable than W(3)O(9)(-).     

Benchmark Calculations on the Atomization Enthalpy, Geometry and Vibrational Frequencies of UF6 with Relativistic DFT Methods

Benchmark calculations on the molar atomization enthalpy, geometry, and vibrational frequencies of uranium hexafluoride （UF6） have been performed by using relativistic density functional theory （DFT） with various levels of relativistic effects, different types of basis sets, and exchange-correlation functionals. Scalar relativistic effects are shown to be critical for the structural properties. The spin-orbit coupling effects are important for the calculated energies, but are much less important for other calculated ground-state properties of closed-shell UF6. We conclude through systematic investigations that ZORA- and RECP-based relativistic DPT methods are both appropriate for incorporating relativistic effects. Comparisons of different types of basis sets （Slater, Gaussian, and plane-wave types） and various levels of theoretical approximation of the exchange-correlation functionals were also made.     

Optical Spectra of Oligofurans: A Theoretical Approach to the Transition Energies,Reorganization Energies,and the Vibronic Activity

There is experimental evidence of high vibronic activity that accompanies the allowed transition between the ground state and the lowest electronic singlet excited state of oligofurans that contain two, three, and four furan rings. The absorption and emission spectra of the three lowest oligofurans measured at liquid nitrogen temperature show distinct fine structures that are reproduced using the projection-based model of vibronic coupling (with Dushinsky rotation included) parameterized utilizing either Density Functional Theory (DFT, with several different exchange-correlation functionals) or ab initio (CC2) quantum chemistry calculations. Using as a reference the experimental data concerning the electronic absorption and fluorescence for the eight lowest oligofurans, we first analyzed the performance of the exchange-correlation functionals for the electronic transition energies and the reorganization energies. Subsequently, we used the best functionals alongside with the CC2 method to explore how the reorganization energies are distributed among the totally symmetric vibrations, identify the normal modes that dominate in the fine structures present in the absorption and emission bands, and trace their evolution with the increasing number of rings in the oligofuran series. Confrontation of the simulated spectra with the experiment allows for the verification of the performance of the selected DFT functionals and the CC2 method.     

Comparative theoretical investigation of the vertical excitation energies and the electronic structure of [MoVOCl4]-: influence of basis set and geometry

The electronic structures, geometries, and vibration frequencies of the open-shell molybdenum(V) ion, [MoOCl(4)](-), have been calculated at the extended Hückel, semiempirical ZINDO/1, ZINDO/S, and PM3(tm), as well as ab initio and DFT theoretical levels. Electronic structure calculations suggest that the expected metal-fold orbital order can be satisfied only at the DFT level. The time-dependent density functional theory (TDDFT) approach has been used for the calculation of the vertical excitation energies in the UV-vis region with different basis sets, starting geometries, and exchange-correlation functionals. A good agreement between the predicted and the experimental electronic absorption and MCD spectra of the complex, [MoOCl(4)](-), was observed when the B3LYP and B3P86 exchange-correlation functionals were used with a full electron valence double-zeta with polarization basis set for the molybdenum and 6-311G(d) for all other atoms. Similar results were obtained when the LANL2DZ effective core potential for molybdenum atom and 6-31G(d) for all other atoms were used. The best absolute deviation of 0.13 and mean deviation of 0.01 eV were calculated for the bands in the UV-vis region by B3P86, while the results for the B3LYP exchange-correlation functional were less satisfactory. Compared to polarization functions, the inclusion of diffuse functions resulted in little improvement. The calculated excitations energies and charge-transfer band intensities are found to be sensitive to the Mo=O distance and O-Mo-Cl angle.     

Removing critical errors for DFT applications to transition-metal nanoclusters: correct ground-state structures of Ru clusters

As ruthenium plays an important role in heterogeneous catalysis, understanding the structural and electronic properties of Ru clusters is crucial to advancement of technology. Because of its efficiency, density functional theory (DFT) calculations are often utilized in nanoscience, but careful validation is necessary. Recently, small, nonmetallic Ru(n) clusters were reported by Zhang et al. [J. Phys. Chem. B 2004, 108, 2140] to form unusual square and cubic ground-state structures within DFT by treating the exchange-correlation (XC) functional at the level of general-gradient-corrected approximation (GGA). For such clusters, we show that the calculated, energetically preferred structures are sensitive to which XC functional is used and whether relativistic effects are included. We find that a hybrid XC functional with partially exact exchange, such as PBE0, corrects the Ru2 magnetic moment, bond length, and dissociation energy in agreement with experiment and high-level quantum chemistry calculations and changes the Ru4 ground-state structure to a tetrahedron, instead of a square. The change in structural preference is explained by the corrections to the electronic structure of a Ru atom, where the relative position of majority spin s level is shifted with respect to e(g) levels. We also find that standard nonrelativistic DFT-GGA gives similar results to relativistic DFT-PBE0, i.e., relative shifting of s level, but not for the right reasons. Our results again stress the need to validate an XC functional before application to transition-metal nanoclusters.     

Infrared-induced reactivity of N2O on small gas-phase rhodium clusters

Far- and mid-infrared multiple photon dissociation spectroscopy has been employed to study both the structure and surface reactivity of isolated cationic rhodium clusters with surface-adsorbed nitrous oxide, Rh(n)N(2)O(+) (n = 4-8). Comparison of experimental spectra recorded using the argon atom tagging method with those calculated using density functional theory (DFT) reveals that the nitrous oxide is molecularly bound on the rhodium cluster via the terminal N-atom. Binding is thought to occur exclusively on atop sites with the rhodium clusters adopting close-packed structures. In related, but conceptually different experiments, infrared pumping of the vibrational modes corresponding with the normal modes of the adsorbed N(2)O has been observed to result in the decomposition of the N(2)O moiety and the production of oxide clusters. This cluster surface chemistry is observed for all cluster sizes studied except for n = 5. Plausible N(2)O decomposition mechanisms are given based on DFT calculations using exchange-correlation functionals. Similar experiments pumping the Rh-O stretch in Rh(n)ON(2)O(+) complexes, on which the same chemistry is observed, confirm the thermal nature of this reaction.     

Understanding the Effect of the Exchange-Correlation Functionals on Methane and Ethane Formation over Ruthenium Catalysts

Density functional theory (DFT) has been established as a powerful research tool for heterogeneous catalysis research in obtaining key thermodynamic and/or kinetic parameters like adsorption energies, enthalpies of reaction, activation barriers, and rate constants. Understanding of density functional exchange-correlation approximations is essential to reveal the mechanism and performance of a catalyst. In the present work, we reported the influence of six exchange-correlation density functionals, including PBE, RPBE, BEEF+vdW, optB86b+vdW, SCAN, and SCAN+rVV10, on the adsorption energies, reaction energies and activation barriers of carbon hydrogenation and carbon-carbon couplings during the formation of methane and ethane over Ru(0001) and Ru(1011) surfaces. We found the calculated reaction energies are strongly dependent on exchange-correlation density functionals due to the difference in coordination number between reactants and products on surfaces. The deviation of the calculated elementary reaction energies can be accumulated to a large value for chemical reaction involving multiple steps and vary considerably with different exchange-correlation density functionals calculations. The different exchange-correlation density functionals are found to influence considerably the selectivity of Ru(0001) surface for methane, ethylene, and ethane formation determined by the adsorption energies of intermediates involved. However, the influence on the barriers of the elementary surface reactions and the structural sensitivity of Ru(0001) and Ru(1011) are modest. Our work highlights the limitation of exchange-correlation density functionals on computational catalysis and the importance of choosing a proper exchange-correlation density functional in correctly evaluating the activity and selectivity of a catalyst.     

TbSin(n=2-13)团簇的结构、电子及磁学性质

利用相对论密度泛函理论在广义梯度近似下研究TbSi_n (n=2-13)团簇的结构、稳定性、电子和磁学性质. 对团簇的平均结合能、离解能、电荷转移、最高占据分子轨道(HOMO)和最低未占据分子轨道(LUMO)的能级差、Mulliken 电荷分析和磁学性质进行了计算和讨论. TbSi_n团簇并没有像实验推测的那样在n=10形成嵌入式的结构. 我们推断电子亲和势的急剧变化不仅与嵌入式的结构有关, 而且与电子的固有稳定性相关.Mulliken 电荷分析表明电荷总是从Tb 原子转向Si 原子. 团簇的磁矩主要局域在Tb 原子的周围, 并且主要由f电子贡献, f 电子表现出局域性并且不参与化学成键. 以TbSi₁₀为例的分波态密度分析表明Tb与Si 原子间存在很强的sp轨道杂化.     

Assessment of recently developed exchange-correlation functionals for the description of torsion potentials in pi-conjugated molecules

Newly developed exchange-correlation functionals in density functional theory (DFT) have been applied to describe conjugation effects in organic molecules. The performance of the various approaches is assessed through the calculation of torsion energy profiles and their critical comparison with available experimental data. Our results indicate that the OPTX-B95 exchange-correlation functional as well as its corresponding hybrid versions perform better than the well-established BLYP or B3LYP schemes when dealing with pi-conjugated molecules. In contrast, the recently introduced VSXC functional is not as reliable as other DFT methods for the systems examined here.     

The self-interaction error and the description of non-dynamic electron correlation in density functional theory

The self-interaction error (SIE) plays a central role in density functional theory (DFT) when carried out with approximate exchange-correlation functionals. Its origin, properties, and consequences for the development of standard DFT to a method that can correctly describe multi-reference electron systems by treating dynamic and non-dynamic electron correlation on an equal footing, is discussed. In this connection, the seminal work of Colle and Salvetti on wave function-based correlation functionals that do no longer suffer from a SIE is essential. It is described how the Colle–Salvetti correlation functional is an anchor point for the derivation of a functional multi-reference DFT method.     

Low-lying isomers of the B9(-) boron cluster: the planar molecular wheel versus three-dimensional structures

The B(9)(-) cluster was found previously to be an unprecedented molecular wheel containing an octacoordinate planar boron with D(8h) symmetry in a combined photoelectron spectroscopy (PES) and theoretical study [H. J. Zhai et al., Angew. Chem., Int. Ed. 42, 6004 (2003)]. However, the PES spectra of B(9)(-) exhibit minor features that cannot be explained by the global minimum D(8h) structure, suggesting possible contributions from low-lying isomers at finite temperatures. Here we present Car-Parrinello molecular dynamics with simulated annealing simulations to fully explore the potential energy surface of B(9)(-) and search for low-lying isomers that may account for the minor PES features. We performed density functional theory (DFT) calculations with different exchange-correlation functionals and ab initio calculations at various levels of theory with different basis sets. Two three-dimensional low-lying isomers were found, both of C(s) symmetry, 6.29 (C(s)-2) and 10.23 (C(s)-1) kcal/mol higher in energy than the D(8h) structure at the highest CCSD(T) level of theory. Calculated detachment transitions from the C(s)-2 isomer are in excellent agreement with the minor features observed in the PES spectra of B(9)(-). The B(9)(-) cluster proves to be a challenge for most DFT methods and the calculated relative energies strongly depend on the exchange-correlation functionals, providing an excellent example for evaluating the accuracies of various DFT methods.     

The accuracy of DFT-optimized geometries of functional transition metal compounds: a validation study of catalysts for olefin metathesis and other reactions in the homogeneous phase

We have investigated the performance of eight popular density functionals, four of which are "standard" functionals not including dispersion (B3LYP, BP86, PBE, and TPSS) and four of which have been constructed to account for dispersion (B97D, wB97XD, M06, and M06L), in reproducing 18 molecular structures derived from single-crystal X-ray diffraction experiments on ruthenium-based olefin metathesis catalyst precursors. Our analysis of all the internuclear distances reveals that standard DFT predicts systematically expanded structures. In contrast, all the methods accounting for dispersion give rise to more compact structures, removing the systematic overestimation of internuclear distances. The contracting effect of dispersion is general and also affects chemical bonds, thus reducing the general overestimation of bond lengths. The best overall performance is observed for wB97XD, which offers relatively small statistical errors when considering the overall structure as well as selected distances. Only for the coordination center geometry is the accuracy of wB97XD matched by standard functionals such as PBE and TPSS, whereas M06 and M06L are associated with larger errors. At the other end of the scale, B3LYP is seen to give the largest statistical errors in general, both when considering the complete structures and the geometries of the coordination centers alone. For the organic ligands, however, B3LYP performs clearly better than the other standard functionals although not as well as the functionals accounting for dispersion. Extending the basis sets is seen to improve the structures in particular of the coordination center, thus underlining the importance of using sufficiently flexible basis sets if highly accurate geometries are to be obtained. Similar conclusions to those obtained for the ruthenium catalysts can be drawn from comparisons of the X-ray crystal structures of 10 other organometallic complexes of relevance to homogeneous catalysis, covering first (Ti, Fe, Co, Ni), second (Zr, Mo, Rh, Pd) and third (W, Ir) row transition metals, with those of DFT. The latter analyses thus offer a first indication that the picture obtained for the ruthenium alkylidene complexes may be extended to other classes of relatively large transition metal complexes.