Standardized basis sets for high-level-correlated relativistic calculations of atomic and molecular electric properties in the spin-averaged Douglas-Kroll (no-pair) approximation I. Groups Ib and IIb

Summary The technique developed earlier for the generation of the so-called first-order polarized basis sets for accurate non-relativistic calculations of molecular electric properties is used to obtain similar basis sets suitable for calculations in the Douglas-Kroll no-pair approximation. The corresponding (relativistic) basis sets are devised for atoms of the Groups Ib and IIb of the periodic table and tested in calculations of atomic polarizabilities and dipole moments of the coinage metal hydrides. Excellent performance of these basis sets has been found in the case of molecular calculations.     

All-electron and relativistic pseudopotential studies for the group 1 element polarizabilities from K to element 119

Two-component and scalar relativistic energy-consistent pseudopotentials for the group 1 elements from K to element 119 are presented using nine electrons for the valence space definition. The accuracy of such an approximation is discussed for dipole polarizabilities and ionization potentials obtained at the coupled-cluster level as compared to experimental and all-electron Douglas-Kroll results.     

Van der Waals complexes of Cu, Ag, and Au with hydrogen sulfide. The bonding character

The electronic and structural features of the Cu...SH2, Ag...SH2, and Au...SH2 complexes are investigated by using the spin-adapted restricted open-shell HF coupled cluster CCSD(T) method combined with the second-order spin-free Douglas-Kroll-Hess (DKH) relativistic approach. M...SH2 complexes are nonplanar with bonding energies -5.99, -1.99, and -9.08 mHartree, respectively. Comparison with analogous M...OH2 and M...NH3 complexes allows us to establish general features of the bonding between coinage metal atoms and ligand molecules with the participation of their lone electron pairs. Consistent interpretation of the interaction effects can be obtained by using the molecular orbital picture of the M...L region. The bonding character is explained by stressing the importance of the charge transfer from the lone pair of the ligand to the metal atom. Relativistic changes of the metal element electron affinity and polarizability facilitate the understanding of major trends in the pattern of interactions between the coinage metal atoms and different lone pair donating ligands.     

Magic bimetallic cluster anions of M/Pb (M = Au,Ag and Cu) observed and analyzed by laser ablation and time-of-flight mass spectrometry

By using laser ablation on mixtures of coinage metals M (Cu, Ag, Au) and lead, M/Pb binary cluster anions containing up to tens of atoms were produced and analyzed. Most of the magic clusters discovered can be described based on the electron shell models which were deduced from simple homogeneous metal cluster systems. The clustering activities of coinage metals and lead were also compared with the properties of their bulk binary alloys.     

Polarizabilities of the alkali anions: Li- to Fr-

Static dipole polarizabilities are calculated for the ground states of the alkali anions from Li- to Fr-. The polarizabilities include scalar relativistic effects at the second-order Douglas-Kroll level and were computed using the finite-field, coupled-cluster CCSD(T) method with large, carefully optimized basis sets. The relativistic polarizabilities increase with Z, reach a maximum at Cs-, and then decrease again unlike their nonrelativistic counterparts which increase monotonically with Z.     

Equilibrium geometries, stabilities, and electronic properties of the bimetallic M2-doped Au(n) (M = Ag, Cu; n = 1-10) clusters: comparison with pure gold clusters

The density functional method with relativistic effective core potential has been employed to investigate systematically the geometrical structures, relative stabilities, growth-pattern behaviors, and electronic properties of small bimetallic M(2)Au(n) (M = Ag, Cu; n = 1-10) and pure gold Au(n) (n ≤ 12) clusters. The optimized geometries reveal that M(2) substituted Au(n+2) clusters and one Au atom capped M(2)Au(n-1) structures are dominant growth patterns of the stable alloyed M(2)Au(n) clusters. The calculated averaged atomic binding energies, fragmentation energies, and the second-order difference of energies as a function of the cluster size exhibit a pronounced even-odd alternation phenomenon. The analytic results exhibit that the planar structure Ag(2)Au(4) and Cu(2)Au(2) isomers are the most stable geometries of Ag(2)Au(n) and Cu(2)Au(n) clusters, respectively. In addition, the HOMO-LUMO gaps, charge transfers, chemical hardnesses and polarizabilities have been analyzed and compared further.     

Relativistic effects determined using the Douglas-Kroll contracted basis sets and correlation consistent basis sets with small-core relativistic pseudopotentials

The coupled cluster approximation with single, double, and quasiperturbative triple excitations [CCSD(T)] was used in combination with the Douglas-Kroll contracted correlation consistent basis sets [cc-pVnZ-DK, where n = D(2), T(3), Q(4), and 5] and small-core relativistic pseudopotentials (PP) with correlation consistent polarized valence basis sets (cc-pVnZ-PP and aug-cc-pVnZ-PP) to investigate the impact of scalar relativistic corrections on energetic and structural properties of small molecules containing third-row (Ga-Kr) atoms. These molecules were taken from the Gaussian-2 extended test set for third-row atoms. Atomization energies, ionization energies, electron affinities, and proton affinities for molecules in the test set were determined and compared with nonrelativistic results which were obtained in a recent study in which the standard and augmented correlation consistent basis sets were used in combination with CCSD(T). Several schemes were used to extrapolate the energies to the complete basis set limit.     

铜簇Cun-和羰基铜簇CunCO-(n=2～7)的结构与光谱性质的密度泛函理论研究

应用相对论有效核势密度泛函理论计算方法研究了Cun-和CunCO-簇的平衡几何构型、稳定性、主要碎片化模式、CO吸附能及其团簇的光谱性质.计算结果表明,奇数簇Cun-的电离势比其相邻偶数簇Cun-的电离势大;奇数的Cu5CO-簇有最大的CO解离能.奇数铜簇阴离子相对较高的稳定性与近似浆汁模型的8电子电子闭壳层效应一致.计算得到的Cun-簇碎片化能量表明,较小Cun-的优势解离通道与其包含Cu原子数目的奇偶性有关,偶数的Cun-簇主要解离为Cu原子和Cun-1-,而奇数Cun-簇易以解离成铜的二聚物Cu2和Cun-2-.基于密度泛函理论计算,讨论了这些簇的静态极化率和CO吸附性质与簇大小的关系.     

Relativistic small-core energy-consistent pseudopotentials for the alkaline-earth elements from Ca to Ra

Small-core ten-valence electron energy-consistent scalar- and two-component relativistic pseudopotentials for the alkaline-earth elements from Ca to Ra are presented. The accuracy and reliability of these pseudopotentials are discussed in terms of their ability to reproduce all-electron calculated and experimental dipole polarizabilities and ionization potentials.     

Structure, bonding, and linear optical properties of a series of silver and gold nanorod clusters: DFT/TDDFT studies

DFT/TDDFT calculations have been carried out for a series of silver and gold nanorod clusters (Ag(n), Au(n), n = 12-120) whose structures are of cigar-type. Pentagonal Ag(n) clusters with n = 49-121 and hexagonal Au(n) clusters with n = 14-74 were also calculated for comparison. Metal-metal distances, binding energies per atom, ionization potentials, and electron affinities were determined, and their trends with cluster size were examined. The TDDFT calculated excitation energies and oscillator strengths were fit by a Lorentz line shape modification, which gives rise to the simulated absorption spectra. The significant features of the experimental spectra for actual silver and gold nanorod particles are well reproduced by the calculations on the clusters. The calculated spectral patterns are also in agreement with previous theoretical results on different-type Ag(n) clusters. Many differences in the calculated properties are found between the Ag(n) and Au(n) clusters, which can be explained by relativistic effects.     

On the accuracy of computed excited-state dipole moments

The dipole moments of furan and pyrrole in many electronically excited singlet states have been determined using coupled cluster theory including large one-electron basis sets. The inclusion of connected triple excitations is shown to uniformly decrease the equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) excitation energies by 0.04-0.24 eV, with an average reduction of 0.08 eV. Using a basis set larger than DZP (++)D (double-zeta plus polarization augmented with atom- and molecule-centered diffuse functions) uniformly increases the computed EOM-CCSD excitation energies by 0.03-0.29 eV, with an average increase of 0.20 eV. The corresponding shifts in excited-state dipole moments are more erratic. Including connected triple excitations changes the computed dipole moments by an rms amount of 0.17 au. More importantly, using a larger basis set shifts the dipole moments by an rms amount of 0.52 au, with an increase or a decrease being equally likely. The CC dipole moments are compared to those from time-dependent density functional theory (TD-DFT) computed by Burcl, Amos, and Handy [ Chem. Phys. Lett. 2002, 355, 8]. For 29 excited states of furan and pyrrole, the predicted TD-DFT dipole moments differ from the CC results by rms amounts of 1.6 au (HCTH functional) and 1.5 au (B97-1 functional). Including the asymptotic correction to TD-DFT developed by Tozer and Handy [ J. Chem. Phys. 1998, 109, 10180; J. Comput. Chem. 1999, 20, 106] reduces the rms differences for both functionals to 1.2 au. If those Rydberg excited states with very large polarizabilities are excluded, the rms differences from the CC results for the remaining 17 excited states become 1.31 au (HCTH) and 0.88 au (B97-1). For asymptotically corrected functionals and this subset of states, the rms differences from the CC results are only 0.54 au (HCTHc) and 0.34 au (B97-1c). Thus, the Tozer-Handy asymptotic correction for TD-DFT significantly improves the predictions of excited-state dipole moments. For excited states without very large polarizabilities, good agreement is achieved between excited-state dipole moments computed by coupled cluster theory and by the asymptotically corrected B97-1c density functional.     

Detaching thiolates from copper and gold clusters: which bonds to break?

The interaction of alkanethiolates with small coinage metal clusters of copper and gold was studied based on density functional theory with a focus on the metal-thiolate junction. Calculation of fragmentation energies indicate that for Cu(n)-thiolate (n = 1,3,5,7, and 9) there is a progressive lowering in energy for the fragmentation of the S-C bond in the thiolate from a value of 2.9 eV for n = 1 to 1.4 eV for n = 9. The detailed electronic origins of this specific weakening are attributed to a polarization of electron density in the S-C bond as induced by bonding with the Cu(n) cluster. For the gold analogues, this effect is not observed and fragmentation at the S-C bond experiences only a slight 10% destabilization as n increases from 3 to 9. The relativistic origin of this difference between Cu and Au is discussed, and an analysis of bonding considerations is presented.     

New relativistic ANO basis sets for transition metal atoms

New basis sets of the atomic natural orbital (ANO) type have been developed for the first, second, and third row transition metal atoms. The ANOs have been obtained from the average density matrix of the ground and lowest excited states of the atom, the positive and negative ions, and the atom in an electric field. Scalar relativistic effects are included through the use of a Douglas-Kroll-Hess Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of ionization energies, electron affinities, and excitation energies for all atoms and polarizabilities for spherically symmetric atoms. These calculations include spin-orbit coupling using a variation-perturbation approach. Computed ionization energies have an accuracy better than 0.2 eV in most cases. The accuracy of computed electron affinities is the same except in cases where the experimental values are smaller than 0.5 eV. Accurate results are obtained for the polarizabilities of atoms with spherical symmetry. Multiplet levels are presented for some of the third row transition metals.     

过渡金属团簇M20和M20(PMe3)4(M=Cu,Ag,Au)的量子化学理论研究

采用从头计算MP2和DFT理论方法,对过渡金属团簇M20和M20( PMe3)4(M=Cu,Ag,Au)的几何结构、电子结构以及团簇各组成部分之间的结合能进行了研究.所研究的体系具有较大的前线轨道能隙,与C60接近,显示出特别的稳定性.考虑电子相关效应的MP2方法能够对团簇的结构给予可靠的描述.离域泛函GGA对Cu和A...     

All‐Metal Clusters that Mimic the Chemistry of Halogens

Owing to their s²p⁵ electronic configuration, halogen atoms are highly electronegative and constitute the anionic components of salts. Whereas clusters that contain no halogen atoms, such as AlH₄, mimic the chemistry of halogens and readily form salts (e.g., Na⁺(AlH₄)^?), clusters that are solely composed of metal atoms and yet behave in the same manner as a halogen are rare. Because coinage‐metal atoms (Cu, Ag, and Au) only have one valence electron in their outermost electronic shell, as in H, we examined the possibility that, on interacting with Al, in particular as AlX₄ (X=Cu, Ag, Au), these metal atoms may exhibit halogen‐like properties. By using density functional theory, we show that AlAu₄ not only mimics the chemistry of halogens, but also, with a vertical detachment energy (VDE) of 3.98 eV in its anionic form, is a superhalogen. Similarly, analogous to XHX superhalogens (X=F, Cl, Br), XAuX species with VDEs of 4.65, 4.50, and 4.34 eV in their anionic form, respectively, also form superhalogens. In addition, Au can also form hyperhalogens, a recently discovered species that show electron affinities (EAs) that are even higher than those of their corresponding superhalogen building blocks. For example, the VDEs of M(AlAu₄)₂^? (M=Na and K) and anionic (FAuF)? Au? (FAuF) range from 4.06 to 5.70 eV. Au‐based superhalogen anions, such as AlAu₄^? and AuF₂^?, have the additional advantage that they exhibit wider optical absorption ranges than their H‐based analogues, AlH₄^? and HF₂^?. Because of the catalytic properties and the biocompatibility of Au, Au‐based superhalogens may be multifunctional. However, similar studies that were carried out for Cu and Ag atoms have shown that, unlike AlAu₄, AlX₄ (X=Cu, Ag) clusters are not superhalogens, a property that can be attributed to the large EA of the Au atom.     

The effect of geometry on cluster polarizability: studies of sodium, copper, and silicon clusters at shape-transition sizes

The electronic properties of Na(16), Cu(16,) and Si(20-28) clusters were calculated using density functional theory with the generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof. These clusters are special, as transitions in cluster shape occur at these sizes in the Na(n), Cu(n), and Si(n) cluster systems, respectively. Low-energy isomers that are comparable in stability, but possess distinctly different shapes, exist at each of these sizes, making these sets of isomers useful as probes of geometrical effects on cluster properties. Results for ionization potentials, electron affinities, and polarizabilities are shown to have a characteristic dependence on cluster shape. An analysis of the results reveals a close relationship between polarizability and cluster volume for all the isomers studied, despite the differences in cluster type and geometry. This relationship accounts for variations in polarizabilities among isomers of the same size, but different shapes, whereas previously published rules relating the polarizability to other cluster properties do not.     

Core polarization and relativistic effects competition in the first ionization potentials for some systems in the Cu,Ag, and Au isoelectronic sequences

Single-configuration relativistic Hartree–Fock values of the first ionization potentials for Cu through Kr⁷⁺, Ag through I⁶⁺, and Au through Pb³⁺ are computed in “frozen” and “relaxed core” approximations with and without allowance for core polarization. Effects of polarization of the atomic core by the valence electron are included by introducing a polarization potential in the one-electron Hamiltonian of the valence electron. The core polarization potential depends on two parameters, the static dipole polarizability of the core α and the cut-off radius r₀, which are chosen independently of the ionization potential data. It is demonstrated that by including the core polarization potential with α and r₀ parameters, which are simply chosen instead of being empirically fitted, it is still possible to account, on the average, for at least 70% of the discrepancy between the single-configuration relativistic Hartree–Fock ionization potentials and the experiment, a discrepancy usually ascribed to the contribution of valence-core electron correlations, and to bring the theoretical ionization potentials to an average agreement with experiment of around 1%. It can be concluded from this study that for low and medium Z elements the core polarization dominates for neutral systems or systems in low ionization stages, whereas for highly ionized systems the relativistic effects prevail. For heavy elements, however, the core polarization influence is comparable to the relativistic one only for neutral systems, whereas for ions the relativistic effects are overwhelmingly predominant.     

用于二元合金团簇负离子研究的光电子能谱仪

A home-made magnetic-bottle time-of-flight anion photoelectron spectrometer（PES）for the investigation of binary metal cluster geometry and electron structure is described. The photoelectron spectrometer is installed near the first space focus of home-made reflectron time of flight mass spectrometer（RTOFMS）,coupled with laser ablation,pulse supersonic molecular carrier gas cluster source. The magnetic-bottle photoelectron spectrometer's resolution is about 0. 1 eV for 1 eV photoelectrons. The adiabatic electron affinity energies of neutral clusters and some features relative to their excited states can be obtained from the spectra,i. e. ,from the anion's spectra,not only the features of the anion but also the neutral clusters' features can be investigated. The detailed design,construction,and operation of the new apparatus are presented. And studied PbM-（M = Cu,Ag,Au）binary metal cluster anions,the results give clear diagram about their structures and the bond interactions. The adiabatic electron affinity energies obtained by the photoelectron spectrometer agree well with the calculated results using relativistic density functional theory（DFT）method. It show that this anion photoelectron spectrometer can be well used in studying binary metal cluster anions in the experiment condition.     

Al7Ag and Al7Au clusters with large highest occupied molecular orbital-lowest unoccupied molecular orbital gap

The candidate structures for the ground-state geometry of the Al(7)M (M = Li, Cu, Ag, and Au) clusters are obtained within the spin-polarized density functional theory. Absorption energy, vertical ionization potential, vertical electron affinity, and the energy gap between the highest occupied molecular orbital (HOMO) level and the lowest unoccupied molecular orbital (LUMO) level have been calculated to investigate the effects of doping. Doping with Ag or Au can lead to a large HOMO-LUMO gap, low electron affinity, and increased ionization potential of Al(7) cluster. In the lowest-energy structure of the Al(7)Au cluster, the Al atom binding to the Al(6)Au acts monovalent and the other six Al atoms are trivalent. Thus, the Al(7)Au cluster has 20 valence electrons, and its enhanced stability may be due to the electronic shell closure effect.     

Metal effect on the supramolecular structure, photophysics, and acid-base character of trinuclear pyrazolato coinage metal complexes

Varying the coinage metal in cyclic trinuclear pyrazolate complexes is found to significantly affect the solid-state packing, photophysics, and acid-base properties. The three isoleptic compounds used in this study are [[3,5-(CF3)2Pz]M]3 with M = Cu, Ag, and Au (i.e., Cu3, Ag3, and Au3, respectively). They form isomorphous crystals and exist as trimers featuring nine-membered M3N6 rings with linear two-coordinate metal sites. On the basis of the M-N distances, the covalent radii of two-coordinate Cu(I), Ag(I), and Au(I) were estimated as 1.11, 1.34, and 1.25 angstroms, respectively. The cyclic [[3,5-(CF3)2Pz]M]3 complexes pack as infinite chains of trimers with a greater number of pairwise intertrimer M...M interactions upon proceeding to heavier coinage metals. However, the intertrimer distances are conspicuously short in Ag3 (3.204 angstroms) versus Au3 (3.885 angstroms) or Cu3 (3.813 angstroms) despite the significantly larger covalent radius of Ag(I). Remarkable luminescence properties are found for the three M3 complexes, as manifested by the appearance of multiple unstructured phosphorescence bands whose colors and lifetimes change qualitatively upon varying the coinage metal and temperature. The multiple emissions are assigned to different phosphorescent excimeric states that exhibit enhanced M...M bonding relative to the ground state. The startling luminescence thermochromic changes in crystals of each compound are related to relaxation between the different phosphorescent excimers. The trend in the lowest energy phosphorescence band follows the relative triplet energy of the three M(I) atomic ions. DFT calculations indicate that [[3,5-(R)2Pz]M]3 trimers with R = H or Me are bases with the relative basicity order Ag < Cu < Au while fluorination (R = CF3) renders even the Au trimer acidic. These predictions were substantiated experimentally by the isolation of the first acid-base adduct, [[Au3]2:toluene]infinity, in which a trinuclear Au(I) complex acts as an acid.