A density functional theory study on the Ag<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>H (<Emphasis Type="Italic">n</Emphasis> = 1–10) clusters

Density functional GGA-PW91 method with DNP basis set is applied to optimize the geometries of Ag _n H (n = 1–10) clusters. For the lowest energy geometries of Ag _n H (n = 1–10) clusters, the hydrogen atom prefers to occupy the two-fold coordination bridge site except the occupation of single-fold coordination site in AgH cluster. After adsorption of hydrogen atom, most Ag _n structures are slightly perturbed and only the Ag₆ structure in Ag₆H cluster is distorted obviously. The Ag–Ag bond is strengthened and the strength of Ag–H bond exhibits a clear odd–even oscillation like the strength of Au–H bond in Au _n H clusters, indicating that the hydrogen atom is more favorable to be adsorbed by odd-numbered pure silver clusters. The adsorption strength of small silver cluster toward H atom is obviously weaker than that of small gold cluster toward H atom due to the strong scalar relativistic effect in small gold cluster. The pronounced odd–even alternation of the magnetic moments is observed in Ag _n H systems, indicating that the Ag _n H clusters possess tunable magnetic properties by adsorbing hydrogen atom onto odd-numbered or even-numbered small silver cluster.     

Structural,electronic and magnetic properties of small gold clusters with a copper impurity

A set of all-electron scalar relativistic calculations on Au _n Cu (n = 1–12) clusters has been performed using density functional theory with the generalized gradient approximation at PW91 level. The lowest energy geometries of Au _n Cu clusters may be considered as assemblies of triangular Au₃ moieties substituted with one Cu atom at the highest coordinated site. All these lowest energy geometries of the Au _n Cu clusters are slightly distorted but retain the planar structures of the Au _n+1 clusters due to the strong scalar relativistic effects. The Au–Cu bonds are stronger, and a few Au–Au bonds far from the Cu atom are weaker, than the corresponding Au–Au bonds in pure Au _n+1 clusters. After doping with a Cu atom, the thermodynamic stability and chemical reactivity are enhanced to some extent. The odd-numbered Au _n Cu clusters with even numbers of valence electrons are more stable than the neighboring even-numbered Au _n Cu clusters with odd numbers of valence electrons. Odd–even alternations of magnetic moments and electronic configurations for the Au _n Cu clusters can be observed clearly and may be understood in terms of the electron pairing effect.     

All-electron scalar relativistic calculation of the adsorption of NCO species onto small copper clusters

An all-electron scalar relativistic calculation of Cu_nNCO (n = 1?C13) clusters has been made using density functional theory with the generalized gradient approximation at BLYP level. In all Cu_nNCO clusters, the NCO species prefered to occupy the single-fold coordination site and the small copper cluster tended to bond with the nitric. The Cu_n structures were only distorted slightly and the NCO species retained linear structure. The N-C bond-length contraction and C-O bond-length elongation were observed clearly. The reactivity enhancement of NCO species toward CO₂ was obvious. But, no reactivity enhancement of NCO to form N₂ related to the N-C bond strength could be observed. It seems that the NCO species is more favorably adsorbed by odd-numbered small copper clusters, relatively. Some discrepancies between our work and earlier works were found which may be explained in terms of the scalar relativistic effect. Further studies to focus on the reactivity enhancement of NCO to form N₂ are clearly in order.     

The adsorptions of silver-doped small gold clusters toward carbon monoxide molecule

An all-electron scalar relativistic calculation on Au _n AgCO (n = 1–12) clusters has been performed using density functional theory with the generalized gradient approximation at PW91 level. The introduction of impurity silver weakens the adsorption, and, however, promotes the reactivity enhancement of CO molecule. The CO molecule is relatively more favorable to be adsorbed by the odd-numbered Au _n Ag clusters with closed-shell electronic structure. The values of chemical hardness indicate that the Au _n AgCO cluster is less stable than the corresponding Au _n+1CO cluster chemically. This picture of the influence of impurity silver on the adsorption behavior of Au _n Ag (n = 1–12) clusters toward CO molecule is consistent with previous experimental work (Haeck et al. in J Phys Chem A 115:2103, 2011), in which the cluster’s reaction probability toward CO molecule is reduced upon substitution of gold atoms for silver and the clusters with closed electronic shell are the most reactive toward CO molecule.     

Molecular Dynamics Simulation of the Melting and Coalescence in the Mixed Cu–Ni Nanoclusters

Molecular dynamics simulation with the embedded atom method was applied to study the melting and coalescence in the mixed Cu–Ni nanoclusters. The validity of the model was tested by examining the consistency of the phase diagrams of the (Cu_682-mNi_m)₆₈₂ and (Cu_1048-mNi_m)₁₀₄₈ clusters with the Cu–Ni bulk. The coalescences of two mixed Cu–Ni clusters and a pure Cu cluster with a pure Ni cluster were simulated. The coalesced temperature T _c forming a liquid complex and melting temperature T _m of the cluster with the same size were compared. The results indicate that T _c is higher than T _m for the coalescences of both (CuNi)₆₈₂ and (CuNi)₁₀₄₈ clusters. The analysis of the relationship between the Cu–Ni bond content and T _c indicates that the formation of the Cu–Ni bonds contributes a lot to the phenomenon.     

Cage Structure Formation of Singly Doped Aluminum Cluster Cations Al<Subscript><Emphasis Type="BoldItalic">n</Emphasis></Subscript><Emphasis Type="BoldItalic">TM</Emphasis><Superscript>+</Superscript> (<Emphasis Type="BoldItalic">TM</Emphasis> = Ti,V, Cr)

Structural information on free transition metal doped aluminum clusters, Al _n TM ⁺ (TM = Ti, V, Cr), was obtained by studying their ability for argon physisorption. Systematic size (n = 5 – 35) and temperature (T = 145 – 300 K) dependent investigations reveal that bare Al _n ⁺ clusters are inert toward argon, while Al _n TM ⁺ clusters attach one argon atom up to a critical cluster size. This size is interpreted as the geometrical transition from surface-located dopant atoms to endohedrally doped aluminum clusters with the transition metal atom residing in an aluminum cage. The critical size, n _crit , is found to be surprisingly large, namely n _crit = 16 and n _crit = 19 – 21 for TM = V, Cr, and TM = Ti, respectively. Experimental cluster–argon bond dissociation energies have been derived as function of cluster size from equilibrium mass spectra and are in the 0.1–0.3 eV range.     

Structural Growth Sequences and Electronic Properties of Lanthanum-Doped-Gold Clusters

The geometries, stabilities, and electronic properties of Au _n La (n = 2–8) clusters have been systematically investigated by using density-functional theory. The results show that the doped La atom prefers to locate at the center site with the number of Au atom increasing from 2 to 8. Furthermore, the Au _n La clusters are more stable than the Au _n+1 clusters. The charges transfer from La atom to Au atoms at n = 2–4, but charge-transferring is reversed at n = 5.     

Theoretical Study of Hydrogen Adsorption on Ruthenium Clusters

The geometries, stabilities, electronic, and magnetic properties of hydrogen adsorption on Ru _n clusters have been systematically investigated by using density functional theory with generalized gradient approximation. The result indicates the absorbed species does not lead to a rearrangement of the basic cluster. For n > 2, three different adsorption patterns are found for the Ru _n H₂ complexes: One H atom binds to the Ru top site, and another H binds to the bridge site for n = 3, 5, 6, 8; bridge site adsorption for n = 4; hollow site and top site adsorption for n = 7. The adsorption energies display oscillation and reach the peak at n = 2, 4, 7, implying their high chemical reactivity. The small electron transferred number between H atoms and Ru _n clusters indicates that the interaction between H atoms and Ru _n clusters is small. When H₂ is absorbed on the Ru _n clusters, the chemical activity of corresponding clusters is dramatically increased. The absorbed H₂ can lead to an oscillatory behavior of the magnetic moments, and this behavior is rooted in the electronic structure of the preceding cluster and the changes in the magnetic moment are indicative of the relative ordering of the majority and minority LUMO’s. The second order difference indicates 5 is magic number in Ru _n H₂ and Ru _n clusters.     

Combined DFT with NBO and QTAIM studies on the hydrogen bonds in (CH<Subscript>3</Subscript>OH)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 2–8) clusters

The (CH₃OH) _n (n = 2–8) clusters formed via hydrogen bond (H-bonds) interactions have been studied systemically by density functional theory (DFT). The relevant geometries, energies, and IR characteristics of the intermolecular OH···O H-bonds have been investigated. The quantum theory of atoms in molecule (QTAIM) and natural bond orbital (NBO) analysis have also been applied to understand the nature of the hydrogen bonding interactions in clusters. The results show that both the strength of H-bonds and the deformation are important factors for the stability of (CH₃OH) _n clusters. The weakest H-bond was found in the dimer. The strengths of H-bonds in clusters increase from n = 2 to 8, moreover, the strengths of H-bonds in (CH₃OH) _n (n = 4–8) clusters are remarkably stronger than those in (CH₃OH) _n (n = 2, 3) clusters. The small differences of the strengths of H-bonds among (CH₃OH) _n (n = 6–8) clusters indicate that a partial covalent character is attributed to the H-bonds in these clusters. The linear relationships between the electron density of BCP (ρ_b) and the H···O bond length of H-bonds as well as the second-perturbation energies E(2) have also been investigated and used to study the nature of H-bonds, respectively.     

Spectral and electrochemical study of coordination molecules Cu4OX6L4: 3-Methylpyridine and 4-Methylpyridine Cu4OBrnCl(6−n)L4 complexes

The tetranuclear Cu₄OBr_nCl_(6-n)L₄ complexes, where L = 3-methylpyridine (3-Mepy), 4-methylpyridine (4-Mepy) and n=0–6 with trigonal bipyramidal coordination of copper(II) were prepared and their infrared and electronic absorption spectra as well as cyclic voltammograms in nitromethane solutions were measured. The polyhedra in Cu₄OBr_nCl_(6−n) (3-Mepy)₄ molecules are less distorted comparing with those of 4-Mepy analogues as indicated by infrared Cu₄O absorptions, far infrared Cu—Br, Cu—Cl, and Cu—N absorptions, d—d bands in electronic spectra and potentials, measured by cyclic voltammetry. The 3-Mepy complexes exhibit strong single infrared Cu₄O absorptions, while for related 4-Mepy complexes doubly split Cu₄O bands were observed. Two strongly overlapped d—d bands in electronic absorption spectra of the 3-and 4-Mepy complexes in nitromethane were resolved by Gaussian fitting. The 4-Mepy ligand produces slightly stronger ligand field than its 3-Mepy analogue. The maxima of high-energy d—d bands are in a linear correlation with the number of bromide ligands. The correlations for corresponding low-energy bands are considerably deviated from linearity. The halfwave potentials of the complexes in nitromethane correlate with both the number of bromides and the data of electronic absorption spectra suggesting that the reducing electron at the electrode process enters the half-filled d _{z 2} orbital of the copper(II) atom. The origin of a difference between the 3-and 4-Mepy complexes in their spectral and electrochemical properties is also discussed.     

A density functional theory study of the Au7Hn (n = 1–10) clusters

The geometries, electronic, and magnetic properties of the Au₇H_n (n = 1–10) clusters have been systematically investigated by using relativistic all-electron density functional theory with generalized gradient approximation. It is found that the Au₇ on the whole retains its triangle structure after hydrogen atoms adsorption and adsorbing hydrogen atoms can stabilize the Au₇ structure. The Au₇H₇ cluster is much higher stability than the neighboring clusters. The pronounced even–odd alternation of the magnetic moments is observed in the Au₇H_n systems indicating Au₇H_n clusters possess tunable magnetic properties by adding even or odd number of H atoms.     

Structures and bonding patterns of nanoannular carbon clusters (C4–C20) through AIM analyses

Structures, binding energies, harmonic frequencies, dipole moments, HOMO–LUMO energy gaps and particularly atoms in molecules (AIM) analyses of some nanoannular carbon clusters (C₄–C₂₀) are investigated at B3LYP/6-31+G(d) level of theory. No correlation is found by plotting the calculated binding energies as a functional number of carbon atoms of carbon clusters. The calculated binding energies sharply increase from C₄ to C₁₀ while slowly from C₁₀ to C₂₀. The binding energies of C_4n+2 clusters including C₆, C₁₀, C₁₄, and C₁₈ have a clear increase when compared with others indicating their aromatic characters which is confirmed by results of HOMO–LUMO energy gaps and geometrical parameters. AIM analyses show that most of our carbon clusters are topologically normal (non-conflict) with stable structures. Nevertheless, the topological networks of small antiaromatic rings, C₄ and C₈, at their equilibrium geometries may change via molecular vibrations. The existence of straight bond paths in 3D molecular graphs of carbon clusters with n > 10 implies that ring strains are decreased as the ring sizes grow. Except for C₄ and C₈, the ellipticity values for the remaining carbon clusters are small indicating that the C–C bond is conserved in these clusters. Dipole moments of even-numbered structures are negligible, whereas odd-numbered ones have μ values of 0.09−0.73 D.     

Growth Pattern, Electronic Structures and Magnetic Moments of Small Lutetium Clusters

The lowest-energy configurations, electronic structures and magnetic moments of small Lu _n (n = 2–20) clusters have been investigated within the framework of density functional theory. The results show that Lu _n (n = 4, 8, 13, and 18) clusters are more stable than their respective neighbors, and structural transformation reveals at n = 16. As the number of atoms increases, the magnetic moments increase in an alternating fashion until they reach a maximum of 4.00 μ_B for Lu₈ clusters, followed by even–odd oscillation between 0.00 and 1.00 μ_B over the range n = 9–20.     

Geometrical structures and possible dissociation channels of MnP n + (n = 2–8) binary cluster ions

An all-electron (AE) calculation on the geometrical structures and possible dissociation channels of MnP _n ⁺ (n = 2–8) cluster ions has been performed by using density functional theory with the generalized gradient approximation (GGA) at PW91 level. The lowest energy structures of MnP _n ⁺ (n = 2–8) cluster ions may be regarded as the outcome of bonding between Mn atom and one or two units of P₂, P₃, and P₄. The most possible dissociation channels of MnP _n ⁺ (n = 2–8) cluster ions are the detachment of P₂, P₃, or P₄ unit. These conclusions are basically consistent well with previous works in which the P₂ and P₄ structures are regarded as two relatively stable units and easy to be stripped.     

1,ω-Bis(pyridinium)alkane Cation as Templates for the Self-Assembly of the Mo(W)/S/Cu Polymeric Clusters

Self-assembly of a series of effective cation-templates with [Mo(W)/Cu/S]-based clusters was studied. Permanent templated products {(bppp)[MoOS₃Cu₃I₃(4,4′-bipy)_1.5]}_n (1), {(bpbt)[MoOS₃Cu₃I₃(4,4′-bipy)_1.5]}_n (2), {(bppp)[WOS₃Cu₃I₃(4,4′-bipy)_1.5]}_n (3), and {(bpbt)[WOS₃Cu₃Br₃(4,4′-bipy)_1.5]}_n (4) show 1D anionic zigzag pattern (bppp = 1,3-bis(pyridinium) propane, bpbt = 1,4-bis(pyridinium) butane). Compounds 1–4 have been characterized by single-crystal X-ray diffraction, elemental analysis, IR, UV–vis and thermogravimetric Analysis. The results may provide fascinating insights into template effects on the construction of the cluster-based coordination polymers and that coordination modes of compounds 3 and 4 have not been found in the reported one-dimensional zigzag coordination polymers.     

Hydrogenation of B 120/? : A Planar-to-Icosahedral Structural Transition in B12H n0/? (n?=?1–6) Boron Hydride Clusters

A systematic density functional theory and wave function theory investigation performed in this work reveals a planar-to-icosahedral structural transition between n = 4–5 in the partially hydrogenated B₁₂H _n ^0/− clusters (n = 1–6) upon hydrogenation of all-boron B₁₂^0/−. Coupled cluster calculations with triple excitations (CCSD(T)) indicate that a distorted icosahedral B₁₂H₆ cluster with C₂ symmetry is overwhelmingly favored (by 35 kcal/mol) over the recently proposed perfectly planar borozene (D_3h B₁₂H₆) (Szwacki et al., Nanoscale Res Lett 4:1085, 2009) which proves to be a high-lying local minimum. A similar 2D–3D structural transition occurs to the corresponding boron boronyl analogues of B₁₂(BO) _n with n –BO terminals. Detailed adaptive natural density partitioning (AdNDP) analyses reveal the bonding patterns of these quasi-planar or cage-like clusters which are characterized with delocalized σ and π molecular orbitals. The electron detachment energies of the concerned anions and excitation energies of the neutrals are also predicted to facilitate their future experimental characterizations.     

Density functional theory study on (F2AlN3) n (n = 1–4) clusters

Possible geometrical structures and relative stabilities of (F₂AlN₃) _n (n = 1–4) clusters were studied using density functional theory at the B3LYP/6-311+G* level. The optimized clusters (F₂AlN₃) _n (n = 2–4) possess cyclic structure containing Al–N_α–Al linkages, and azido in azides has linear structure. The IR spectra of the optimized (F₂AlN₃) _n (n = 1–4) clusters have three vibrational sections, the whole strongest vibrational peaks lie in 2218–2246 cm⁻¹, and the vibrational modes are N₃ asymmetric stretching vibrations. Trends in thermodynamic properties with temperature and oligomerization degree n are discussed, respectively. A study of their thermodynamic properties suggests that monomer 1A forms the most stable clusters (2A, 3A, and 4B) can occur spontaneously in the gas phase at temperatures up to 800 K.     

Density functional study of hydrogen adsorption and dissociation on small Pdn (n = 1–7) clusters

Density functional theory has been performed to investigate the interaction of H₂ and Pd_n clusters (n = 1–7). The local minima configurations for different H₂ molecule approach modes towards Pd_n clusters are presented. Our results show that in some cases H₂ is physically adsorbed around Pd atom, and in other cases H₂ is dissociated to be H atoms. Except for PdH2, Pd_n clusters with H atoms dissociatively adsorbed are most stable. For these most stable PdnH2 clusters (n  2), the binding energy of hydrogen atom decreases as the number of Pd atom increases until n = 4, and when n  4, the binding energy almost keeps constant with the H atoms bound sites changing from Pd–Pd bonds to Pd triangle planes. Besides, the adsorption of H₂ on other low-lying isomers of Pd_n clusters is also discussed.     

Density-functional calculations of MnC(M = Fe, Co, Ni, Cu, n = 1–6) clusters

The structural, energetic and magnetic properties of M_nC(M = Fe, Co, Ni, Cu, n = 1–6) clusters are systematically investigated by density-functional calculations. We found that the ground-state geometrical structures of M_nC clusters are different from those of pure M_n+1 clusters. Fe₄C, Ni₂C and Cu₄C possess relatively higher stabilities. Doping of a C atom enhances the binding energy of M_n clusters, and the binding energies of Fe_n-C, Co_n-C and Ni_n-C are stronger than that of Cu_n-C.     

Bonding properties of copper(II)-imidazole chromophores: electronic and molecular structure of tetrakis(imidazole)bis(tetrafluoroborato)copper(II)bis(hexamethylphosphoramide)

The crystal and molecular structure of [Cu(HIm)₄(BF₄)₂]-2hmpa (HIm=imidazole; hmpa=hexamethylphosphoramide) has been determined using three-dimensional x-ray diffraction data. The Cu^II ion is coordinated centrosymmetrically by four imidazole ligands forming a basal plane, mean Cu−N 2.005 Å, and by two tetrafluoroborate anions on the z axis, mean Cu−F 2.506 Å. The four imidazole ligands are inclined at 64.6±0.5° to the CuN₄ coordination plane. The discrete Cu^II complexes and hexamethylphosphoramide molecules are interconnectedvia hydrogen bonding between the imidazole N−H group and hmpa oxygen atom. The hmpa has a tetrahedral configuration around P with P=O 1.489 Å and mean P−N 1.629 Å. The deconvoluted d-d absorptions of the title compound yield an orbital sequence: d_x ²−y²>d_z ²>d_xy>d_yz=d_xz. The properties of the Cu-imidazole bonds are discussed with reference to the electronic structures of the chromophores of tetrakis(imidazole)copper(II) complexes having effective local symmetriesD _4h andD _2h .