Geometry and stability of BenCm (n=1-10; m=1, 2, ..., to 11-n) clusters

Density functional theory B3PW91/6-31+G* calculations on BenCm (n=1-10; m=1, 2, ..., to 11-n) clusters have been carried out to examine the effect of cluster size, relative composition, binding energy per atom, HOMO-LUMO gap, vertical ionization potential, and electron affinity on their relative stabilities. The most stable planar cyclic conformations of these clusters always show at least a set of two carbon atoms between two beryllium atoms, while structures where beryllium atoms cluster together, or allow the intercalation of one carbon atom between two of them, generally seem to be the least stable ones. Clusters containing 1, 2, and 3 beryllium atoms (Be2C8, Be3C6, Be2C6, BeC6, Be2C4, BeC4, Be2C2, and BeC2) are identified as clusters of "magic numbers" in terms of their high binding energy per atom, high HOMO-LUMO gap, vertical ionization potential, and second difference in energy per beryllium atom.     

Structures and stability of B-doped Al clusters: AlnB and AlnB2 (n=1-7)

Various structural possibilities for Al(n)B(m) (n=1-7, m=1-2) neutral isomers were investigated using B3LYP6-311G(d) and CCSD(T)6-311G(d) methods. Our calculations predicted the existence of a number of previously unknown isomers. The B atom favors to locate over/inside of all clusters in this series. All structures of the Al(n)B (n=2-7) may be derived from capping/putting a B atom over/inside the Al(n) cluster. All Al(n)B(2) (n=1-5) may be understood as two substitutions of Al atoms by B atoms in the Al(n+2) molecule. The strong B-B bond is a dominant factor in the building-up principle of mixed Al(n)B(2) neutral clusters. The second difference in energy showed that the Al(n)B(m) clusters with even n+m are more stable than those with odd n+m. Our results and analyses revealed that the mixed Al-B clusters exhibit aromatic behaviors.     

A G3 study of the structure of carbon-nitrogen nanoclusters

Possible structures of the carbon-nitrogen clusters of the form C(m)N(n) (m = 1-4, n = 1-4, m + n = 2-5) were predicted for the neutral, anion, and cation species in the singlet, doublet, and triplet states, whenever appropriate. The calculations were performed at the G3, MP2(fc)/6-311+G*, and B3LYP/6-311+G* levels of theory. Several molecular properties related to the experimental data--such as the electronic energy, equilibrium geometry, binding energy, HOMO-LUMO gap (HLG), and spin contamination --were calculated. In addition the vertical electron attachment, the adiabatic electron affinity, and vertical ionization energy, of the neutral clusters were calculated. Most of the predicted lowest energy structures were linear, whereas bent structures became more stable with the increase of the cluster size and increase of the number of the N atoms. In most of the predicted lowest energy structures, the N atom prefers the terminal position with acetylenic bond. The calculated BE of the predicted clusters increases with the increase of the cluster size for the neutral and cation clusters but decreases with the increase of the cluster size for the anion clusters. The predicted clusters are characterized by high HLG of about 11 eV on the average, with that of the anion clusters is smaller than that for the neutral and cation clusters. It is concluded then that the anion clusters are less stable than the corresponding neutral and cation clusters. Finally, the N(2) loss reaction is treated.     

Stabilizing carbon-lithium stars

We have explored in silico the potential energy surfaces of the C(5)Li(n)(n-6) (n = 5, 6, and 7) clusters using the Gradient Embedded Genetic Algorithm (GEGA) and other computational strategies. The most stable forms of C(5)Li(5)(-) and C(5)Li(6) are two carbon chains linked by two lithium atoms in a persistent seven membered ring capped by two Li atoms. The other Li atoms are arrayed on the edge of the seven membered ring. In contrast, the global minimum structure for C(5)Li(7)(+) is a bicapped star of D(5h) symmetry. The molecular orbital analysis and computed magnetic field data suggest that electron delocalization, as well as the saturation of the apical positions of the five-membered carbon ring with lithium atoms in C(5)Li(7)(+) plays a key role in the stabilization of the carbon-lithium star. In fact, the planar star sub-structure for the carbon ring are unstable without the apical caps. This is also what has been found for the Si analogues. The split of the B(ind)(z) in its σ- and π-contribution indicates that C(5)Li(7)(+) is a π-aromatic and σ-nonaromatic system.     

Hydrogenation reactions of ethylene on neutral vanadium sulfide clusters: experimental and theoretical studies

The reactions of C(2)H(4) with H(2) on neutral vanadium sulfide clusters in a fast flow reactor are investigated by time-of-flight mass spectrometry employing 118 nm (10.5 eV) single photon ionization. The experimental products of these reactions are V(m)S(n)C(2)H(x) (m=1, n=1-3; m=2, n=1-5, and x=4-6). Observation of these products indicates that these V(m)S(n) clusters have high catalytic activity for hydrogenation reactions of C(2)H(4). Density functional theory calculations at the BPW91/TZVP level are carried out to explore the geometric and electronic structures of the V(m)S(n) clusters and to determine reaction intermediates and transition states, as well as reaction mechanisms. All reactions are estimated as overall barrierless or with only a small barrier (0.1 eV), and are thermodynamically favorable processes at room temperature. The ethylene molecule is predicted to connect with active V atoms through its π-orbital or form a σ-bond with active V atoms of catalytic V(m)S(n) clusters. The S atoms bonding with active V atoms play an important role in the dissociation of the H(2) molecule; H atoms transfer to the C(2)H(4) (one after another) following breaking of the H-H bond. A catalytic cycle for C(2)H(4) hydrogenation reactions on a vanadium sulfide catalyst surface is suggested based on our experimental and theoretical investigations.     

Theoretical Study and NBO Analysis of the Decomposition Kinetics of Oxetane, 2-Methyloxetane and 2,2-Dimethyloxetane

A theoretical study of the thermal decomposition kinetics of oxetane (1), 2-methyloxetane (2), and 2,2-dimethyloxetane (3) has been carried out at the B3LYP/6-311+G**, B3PW91/6-311+G**, and MPW1PW91/6-311+G** levels of theory. The MPW1PW91/6-311+G** method was found to give a reasonable good agreement with the experimental kinetics and thermodynamic parameters. The decomposition reaction of compounds 1～3 yields formaldehyde and the corresponding substituted olefin. Based on the optimized ground state geometries using MPW1PW91/6-311+G** method, the natural bond orbital (NBO) analysis of donor-acceptor (bond-antibond) interactions revealed that the stabilization energies associated with the electronic delocalization from σC3-C4 bonding to σ*O1-C2 antibonding orbitals decrease from compounds 1 to 3. The σC3-C4→σO1-C2 resonance energies for compounds 1～3 are 2.63, 2.59 and 2.45 kcal mol-1, respectively. Further, the results showed that the energy gaps between σC3-C4 bonding and σ*O1-C2 antibonding orbitals decrease from compounds 1 to 3. Also, the decomposition process in these compounds are controlled by σ→σ* resonance energies. Moreover, the obtained order of energy barriers could be explained by the number of electron-releasing methyl groups substituted to the Csp3 atom (which is attached to oxygen atom). NBO analysis shows that the occupancies of σCsp3-O bonds decrease for compounds 1～3 as 3<2<1, and those of σCsp3-O bonds increase in the opposite order (3 > 2 > 1). This fact illustrates a comparatively easier thermal decomposition of the sCsp3-O bond in compound 3 compared to compound 2, and in compound 2 compared to compound 1. NBO results indicate that these reactions are occurring through a concerted and asynchronous four-membered cyclic transition state type of mechanism.     

二氮双环阳离子游离基中N,N'-三电子键

用从头算HF/3-21+G^*优化了二氮双环[m,n,l]游离基阳离子(m,n,l≥2～5)。分子[4,4,4]和[2,2,2]^+.,[3,3,3]^+.,[4,4,4]^+.游离基阳离子的优势构型有D3对称性,而其它游离基阳离子的优势构型为非对称性。通过比较这些阳离子几何构型,HOMO和NHOMO(即NextHOMO和HOMO-1),和由MNDO计算确定的原子对作用能,表明当二氮双环游离基阳离子的桥链(CH2)n的n≥3时,桥头氮原子通过空间相互用用形成了一个弱的N,N'-三电子σ键。形成的三电子键强度不随环的扩大而增强。而三电子键强度被两个因素影响：一个是桥头氮原子间的p轨道重叠的取向;另一个是它们相应p轨道成分。     

Density-functional study of structural and electronic properties of Si(n)C(n) (n=1-10) clusters

Density-functional theory with generalized gradient approximation for the exchange-correlation potential has been used to calculate the structural and electronic structure of Si(n)C(n) (n=1-10) clusters. The geometries are found to undergo a structural change from two dimensional to three dimensional when the cluster size n equals 4. Cagelike structures are favored as the cluster size increases. A distinct segregation between the silicon and carbon atoms is observed for these clusters. It is found that the C atoms favor to form five-membered rings as the cluster size n increases. However, the growth motif for Si atoms is not observed. The Si(n)C(n) clusters at n=2, 6, and 9 are found to possess relatively higher stability. On the basis of the lowest-energy geometries obtained, the size dependence of cluster properties such as binding energy, HOMO-LUMO gap, Mulliken charge, vibrational spectrum, and ionization potential has been computed and analyzed. The bonding characteristics of the clusters are discussed.     

Relativistic effect on 77Se NMR chemical shifts of various selenium species in the framework of zeroth-order regular approximation

The relativistic effects on absolute magnetic shielding tensors (σ(Se)) are explicitly evaluated for various selenium species (40 species) with the DFT(BLYP)-GIAO method. Calculations are performed under relativistic and nonrelativistic conditions with the Slater-type basis sets in ADF 2010 in the framework of ZORA, employing the optimized structures under nonrelativistic conditions at B3LYP of Gaussian 03. Quadruple zeta all electron with four polarization functions (QZ4Pae) are mainly applied to evaluate σ(Se). Ranges of the effect on diamagnetic (σ(d)(Se)), paramagnetic shielding tensors (σ(p)(Se)), and σ(d+p)(Se) (= σ(d)(Se) + σ(p)(Se)) are -24 to -20 ppm, -115 to -3 ppm, and -136 to -26 ppm, respectively. The spin-orbit terms (σ(so)(Se)) are evaluated to be 92-225 ppm with QZ4Pae, which clarifies the effect on total shielding tensors (σ(t)(Se) = σ(d+p)(Se) + σ(so)(Se)) to be -8 to 152 ppm, at the spin-orbit ZORA level. The calculated σ(t)(Se) values reproduced well the observed values.     

Reaction of Cationic Vanadium Oxide Clusters with Ethylene in a Flow Tube Reactor

A time of °ight mass spectrometer coupled with a cluster formation and reaction source is employed to study the reactivity of cationic vanadium oxide clusters (VmOn+) toward ethylene (C2H4) in the gas phase. The cationic vanadium oxide clusters with m=1-10 and n=1-26 (depending on m) are generated by reaction of laser ablation created vanadium plasma with O2 in a supersonic expansion and then reacted with the ethylene in a °ow tube reactor. Hydrogen atoms are attached in most of the oxygen saturated clusters(2n?5m) in our experimental condition. The reactivity of VmOn+ toward C2H4 is usually higher than that of hydrogen containing clusters, VmOnH2x+. Larger clusters show less reactivity than smaller ones. Most of the observed products are in the forms of VmOnC2H4+ and VmOnH2xC2H4+ due to direct association. C2H4 clustering products ((C2H4)n+, n=2-6) are also observed.     

InnNa和InnNa+(n=2-8)的团簇结构和电子性质

在密度泛函理论B3LYP水平上, 对InnNa和InnNa+(n=2-8)团簇进行了结构优化和振动频率计算. 计算结果表明, InnNa(n=2、3、4、6)最稳定结构中的对称性分别为C2v、C3v、C4v和C2v, 而InnNa(n=5、7、8)的最稳定结构的对称性为C1点群. 从InnNa(n=4-8)的最稳定结构可以看出, Na原子均位于四个In原子形成的四边形面上. 对于InnNa+(n=2-8), 除了In2Na+、In4Na+和In7Na+, 其它结构都与其中性结构相似. 进一步计算InnNa(n=2-8)团簇的平均结合能、能量的二阶差分以及绝热电离能表明, InnNa(n=2-8)团簇能量的二阶差分呈现奇偶交替特征, In4Na和In6Na较其它团簇更为稳定, 而且理论计算得到的绝热电离能和实验结果吻合得很好.     

Guided ion-beam studies of the reactions of Co(n)+ (n=2-20) with O2: cobalt cluster-oxide and -dioxide bond energies

The kinetic-energy dependence for the reactions of Co(n)+ (n=2-20) with O2 is measured as a function of kinetic energy over a range of 0 to 10 eV in a guided ion-beam tandem mass spectrometer. A variety of Co(m)+, Co(m)O+, and Co(m)O2+ (m < or = n) product ions is observed, with the dioxide cluster ions dominating the products for all larger clusters. Reaction efficiencies of Co(n)+ cations with O2 are near unity for all but the dimer. Bond dissociation energies for both cobalt cluster oxides and dioxides are derived from threshold analysis of the energy dependence of the endothermic reactions using several different methods. These values show little dependence on cluster size for clusters larger than three atoms. The trends in this thermochemistry and the stabilities of oxygenated cobalt clusters are discussed. The bond energies of Co(n)+-O for larger clusters are found to be very close to the value for desorption of atomic oxygen from bulk-phase cobalt. Rate constants for O2 chemisorption on the cationic clusters are compared with results from previous work on cationic, anionic, and neutral cobalt clusters.     

Theoretical studies on the bonding and thermodynamic properties of Ge n Si m (m+n=5) clusters: the precursors of germanium/silicon nanomaterials

Theoretical studies on the Ge n Si m clusters have been carried out using advanced ab initio approaches. The lowest energy isomers were determined for the clusters with compositions n+m=2-5. All possible isomers arising due to permutations of Ge and Si atoms were investigated. The L-shaped structure for the trimers, tetragonal with diagonal bond for tetramers, and a trigonal bipyramid for pentamers represent the energy optimized ground state geometries. The bonding analyses revealed that the trimers and tetramers are stabilized through multicenter pi bonding. In pentamers, this stabilizing factor is eliminated due to the further cluster growth. The ionization of clusters does not change their geometrical characteristics. The agreement of the calculated ionization and atomization energies with those obtained from the mass spectrometric studies (through estimated appearance potential) validated the reported structures of the clusters. The bonding properties of these species are discussed using their molecular orbital characteristics and analysis of natural bond orbital population data.     

B2Cn+(n=1～9)团簇的结构及其稳定性

采用密度泛函理论(DFT)的B3LYP泛函, 在6-311G*水平上对B2Cn+(n=1～9)团簇的几何构型和电子结构进行了优化和振动频率计算. 结果表明, 在B2Cn+(n=1～9)团簇的基态构型中, B2C2+、B2C3+为具有D∞h对称性的线形结构, B2C7+为具有Cs对称性的立体环状结构, 其余均为平面构型; 其成键顺序为C—C成键优于B—C 成键, B—C成键优于B—B成键. 进一步得到了B2Cn+(n=1～9)团簇的总能量(ET)、零点能(EZ)、摩尔热容(Cp)、标准熵(S0)以及原子化能(ΔEn+). 其结果显示, 随着n的递增, ET、EZ、Cp、S0和ΔEn+数值均呈现增大趋势, 其中EZ数值呈现近似等梯度的增加趋势. 通过对B2Cn+(n=1～9)团簇基态结构的垂直电子亲合势的研究发现, n为奇数的B2Cn+团簇比n为偶数的稳定.     

Singly and doubly lithium doped silicon clusters: geometrical and electronic structures and ionization energies

The geometric structures of neutral and cationic Si(n)Li(m)(0/+) clusters with n = 2-11 and m = 1, 2 are investigated using combined experimental and computational methods. The adiabatic ionization energy and vertical ionization energy (VIE) of Si(n)Li(m) clusters are determined using quantum chemical methods (B3LYP/6-311+G(d), G3B3, and CCSD(T)/aug-cc-pVxZ with x = D,T), whereas experimental values are derived from threshold photoionization experiments in the 4.68-6.24 eV range. Among the investigated cluster sizes, only Si(6)Li(2), Si(7)Li, Si(10)Li, and Si(11)Li have ionization thresholds below 6.24 eV and could be measured accurately. The ionization threshold and VIE obtained from the experimental photoionization efficiency curves agree well with the computed values. The growth mechanism of the lithium doped silicon clusters follows some simple rules: (1) neutral singly doped Si(n)Li clusters favor the Li atom addition on an edge or a face of the structure of the corresponding Si(n)(-) anion, while the cationic Si(n)Li(+) binds with one Si atom of the bare Si(n) cluster or adds on one of its edges, and (2) for doubly doped Si(n)Li(2)(0/+) clusters, the neutrals have the shape of the Si(n+1) counterparts with an additional Li atom added on an edge or a face of it, while the cations have both Li atoms added on edges or faces of the Si(n)(-) clusters.     

Size-specific interaction of alkali metal ions in the solvation of M+-benzene clusters by Ar atoms

The size-specific influence of the M+ alkali ion (M = Li, Na, K, Rb, and Cs) in the solvation process of the M+-benzene clusters by Ar atoms is investigated by means of molecular dynamic simulations. To fully understand the behavior observed in M+-bz-Ar(n) clusters, solvation is also studied in clusters containing either M+ or benzene only. The potential energy surfaces employed are based on a semiempirical bond-atom decomposition, which has been developed previously by some of the authors. The outcome of the dynamics is analyzed by employing radial distribution functions, studying the evolution of the distances between the Ar atoms and the alkali ion M+ or the benzene molecule for all M+-bz-Ar(n) clusters. For all members, in the M+-bz series, the benzene molecule (bz) is found to remain strongly bound to M+ even in the presence of solvent atoms. The radial distribution functions for the heavier clusters (K+-bz, Rb+-bz, and Cs+-bz), are found to be different than for the lighter (Na+-bz and Li+-bz) ones.     

Influence of copper substitution on the interaction of ethylene over iron clusters: a theoretical study

We report the results of density functional theory (DFT) calculations of ethylene adsorption over the most stable pure and bimetallic clusters of Fe(n)Cu(m) (2 ≤ m+n ≤ 4), in two adsorption modes of π and di-σ. Our results show that the quality of interaction of ethylene with iron center in bimetallic clusters of iron-copper is characteristically different from what is found over pure iron. Over the range of our studies for dimers, trimers, and tetramers, whether for π or di-σ mode, alloying iron clusters results in a substantial improvement in adsorption of ethylene over cluster and exhibits a notable increase in binding and interaction energies compared with pure iron clusters. One of the interesting features of this adsorption is that ethylene never orients toward di-σ mode for Cu-Cu or Fe-Cu bonds, and π orientation is strongly preferred. Ethylene adsorption in di-σ coordination is accompanied by the sever restructuring, larger deformation energy, and the larger interaction energy. In the next part, we answer this question of how electronic perturbations induced by copper atoms can enhance the activity of iron toward ethylene. This interpretation is done within the framework of natural bond orbital (NBO) and natural resonance theory (NRT) analyses. Different reaction pathways detected by NRT analysis (donor-acceptor, metallacyclic, and carbanion) reveal interesting aspects of differences between the nature of metal-alkene coordination in bimetallic and purely metallic clusters.     

Stern-gerlach study of multidecker lanthanide-cyclooctatetraene sandwich clusters

Multilayer lanthanide-cyclooctatetraene organometallic clusters, Lnn(C8H8)m (Ln = Eu, Tb, Ho, Tm; n = 1-7; m = n - 1, n, n + 1) were produced by a laser vaporization synthesis method. The magnetic deflections of these organometallic sandwich clusters were measured by a molecular beam magnetic deflection technique. Most of the sandwich species displayed one-sided deflection, while some of smaller Ln-C8H8 clusters showed symmetric broadening without or with only very small (or absent) net high-field deflection. In general, the total magnetic moments, calculated from the magnitude of the beams deflections, increase with the number of lanthanide atoms (i.e., with increasing sandwich layers); however for Tb-, Ho-, and Tm-C8H8 clusters with n > 3, the suppression of the magnetic moments was observed, possibly through antiferromagnetic interactions. For Eu-C8H8 clusters, we observe a linear increase of the magnetic moments with the number of Eu atoms up to n = 7, with average magnetic moment per Eu atom around 7 muB--similar to that displayed by conventionally synthesized mononuclear EuIIC8H8 complexes, indicating that Eu atoms exist as Eu2+ ions in the full sandwich Eun(C8H8)n+1 clusters. These results suggest that Eun(C8H8)n+1 is a promising candidate for a high-spin, one-dimensional building block in organometallic magnetic materials.     

Structure-dependent optical properties of single-walled silicon nanotubes

The electron excitations of Single-Walled Silicon Nanotubes (SWSiNTs), with sp(2) and sp(3) hybridization, were studied using the localized-density-matrix (LDM) method with INDO/S parameters. Strong anisotropic characteristics of the dynamic polarizabilities were found for all the nanotubes. The transitional intensity along the tubular axis is much larger than that perpendicular to the axis for all the nanotubes. The optical gaps of sp(3)-hybridized infinitely-long pentagonal SWSiNTs are near 3.0 eV and 4.7 eV owing to σ-σ* transitions along the direction of the tubular axis. The optical gaps of sp(2)-hybridized infinitely-long armchair SWSiNTs along the tube axis direction are about 0.7 eV and 2.4 eV for Si(3,3) SWSiNTs and 0.7 eV and 2.7 eV for Si(4,4) SWSiNTs. The former peak at 0.7 eV originated from π-π* electron transitions and the latter peak at 2.4 eV or 2.7 eV originated from σ-σ* electron transitions. Meanwhile, the intensities of π-π* electron transitions are stronger than those of σ-σ* electron transitions in SWSiNTs. The low sp(2) transition energy derived from the weak overlap of unpaired p(z) orbitals of silicon atoms. Moreover, the electronic excitations of zigzag SWSiNTs are similar to those of armchair structures. This indicates that sp(2)-hybridized silicon nanotubes possess much greater potential for application in optical fields.     

Stern-Gerlach experiments of one-dimensional metal-benzene sandwich clusters: Mn(C6H6)m (M = Al, Sc, Ti, and V)

A molecular beam of multilayer metal-benzene organometallic clusters Mn(C6H6)m (M = Al, Sc, Ti, and V) was produced by a laser vaporization synthesis method, and their magnetic deflections were measured. Multidecker sandwich clusters of transition-metal atoms and benzene Scn(C6H6)n+1 (n = 1, 2) and Vn(C6H6)n+1 (n = 1-4) possess magnetic moments that increase monotonously with n. The magnetic moments of Al(C6H6), Scn(C6H6)n+1, and Vn(C6H6)n+1 are smaller than that of their spin-only values as a result of intracluster spin relaxation, an effect that depends on the orbital angular momenta and bonding characters of the orbitals containing electron spin. While Ti(C6H6)2 was found to be nonmagnetic, Tin(C6H6)n+1 (n = 2, 3) possess nonzero magnetic moments. The mechanism of ferromagnetic spin ordering in M2(C6H6)3 (M = Sc, Ti, V) is discussed qualitatively in terms of molecular orbital analysis. These sandwich species represent a new class of one-dimensional molecular magnets in which the transition-metal atoms are formally zerovalent.