Structure and stability of oxygen adsorption on Si(n) (n = 5-10) clusters

The structures, binding energies, and electronic properties of one oxygen atom (O) and two oxygen atoms (2O) adsorption on silicon clusters Si(n) with n ranging from 5 to 10 are studied systematically by ab initio calculations. Twelve stable structures are obtained, two of which are in agreement with those reported in previous literature and the others are new structures that have not been proposed before. Further investigations on the fragmentations of Si(n)O and Si(n)O2 (n = 5-10) clusters indicate that the pathways Si(n)O --> Si(n-1) + SiO and Si(n)O2 --> Si(n-2) + Si2O2 are most favorable from thermodynamic viewpoint. Among the studied silicon oxide clusters, Si8O, Si9O, Si5O2 and Si8O2 correspond to large adsorption energies of silicon clusters with respect to O or 2O, while Si8O, with the smallest dissociation energy, has a tendency to separate into Si7 + SiO. Using the recently developed quasi-atomic minimal-basis-orbital method, we have also calculated the unsaturated valences of the neutral Si(n) clusters. Our calculation results show that the Si atoms which have the largest unsaturated valences are more attractive to O atom. Placing O atom right around the Si atoms with the largest unsaturated valences usually leads to stable structures of the silicon oxide clusters.     

Geometries and stabilities of Ag-doped Si n (n=1-13) clusters: a first-principles study

The structures of AgSi(n) (n=1-13) clusters are investigated using first-principles calculations. Our studies suggest that AgSi(n) clusters with n=7 and 10 are relatively stable isomers and that these clusters prefer to be exohedral rather than endohedral. Moreover, doping leaves the inner core structure of the clusters largely intact. Additionally, the plot of fragmentation energies as a function of silicon atoms shows that the AgSi(n) are favored to dissociate into one Ag atom and Si(n) clusters. Alternative pathways exist for n>7 (except n=11) in which the Ag-Si cluster dissociates into a stable Si(7) and a smaller fragment AgSi(n-7). The AgSi(11) cluster dissociates into a stable Si(10) and a small fragment AgSi. Lastly, our analysis indicates that doping of Ag atom significantly decreases the gaps between the highest occupied molecular orbital and the lowest unoccupied molecular orbital for n>7.     

Electronic structure and thermochemical properties of silicon-doped lithium clusters Li(n)Si0/+, n = 1-8: new insights on their stability

A theoretical investigation on small silicon-doped lithium clusters Li(n)Si with n = 1-8, in both neutral and cationic states is performed using the high accuracy CCSD(T)/complete basis set (CBS) method. Location of the global minima is carried out using a stochastic search method and the growth pattern of the clusters emerges as follows: (i) the species Li(n)Si with n ≤ 6 are formed by directly binding one Li to a Si of the smaller cluster Li(n-1)Si, (ii) the structures tend to have an as high as possible symmetry and to maximize the coordination number of silicon. The first three-dimensional global minimum is found for Li(4)Si, and (iii) for Li(7)Si and Li(8)Si, the global minima are formed by capping Li atoms on triangular faces of Li(6)Si (O(h)). A maximum coordination number of silicon is found to be 6 for the global minima, and structures with higher coordination of silicon exist but are less stable. Heats of formation at 0 K (Δ(f)H(0)) and 298 K (Δ(f)H(298)), average binding energies (E(b)), adiabatic (AIE) and vertical (VIE) ionization energies, dissociation energies (D(e)), and second-order difference in total energy (Δ(2)E) of the clusters in both neutral and cationic states are calculated from the CCSD(T)/CBS energies and used to evaluate the relative stability of clusters. The species Li(4)Si, Li(6)Si, and Li(5)Si(+) are the more stable systems with large HOMO-LUMO gaps, E(b), and Δ(2)E. Their enhanced stability can be rationalized using a modified phenomenological shell model, which includes the effects of additional factors such as geometrical symmetry and coordination number of the dopant. The new model is subsequently applied with consistency to other impure clusters Li(n)X with X = B, Al, C, Si, Ge, and Sn.     

Clusters of hydrated methane sulfonic acid CH3SO3H.(H2O)n (n = 1-5): a theoretical study

Ab initio and density functional methods have been used to examine the structures and energetics of the hydrated clusters of methane sulfonic acid (MSA), CH3SO3H.(H2O)n (n = 1-5). For small clusters with one or two water molecules, the most stable clusters have strong cyclic hydrogen bonds between the proton of OH group in MSA and the water molecules. With three or more water molecules, the proton transfer from MSA to water becomes possible, forming ion-pair structures between CH3SO3- and H3O+ moieties. For MSA.(H2O)3, the energy difference between the most stable ion pair and neutral structures are less than 1 kJ/mol, thus coexistence of neutral and ion-pair isomers are expected. For larger clusters with four and five water molecules, the ion-pair isomers are more stable (>10 kJ/mol) than the neutral ones; thus, proton transfer takes place. The ion-pair clusters can have direct hydrogen bond between CH3SO3- and H3O+ or indirect one through water molecule. For MSA.(H2O)5, the energy difference between ion pairs with direct and indirect hydrogen bonds are less than 1 kJ/mol; namely, the charge separation and acid ionization is energetically possible. The calculated IR spectra of stable isomers of MSA.(H2O)n clusters clearly demonstrate the significant red shift of OH stretching of MSA and hydrogen-bonded OH stretching of water molecules as the size of cluster increases.     

Efficient silicon surface and cluster modeling using quantum capping potentials

A one-electron, silicon quantum capping potential for use in capping the dangling bonds formed by artificially limiting silicon clusters or surfaces is developed. The quantum capping potentials are general and can be used directly in any computational package that can handle effective core potentials. For silicon clusters and silicon surface models, we compared the results of traditional hydrogen atom capping with those obtained from capping with quantum capping potentials. The results clearly show that cluster and surface models capped with quantum capping potentials have ionization potentials, electron affinities, and highest occupied molecular orbital-lowest unoccupied molecular orbital gaps that are in very good agreement with those of larger systems. The silicon quantum capping potentials should be applied in cases where one wishes to model processes involving charges or low-energy excitations in silicon clusters and surfaces consisting of more than ca. 150 atoms.     

Nin(n=3～39)团簇结构，能量和稳定性的研究

The stable geometric structure and energy of Ni_n(n=3～39) clusters as a function of cluster size are studied by the Monte Carlo simulation. The interaction among atoms is calculated through Lennard-Jones plus Axilrod-Teller potentials. It is found that the clusters grow through adding atoms on one or more surfaces of Ni₇ or Ni₁₃ after the cluster size n is larger than 7. It is also found that there exists direct correlation between the stability and geometrical structures of clusters. Relatively, highly symmetry clusters are more stable. In addition, the nickel clusters with fcc-like structure such as Ni₃₃, Ni₃₆ and Ni₃₈ are more stable than their neighboring clusters.     

Theoretical studies on photoelectron and IR spectral properties of Br2.-(H2O)n clusters

We report vertical detachment energy (VDE) and IR spectra of Br2.-.(H2O)n clusters (n=1-8) based on first principles electronic structure calculations. Cluster structures and IR spectra are calculated at Becke's half-and-half hybrid exchange-correlation functional (BHHLYP) with a triple split valence basis function, 6-311++G(d,p). VDE for the hydrated clusters is calculated based on second order Moller-Plesset perturbation (MP2) theory with the same set of basis function. On full geometry optimization, it is observed that conformers having interwater hydrogen bonding among solvent water molecules are more stable than the structures having double or single hydrogen bonded structures between the anionic solute, Br2.-, and solvent water molecules. Moreover, a conformer having cyclic interwater hydrogen bonded network is predicted to be more stable for each size hydrated cluster. It is also noticed that up to four solvent H2O units can reside around the solute in a cyclic interwater hydrogen bonded network. The excess electron in these hydrated clusters is localized over the solute atoms. Weighted average VDE is calculated for each size (n) cluster based on statistical population of the conformers at 150 K. A linear relationship is obtained for VDE versus (n+3)(-1/3) and bulk VDE of Br2.- aqueous solution is calculated as 10.01 eV at MP2 level of theory. BHHLYP density functional is seen to make a systematic overestimation in VDE values by approximately 0.5 eV compared to MP2 data in all the hydrated clusters. It is observed that hydration increases VDE of bromine dimer anion system by approximately 6.4 eV. Calculated IR spectra show that the formation of Br2.--water clusters induces large shifts from the normal O-H stretching bands of isolated water keeping bending modes rather insensitive. Hydrated clusters, Br2.-.(H2O)n, show characteristic sharp features of O-H stretching bands of water in the small size clusters.     

(MN)nHm(M=Ga,In; n=1-4; m=1, 2)团簇的结构与稳定性

采用密度泛函理论(DFT)的B3LYP方法, 在6-31G**和Lanl2dz水平上分别对(MN)nHm(M=Ga, In; n=1-4; m=1, 2)进行了优化和振动频率计算. 得到了上述团簇的最稳定构型、H原子的结合能以及它们的能隙. 结果表明, (MN)nH(M=Ga, In; n=1-4)的基态构型均为双重态, (MN)nH2(M=Ga, In; n=1-4)的基态构型均为单重态; 当氢的个数为1时, 加在N原子上比加在M(M=Ga, In)原子上稳定, 如有N3单元, 那么加在N3单元两侧的构型是相同的, 且它是最稳定的; 当氢的个数为2时, 除n=1外, 分别加在两个N原子上的构型是最稳定的, 如有N3单元, 那么分别加在N3单元分离最远的两个N原子的构型是最稳定的. GaNH、(GaN)3H 和InNH的结合能和能隙都很大, 说明这些团簇都有很高的稳定性.     

Dihydrogen bond cooperativity in (HCCBeH)n clusters

A theoretical study has been carried out on the clusters formed by the association of ethynylhydroberyllium (HC[triple bond]CBeH) monomers. The monomer presents a linear disposition with a dipole moment of 0.94 D. Clusters from two to six monomers have been calculated for three different configurations (linear, cyclic with dihydrogen bonds, and cyclic with hydrogen bonds to the pi-cloud), the third one being the most stable. The electronic properties of the clusters have been analyzed by means of the atoms in molecules and natural bond orbitals methodologies. Cooperative effects, similar to the ones described for standard hydrogen bonded clusters, are observed in those configurations where dihydrogen bonds are the main interacting force.     

Comparison among four different ways to condense the Fukui function

Four different ways to condense the Fukui function are compared. Three of them perform a numerical integration over different basins to define the condensed Fukui function, and the other one is the most traditional Fukui function using Mulliken population analysis. The basins are chosen to be the basins of the electron density (AIM), the basins of the electron localization function (ELF), and the basins of the Fukui function itself. The use of the last two basins is new and presented for the first time here. It is found that the last three methods yield results which are stable against a change in the basis set. The condensed Fukui function using the basins of the ELF is not able to give information on the reactivity of an acceptor molecule. In general, the condensed Fukui function using the basins of the density or the basins of the Fukui function describe the reactivity trends well. The latter is preferred, because it only contains information about the Fukui function itself and it gives the right information for donor as well as acceptor centers.     

Theoretical investigation of gas phase ethanol–(water)n (n = 1–5) clusters and comparison with gas phase pure water clusters (water)n (n = 2–6)

Various properties (such as optimal structures, structural parameters, hydrogen bonds, natural bond orbital charge distributions, binding energies, electron densities at hydrogen bond critical points, cooperative effects, and so on) of gas phase ethanol–(water)_n (n = 1–5) clusters with the change in the number of water molecules have been systematically explored at the MP2/aug‐cc‐pVTZ//MP2/6‐311++G(d,p) computational level. The study of optimal structures shows that the most stable ethanol‐water heterodimer is the one where exists one primary hydrogen bond (O? H…O) and one secondary hydrogen bond (C? H …O) simultaneously. The cyclic geometric pattern formed by the primary hydrogen bonds, where all the molecules are proton acceptor and proton donor simultaneously, is the most stable configuration for ethanol–(water)_n (n = 2–4) clusters, and a transition from two‐dimensional cyclic to three‐dimensional structures occurs at n = 5. At the same time, the cluster stability seems to correlate with the number of primary hydrogen bonds, because the secondary hydrogen bond was extremely weaker than the primary hydrogen bond. Furthermore, the comparison of cooperative effects between ethanol–water clusters and gas phase pure water clusters has been analyzed from two aspects. First of all, for the cyclic structure, the cooperative effect in the former is slightly stronger than that of the latter with the increasing of water molecules. Second, for the ethanol–(water)₅ and (water)₆ structure, the cooperative effect in the former is also correspondingly stronger than that of the latter except for the ethanol–(water)₅ book structure. © 2012 Wiley Periodicals, Inc.     

Efficiency of random search procedures along the silicon cluster series: Si(n) (n=5-10, 15, and 20)

The efficiency of the simplest isomeric search procedure consisting in random generation of sets of atomic coordinates followed by density functional theory geometry optimization is tested on the silicon cluster series (Si(5-10, 15, 20)). Criteria such as yield, isomer distributions and recurrences are used to clearly establish the performance of the approach with respect to increasing cluster size. The elimination of unphysical candidate structures and the use of distinct box shapes and theoretical levels are also investigated. For the smaller Si(n) (n=5-10) clusters, the generation of random coordinates within a spherical box is found to offer a reasonable alternative to more complex algorithms by allowing straightforward identification of every known low-lying local minima. The simple stochastic search of larger clusters (i.e. Si(15) and Si(20)) is however complicated by the exponentially increasing number of both low- and high-lying minima leading to rather arbitrary and non-comprehensive results.     

Ab initio SCF molecular dynamics: Exploring the potential energy surface of small silicon clusters

A few classical nuclear trajectories at finite temperature have been calculated from ab initio SCF energy gradients. They have been used as an alternative means to search for local minimum energy structures on the Born–Oppenheimer surfaces for some elemental silicon clusters. The approach is found to be beneficial in yielding different structures of silicon clusters. In other cases, the trajectories stay trapped in only one region of the phase space.     

Theoretical Studies on the Stabilities and Hydrogen Bond Actions of （H2O）n Clusters

1 INTRODUCTION In the latest ten years, the structure and function of water clusters have captured the interest of chemists. One of the most important study objects in water cluster is to describe the behavior of water so- lution quantitatively at molecule level, which will pave the way for the solving of some environmental and other scientific problems, such as the formation of acid rain and nucleation mechanism of little water drop. Besides, weak interaction in water clusters could be al…     

Geometries, stabilities, and electronic properties of different-sized ZrSi(n) (n=1-16) clusters: a density-functional investigation

The ZrSi(n) (n=1-16) clusters with different spin configurations have been systematically investigated by using the density-functional approach. The total energies, equilibrium geometries, growth-pattern mechanisms, natural population analysis, etc., are discussed. The equilibrium structures of different-sized ZrSi(n) clusters can be determined by two evolution patterns. Theoretical results indicate that the most stable ZrSi(n) (n=1-7) geometries, except ZrSi3, keep the analogous frameworks as the lowest-energy or the second lowest-energy Si(n+1) clusters. However, for large ZrSi(n) (n=8-16) clusters, Zr atom obviously disturbs the framework of silicon clusters, and the localized position of the transition-metal (TM) Zr atom gradually varies from the surface insertion site to the concave site of the open silicon cage and to the encapsulated site of the sealed silicon cage. It should be mentioned that the lowest-energy sandwich-like ZrSi12 geometry is not a sealed structure and appears irregular as compared with other TM@Si12 (TM = Re,Ni). The growth patterns of ZrSi(n) (n=1-16) clusters are concerned showing the Zr-encapsulated structures as the favorable geometries. In addition, the calculated fragmentation energies of the ZrSi(n) (n=1-16) clusters manifest that the magic numbers of stabilities are 6, 8, 10, 14, and 16, and that the fullerene-like ZrSi16 is the most stable structure, which is in good agreement with the calculated atomic binding energies of ZrSi(n) (n=8-16) and with available experimental and theoretical results. Natural population analysis shows that the natural charge population of Zr atom in the most stable ZrSi(n) (n=1-16) structures exactly varies from positive to negative at the critical-sized ZrSi8 cluster; furthermore, the charge distribution around the Zr atom appears clearly covalent in character for the small- or middle-sized clusters and metallic in character for the large-sized clusters. Finally, the properties of frontier orbitals and polarizabilities of ZrSi(n) are also discussed.     

Structure, energy, and IR spectra of I2*-.nH2O clusters (n=1-8): a theoretical study

The authors report theoretical results on structure, bonding, energy, and infrared spectra of iodine dimer radical anion hydrated clusters, I(2) (-).nH(2)O (n=1-8), based on a systematic study following density functional theory. Several initial guess structures are considered for each size cluster to locate minimum energy conformers with a Gaussian 6-311++G(d,p) split valence basis function (triple split valence 6-311 basis set is applied for iodine). It is observed that three different types of hydrogen bonded structures, namely, symmetrical double hydrogen bonding, single hydrogen bonding, and interwater hydrogen bonding structures, are possible in these hydrated clusters. But conformers having interwater hydrogen bonding arrangements are more stable compared to those of double or single hydrogen bonded structures. It is also noticed that up to four solvent H(2)O units can reside around the solute in interwater hydrogen bonding network. At the maximum six H(2)O units are independently linked to the dimer anion having four double hydrogen bonding and two single hydrogen bonding, suggesting the hydration number of I(2) (-) to be 6. However, conformers having H(2)O units independently linked to the iodine dimer anion are not the most stable structures. In all these hydrated clusters, the odd electron is found to be localized over two I atoms and the two atoms are bound by a three-electron hemi bond. The solvation, interaction, and vertical detachment energies are calculated for all I(2) (-).nH(2)O clusters. Energy of interaction and vertical detachment energy profiles show stepwise saturation, indicating geometrical shell closing in the hydrated clusters, but solvation energy profile fails to show such behavior. A linear correlation is observed between the calculated energy of interaction and vertical detachment energy. It is observed that formation of I(2) (-)-water cluster induces significant shifts from the normal O-H stretching modes of isolated H(2)O. However, bending mode of H(2)O remains insensitive to the successive addition of solvent H(2)O units. Weighted average energy profiles and IR spectra are reported for all the hydrated clusters based on the statistical population of individual conformers at room temperature.     

A theoretical study on small iridium clusters: structural evolution, electronic and magnetic properties, and reactivity predictors

The structural, electronic, and magnetic properties of iridium clusters with sizes of n = 2-15 are investigated by employing the generalized gradient approximation of density functional theory. Simple cube evolution pattern is revealed for Ir(2-15) clusters, as predicted by previous reports. It is remarkable that for Ir(10), Ir(11) clusters, new generated isomers with higher stabilities relative to those reported in previous studies are obtained. The even-sized clusters are more stable than the odd-sized species. The Ir-Ir bonds in the cubic Ir(8) and Ir(12) clusters, which are considered as the basic units in the structural evolution present covalent character. Starting from n = 8, the magnetic moments of Ir(n) clusters decrease sharply. The moments of magnetic clusters show 5d characters. The reactive site selectivity of studied clusters with n = 5-15 is analyzed with condensed Fukui function. The capped atoms in certain clusters (Ir(9), Ir(10), Ir(11), and Ir(13)) generally show extraordinary activity for both nucleophilic and electrophilic attack.     

Stability of hollow spheroidal silicon clusters Sin and SinHn

The structures of Si_n and Si_nH_n fullerenes with 20 ≶n ≶60 are calculated in the MINDO/3 approximation using the Monte Carlo technique for geometry optimization. The calculations show that spheroidal silicon clusters consisting of more than 36 atoms are stable and the bond energy increases with their size. This increase is not noticed for compact clusters calculated as an alternative. For n ≥40-50, the latter have lower bond energies compared to fullerenes. The geometry optimization of the tetrahedral cluster Si₄₅ results in a structure close to spheroidal, which gains in bond energy. The addition of hydrogen atoms to small deformed fullerenes and their geometry optimization make it possible to obtain stable spheroidal structures Si_nH_n whose bond energy is greater than that of alternative compact silicon hydride clusters. When the size of spheroidal clusters Si_nH_n increases, i. e., when n > 36, the hydrogen elimination barriers decrease abruptly; the Si_nH_n diamond structure of the cluster is more advantageous when n ≥50.     

Global search for minimum energy (H2O)n clusters, n = 3-5

The Gaussian-3 (G3) model chemistry method has been used to calculate the relative deltaG(o) values for all possible conformers of neutral clusters of water, (H2O)n, where n = 3-5. A complete 12-fold conformational search around each hydrogen bond produced 144, 1728, and 20,736 initial starting structures of the water trimer, tetramer, and pentamer. These structures were optimized with PM3, followed by HF/6-31G* optimization, and then with the G3 model chemistry. Only two trimers are present on the G3 potential energy hypersurface. We identified 5 tetramers and 10 pentamers on the potential energy and free-energy hypersurfaces at 298 K. None of these 17 structures were linear; all linear starting models folded into cyclic or three-dimensional structures. The cyclic pentamer is the most stable isomer at 298 K. On the basis of this and previous studies, we expect the cyclic tetramers and pentamers to be the most significant cyclic water clusters in the atmosphere.     

Low-lying isomers of Si(n)(+) and Si(n)(-) (n=31-50) clusters

We carry out a systematic search for the atomic structures of silicon cluster cations and anions in the size range n=31-50 using density functional theory in the generalized-gradient approximation. The obtained lowest-energy candidates feature cagelike structures. We find that the computed binding energies and the dissociation pathways as well as the mobilities of our lowest-energy isomers of the cations are all in good agreement with the measured data from experiments. Furthermore, based on these isomers, we reveal that the steplike feature appearing in the measured high-resolution mobilities can be correlated with the corresponding fullerenes explicitly, which strongly support the notion that endohedral silicon fullerenelike structures are the most favored growth pattern for silicon clusters in the range n=31-50. Our calculation and analysis suggest that the proposed isomers are probably very close to the major-abundance isomers observed in experiments.