Structural evolution of anionic silicon clusters SiN (20 <or= N <or= 45)

Results of a combined photoelectron spectroscopy and first-principles density-functional study of SiN- clusters in the size range 20 or= 20. For 28 相似文献   

Exohedral silicon fullerenes: SiNPtN/2 (20<or=N<or=60)

Using density functional theory method we show that hollow silicon fullerene cages, SiN (20相似文献   

An unbiased population-based search for the geometry optimization of Lennard-Jones clusters: 2 < or = N < or = 372

This article presents the results obtained using an unbiased Population Based Search (PBS) for optimizing Lennard-Jones clusters. PBS is able to repeatedly obtain all putative global minima, for Lennard-Jones clusters in the range 2 < or = N < or = 372, as reported in the Cambridge Cluster Database. The PBS algorithm incorporates and extends key techniques that have been developed in other Lennard-Jones optimization algorithms over the last decade. Of particular importance are the use of cut-and-paste operators, structure niching (using the cluster strain energy as a metric), two-phase local search, and a new operator, Directed Optimization, which extends the previous concept of directed mutation. In addition, PBS is able to operate in a parallel mode for optimizing larger clusters.     

Geometry optimization of carbon dioxide clusters (CO2)n for 4 < or = n < or = 40

Geometry optimization of carbon dioxide clusters (CO2)n with the size of 4 < or = n < or = 40 is performed by a heuristic and unbiased method combined with geometrical perturbations. Comparison with the global minima reported in the literature shows that the present method reproduces the global minima for clusters with n = 6, 8, 13, 19, 28, 30, and 32 and yields new global minima for (CO2)23, (CO2)25, and (CO2)35. For the other clusters under investigation, global minima are first reported in this article. Structural features of CO2 clusters and efficiency of the optimization method are discussed.     

Global minimum structures of morse clusters as a function of the range of the potential: 81<or=N<or=160

We have attempted to find the putative global minimum structures of Morse clusters for cluster size N=81-160 as a function of the range of the potential (with potential range rho0>or=3.0). Moreover, compared to the results for N相似文献   

Structures and relative stability of medium-sized silicon clusters. V. Low-lying endohedral fullerenelike clusters Si31-Si40 and Si45

We have performed unconstrained search for low-lying structures of medium-sized silicon clusters Si(31)-Si(40) and Si(45), by means of the minimum-hopping global optimization method coupled with a density-functional based tight-binding model of silicon. Subsequent geometric optimization by using density-functional theory with the PBE, BLYP, and B3LYP functionals was carried out to determine the relative stability of various candidate low-lying silicon clusters obtained from the unconstrained search. The low-lying characteristics of these clusters can be affirmed by comparing the binding energies per atom of these clusters with previously determined lowest-energy clusters(Si(n)) in the size range of 21相似文献   

Structures and relative stability of medium- and large-sized silicon clusters. VI. Fullerene cage motifs for low-lying clusters Si(39), Si(40), Si(50), Si(60), Si(70), and Si(80)

We performed a constrained search, combined with density-functional theory optimization, of low-energy geometric structures of silicon clusters Si(39), Si(40), Si(50), Si(60), Si(70), and Si(80). We used fullerene cages as structural motifs to construct initial configurations of endohedral fullerene structures. For Si(39), we examined six endohedral fullerene structures using all six homolog C(34) fullerene isomers as cage motifs. We found that the Si(39) constructed based on the C(34)(C(s):2) cage motif results in a new leading candidate for the lowest-energy structure whose energy is appreciably lower than that of the previously reported leading candidate obtained based on unbiased searches (combined with tight-binding optimization). The C(34)(C(s):2) cage motif also leads to a new candidate for the lowest-energy structure of Si(40) whose energy is notably lower than that of the previously reported leading candidate with outer cage homolog to the C(34)(C(1):1). Low-lying structures of larger silicon clusters Si(50) and Si(60) are also obtained on the basis of preconstructed endohedral fullerene structures. For Si(50), Si(60), and Si(80), the obtained low-energy structures are all notably lower in energy than the lowest-energy silicon structures obtained based on an unbiased search with the empirical Stillinger-Weber potential of silicon. Additionally, we found that the binding energy per atom (or cohesive energy) increases typically >10 meV with addition of every ten Si atoms. This result may be used as an empirical criterion (or the minimal requirement) to identify low-lying silicon clusters with size larger than Si(50).     

Size effect of fullerene cages and encaged clusters in M<Subscript>3</Subscript>N@C<Subscript>2<Emphasis Type="Italic">n</Emphasis></Subscript>

Based on the calculated findings that the sizes of encaged clusters determine the structures and the stability of C₈₀-based trimetallic nitride fullerenes (TNFs), more extensive density functional theory calculations were performed on M₃N@C₆₈, M₃N@C₇₈ and M₃N@C₈₀ (M=Sc, Y and La). The calculated results demonstrated that the structures and stability undergo a transition with the increasing of the sizes of the cages and clusters. Sc₃N is planar inside the three considered cages, Y₃N is slightly pyramidal inside C₆₈-6140 and C₇₈-5 and planar inside I_h C₈₀-7, however, La₃N is pyramidal inside all the three cages. Those cages with pyramidal clusters inside deformed considerably, compared with their parent cages. In these cases, the bonding of metallic atoms toward the cages does not play an important role, and the encaged cluster tends to be located inside the cages with the largest M-M and M-C distances so that the strain energy can be released mostly. These calculations revealed the size effect of fullerene cages and encaged clusters, and can explain the position priority of M3N inside fullerene cages and the differences in yield of M₃N@C_2n . Supported by the Southwest University, China (Grant No. SWNUB2005002)     

Global optimization study of small (10 < or = N < or = 120) Pd clusters supported on MgO(100)

Experimental evidence suggests that Pd clusters on MgO, known to be good reaction catalysts, have face centered cubic (fcc) epitaxial structures. The structure of such clusters is the result of the interplay of Pd-Pd and Pd-substrate bonds, the former inclined to favor icosahedral (Ih) and decahedral (Dh)-like structures, the latter leading to place Pd atoms on top of oxygen sites, according to an epitaxial stacking. This paper shows the results of a basin-hopping global optimization procedure applied to free and MgO-supported Pd clusters in the size range 10 < or = N < or = 120. Pd-MgO interactions are modeled by an analytical function fitted to ab initio results, while Pd-Pd interactions are modeled by a semiempirical potential. Besides the tight-binding Rosato-Guillopé-Legrand (RGL) potential, we have adopted a modified version of RGL that better reproduces the experimental surface energy of palladium, modifying the attractive part of Pd atoms potential energy. We have compared the two potential models, and as a result, the RGL potential favors clusters with epitaxial arrangements, so that cluster structures are epitaxial fcc in almost all the size ranges considered. On the contrary, the alternative potential model preserves some Ih-like characteristics typical of the free Pd clusters, and it suggests that a transition size from Ih-like to epitaxial structures can take place at about 100 atoms.     

Ab initio study of neutral and charged SinNap(+) (n <or= 6, p <or= 2) clusters

Ab initio calculations in the framework of the density functional theory, with B3LYP functional, are performed to study the lowest-energy isomers of silicon sodium clusters Si(n)Na(p)(+) (n 相似文献   

Theoretical study of isomerism in nitrogen- and phosphorus-substituted aluminum clusters M<Subscript>6</Subscript>Al<Subscript>38</Subscript> and M<Subscript>12</Subscript>Al<Subscript>32</Subscript> (M = N,P)

More than 20 М₆Al₃₈ isomers and several М₁₂Al₃₂ isomers for nitrogen- and phosphorus-substituted clusters with six and twelve dopant atoms M = N and P substituted for Al atoms in different positions at the surface of the aluminum cage and inside it have been studied by the density functional theory method. In the preferred N₆Al₃₈ isomer, all N atoms are substituted for Al atoms initially located in one outer layer of the cluster. In the course of geometry optimization, the nitrogen atoms are incorporated into positions in the neighboring intermediate layer, thus converting it into a 12-atom face consisting of three vertex-sharing adjacent six-membered rings with short N–Al bonds. For Р₆Al₃₈, a distribution of the dopant either in both surface layers or in the intermediate space between the surface layers and the inner core of the cluster is preferred. Optimization of alternative structures of the N₁₂Al₃₂ cluster with N atoms substituted for Al atoms in both outer layers is evidence in favor of the isomer in which the dopants are dispersed as separated monatomic anions N–. Together with their bridging Al atoms, these anions form the inner [N₁₂Al₁₄] cage with an unusual dumbbell-like structure in which the upper and lower halves are linked through N–Al bonds with the equatorial aluminum atoms. In the next low-lying isomer being ~23 kcal/mol higher on the energy scale, there is observed the “microclustering” of the dopant to form three covalently bonded diatomic dianions N₂^2-; the latter, together with the bridging Al atoms are combined into a [N₆Al₆] “subcluster” inside the severely distorted outer cage. In P₁₂Al₃₂, the aluminum cage is subjected only to moderate distortions: the phosphorus atoms remain in the outer layers and form two three-membered rings [Р₃]. The estimated energies of the model substitution reactions Al₄₄ + M₆ → M₆Al₃₈ + Al₆ (1) and Al₄₄ + 2M₆ → M₁₂Al₃₈ + 2A_l6 (2) demonstrate that all these reactions are exothermic; however, for the nitrogen-containing clusters, the decrease in energy with increasing number of substitutions increases from 66 (1) to 113 (2) kcal/mol, while in the case of phosphorus, it decreases from 45 (1) to 4 (2) kcal/mol. The results obtained for N₆Al₃₈, N₁₂Al₃₂, Р₆Al₃₈, and Р₁₂Al₃₂ are compared with the previous calculations for the C₆Al₃₈, C₁₂Al₃₂, Si₆Al₃₈, and Si₁₂Al₃₂ clusters.     

Lanthanum nitride endohedral fullerenes La3N@C2n (43 <or= n <or= 55): preferential formation of La3N@C96

While the trimetallic nitrides of Sc, Y and the lanthanides between Gd and Lu preferentially template C(80) cages, M(3)N@C(80), and while those of Ce, Pr and Nd preferentially template the C(88) cage, M(3)N@C(88), we show herein that the largest metallic nitride cluster, La(3)N, preferentially leads to the formation of La(3)N@C(96) and to a lesser extent the La(3)N@C(88). This is the first time that La(3)N is successfully encapsulated inside fullerene cages. La(3)N@C(2n) metallofullerenes were synthesized by arcing packed graphite rods in a modified Kr?tschmer-Huffman arc reactor, extracted from the collected soot and identified by mass spectroscopy. They were isolated and purified by high performance liquid chromatography (HPLC). Different arcing conditions were studied to maximize fullerene production, and results showed that yields have a high La(2)O(3)/C dependence. Relatively high yields were obtained when a 1:5 ratio was used. Three main fractions, La(3)N@C(88), La(3)N@C(92), and La(3)N@C(96), were characterized by UV/Vis-NIR and cyclic voltammetry. Unlike other trimetallic nitride metallofullerenes of the same carbon cage size, La(3)N@C(88) exhibits a higher HOMO-LUMO gap and irreversible reduction and oxidation steps.     

Structural and electronic properties of Si(n), Si(n)-, and PSi(n-1) clusters (2 < or = n < or = 13): Theoretical investigation based on ab initio molecular orbital theory

The geometric and electronic structures of Si(n), Si(n)-, and PSi(n-1) clusters (2 < or = n < or = 13) have been investigated using the ab initio molecular orbital theory formalism. The hybrid exchange-correlation energy functional (B3LYP) and a standard split-valence basis set with polarization functions (6-31+G(d)) were employed to optimize geometrical configurations. The total energies of the lowest energy isomers thus obtained were recalculated at the MP2/aug-cc-pVTZ level of theory. Unlike positively charged clusters, which showed similar structural behavior as that of neutral clusters [Nigam et al., J. Chem. Phys. 121, 7756 (2004)], significant geometrical changes were observed between Si(n) and Si(n)- clusters for n = 6, 8, 11, and 13. However, the geometries of P substituted silicon clusters show similar growth as that of negatively charged Si(n) clusters with small local distortions. The relative stability as a function of cluster size has been verified based on their binding energies, second difference in energy (Delta2 E), and fragmentation behavior. In general, the average binding energy of Si(n)- clusters is found to be higher than that of Si(n) clusters. For isoelectronic PSi(n-1) clusters, it is found that although for small clusters (n < 4) substitution of P atom improves the binding energy of Si(n) clusters, for larger clusters (n > or = 4) the effect is opposite. The fragmentation behavior of these clusters reveals that while small clusters prefer to evaporate monomer, the larger ones dissociate into two stable clusters of smaller size. The adiabatic electron affinities of Si(n) clusters and vertical detachment energies of Si(n)- clusters were calculated and compared with available experimental results. Finally, a good agreement between experimental and our theoretical results suggests good prediction of the lowest energy isomeric structures for all clusters calculated in the present study.     

Geometrical and electronic structures of Au(m)Ag(n) (2 < or = m + n < or = 8)

The structural and electronic properties of Au(m)Ag(n) binary clusters (2 < or = m + n < or = 8) have been investigated by density functional theory with relativistic effective core potentials. The results indicate that Au atoms tend to occupy the surface of Au(m)Ag(n) clusters (n > or = 2 and m > or = 2). As a result, segregation of small or big bimetallic clusters can be explained according to the atomic mass. The binding energies of the most stable Au(m)Ag(n) clusters increase with increasing m+n. The vertical ionization potentials of the most stable Au(m)Ag(n) clusters show odd-even oscillations with changing m+n. The possible dissociation channels of the clusters considered are also discussed.     

Expanding the world of endohedral fullerenes--the Tm3N@C2n (39< or =n< or =43) clusterfullerene family

A new family of endohedral fullerenes, based on an encaged trithulium nitride (Tm(3)N) cluster, was synthesised, isolated and characterised by HPLC, mass spectrometry, and visible-NIR and FTIR spectroscopy. Tm(3)N clusterfullerenes with cages as small as C(76) and as large as C(88) were prepared and six of them were isolated. Tm(3)N@C(78) is a small clusterfullerene. The two isomers of Tm(3)N@C(80) (I and II) were the most abundant structures in the fullerene soot. Tm(3)N@C(82), Tm(3)N@C(84), and Tm(3)N@C(86) represent a new series of higher clusterfullerenes. All six isolated Tm(3)N clusterfullerenes were classified as large energy-gap structures with optical energy gaps between approximately 1.2 and approximately 1.75 eV. Tm(3)N@C(80) (I) and Tm(3)N@C(80) (II) were assigned to the C(80) cages C(80):7 (I(h)) and C(80):6 (D(5h)). For Tm(3)N@C(78), the analysis pointed to an elliptical carbon cage with C(78):1 (D(3)) or C(78):4 (D(3h)) being the probable structures.     

Theoretical investigation of geometry and stability of small lithium‐iodide LinI (n = 2–6) clusters

We present theoretical investigation of the structural characteristics and stabilities of neutral and positively charged Li_nI (n = 2‐6) species. The structural isomers were found by using a randomized algorithm to search for minima structures, followed by B3LYP optimizations; the single‐point RCCSD(T)/cc‐pwCVTZ(‐PP) calculations were performed in order to compute relative energies, binding energies per atom, adiabatic and vertical ionization energies, and dissociation energies. Stability was compared to the pure lithium clusters; there is a typical odd‐even alternation; iodine doped clusters are more stable than pure lithium clusters. Lithium “cage” transfers its valence electron to the iodine atom to form neutral and cationic clusters. An electron departures the lithium cage upon ionization. An important reason for the larger stability of closed‐shell species is the existence of the HOMO 3c/2e natural bond orbitals. © 2013 Wiley Periodicals, Inc.     

How to not build a cage: endohedral functionalization of polyoxometalate-based metal–organic polyhedra

Introducing functionalities into the interior of metal–organic cage complexes can confer properties and utilities (e.g. catalysis, separation, drug delivery, and guest recognition) that are distinct from those of unfunctionalized cages. Endohedral functionalization of such cage molecules, for decades, has largely relied on modifying their organic linkers to covalently append targeted functional groups to the interior surface. We herein introduce an effective coordination method to bring in functionalities at the metal sites instead, for a set of polyhedral cages where the nodes are in situ formed polyoxovanadate clusters, [V^IV₆O₆(OCH₃)₉(μ₆-SO₄)(COO)₃]²⁻. Replacing the central sulfates of these hexavanadate clusters with more strongly coordinating phosphonate groups allows the installation of functionalities within the cage cavities. Organophosphonates with phenyl, biphenyl, and terphenyl tails were examined for internalization. Depending on the size/shape of the cavities, small phosphonates can fit into the molecular containers whereas larger ones inhibit or transform the framework architecture, whereby the first non-cage complex was isolated from a reaction that otherwise would lead to entropically favored regular polyhedra cages. The results highlight the complex and dynamic nature of the self-assembly process involving polyoxometalates and the scope of molecular variety accessible by the introduction of endo functional groups.

Installation of oversized functions within a metal–organic cage may “burst” or even transform the molecular cage itself.     

Structure, stability, and cluster-cage interactions in nitride clusterfullerenes M3N@C2n (M = Sc, Y; 2n = 68-98): a density functional theory study

Extensive semiempirical calculations of the hexaanions of IPR (isolated pentagon rule) and non-IPR isomers of C(68)-C(88) and IPR isomers of C(90)-C(98) followed by DFT calculations of the lowest energy structures were performed to find the carbon cages that can provide the most stable isomers of M(3)N@C(2n) clusterfullerenes (M = Sc, Y) with Y as a model for rare earth ions. DFT calculations of isomers of M(3)N@C(2n) (M = Sc, Y; 2n = 68-98) based on the most stable C(2n)(6-) cages were also performed. The lowest energy isomers found by this methodology for Sc(3)N@C(68), Sc(3)N@C(78), Sc(3)N@C(80), Y(3)N@C(78), Y(3)N@C(80), Y(3)N@C(84), Y(3)N@C(86), and Y(3)N@C(88) are those that have been shown to exist by single-crystal X-ray studies as Sc(3)N@C(2n) (2n = 68, 78, 80), Dy(3)N@C(80), and Tb(3)N@C(2n) (2n = 80, 84, 86, 88) clusterfullerenes. Reassignment of the carbon cage of Sc(2)@C(76) to the non-IPR Cs: 17490 isomer is also proposed. The stability of nitride clusterfullerenes was found to correlate well with the stability of the empty 6-fold charged cages. However, the dimensions of the cage in terms of its ability to encapsulate M(3)N clusters were also found to be an important factor, especially for the medium size cages and the large Y(3)N cluster. In some cases the most stable structures are based on the different cage isomers for Sc(3)N and Y(3)N clusters. Up to the cage size of C(84), non-IPR isomers of C(2n)(6-) and M(3)N@C(2n) were found to compete with or to be even more stable than IPR isomers. However, the number of adjacent pentagon pairs in the most stable non-IPR isomers decreases as cage size increases: the most stable M(3)N@C(2n) isomers have three such pairs for 2n = 68-72, two pairs for n = 74-80, and only one pair for n = 82, 84. For C(86) and C(88) the lowest energy IPR isomers are much more stable than any non-IPR isomer. The trends in the stability of the fullerene isomers and the cluster-cage binding energies are discussed, and general rules for stability of clusterfullerenes are established. Finally, the high yield of M(3)N@C(80) (Ih) clusterfullerenes for any metal is explained by the exceptional stability of the C(80)(6-) (Ih: 31924) cage, rationalized by the optimum distribution of the pentagons leading to the minimization of the steric strain, and structural similarities of C(80) (Ih: 31924) with the lowest energy non-IPR isomers of C(760(6-), C(78)(6-), C(82)(6-), and C(84)(6-) pointed out.     

B<Subscript>24</Subscript>N<Subscript>24</Subscript> nanocages: a GIAO density functional theory study of <Superscript>14</Superscript>N and <Superscript>11</Superscript>B nuclear magnetic shielding and electric field gradient tensors

Abstract  Density functional theory (DFT) calculations were performed to determine boron-11 and nitrogen-14 nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) spectroscopy parameters in the three most stable B₂₄N₂₄ fullerenes for the first time. The considered samples were first allowed to relax entirely, and then the NMR and NQR calculations were performed on the geometrically optimized models. The calculations of the ¹¹B and ¹⁴N nuclear magnetic shielding tensors and electric field gradient tensors employed the Gaussian 98 software implementation of the gauge-including atomic orbital (GIAO) method using the Becke3, Lee-Yang-Parr (B3LYP) DFT level and 6-311G** and 6-311++G** standard basis sets in each of the three optimized forms, and converted the results to experimentally measurable NMR parameters.The calculated NMR chemical shieldings of the three cages show significant differences, providing a way to identify these clusters. The evaluated NQR parameters of the ¹¹B and ¹⁴N nuclei in the clusters are also reported and discussed. Graphical abstract        

Inelastic collisions in molecular nitrogen at low temperature (2 < or = T < or = 50 K)

Theory and experiment are combined in a novel approach aimed at establishing a set of two-body state-to-state rates for elementary processes ij --> lm in low temperature N(2):N(2) collisions involving the rotational states i,j,l,m. First, a set of 148 collision cross sections is calculated as a function of the collision energy at the converged close-coupled level via the MOLSCAT code, using a recent potential energy surface for N(2)-N(2). Then, the corresponding rates for the range of 2 < or = T < or = 50 K are derived from the cross sections. The link between theory and experiment, aimed at assessing the calculated rates, is a master equation which accounts for the time evolution of rotational populations in a reference volume of gas in terms of the collision rates. In the experiment, the evolution of rotational populations is measured by Raman spectroscopy in a tiny reference volume (approximately 2 x 10(-3) mm(3)) of N(2) traveling along the axis of a supersonic jet. The calculated collisional rates are assessed experimentally in the range of 4 < or = T < or = 35 K by means of the master equation, and then are scaled by averaging over a large set of experimental data. The scaled rates account accurately for the evolution of the rotational populations measured in a wide range of conditions. Accuracy of 10% is estimated for the main scaled rates.