Theoretical study of Al(n) and Al(n)O (n = 2-10) clusters

The stable structures, energies, and electronic properties of neutral, cationic, and anionic clusters of Al(n) (n = 2-10) are studied systematically at the B3LYP/6-311G(2d) level. We find that our optimized structures of Al5(+), Al9(+), Al9(-), Al10, Al10(+), and Al10(-) clusters are more stable than the corresponding ones proposed in previous literature reports. For the studied neutral aluminum clusters, our results show that the stability has an odd/even alternation phenomenon. We also find that the Al3, Al7, Al7(+), and Al7(-) structures are more stable than their neighbors according to their binding energies. For Al7(+) with a special stability, the nucleus-independent chemical shifts and resonance energies are calculated to evaluate its aromaticity. In addition, we present results on hardness, ionization potential, and electron detachment energy. On the basis of the stable structures of the neutral Al(n) (n = 2-10) clusters, the Al(n)O (n = 2-10) clusters are further investigated at the B3LYP/6-311G(2d), and the lowest-energy structures are searched. The structures show that oxygen tends to either be absorbed at the surface of the aluminum clusters or be inserted between Al atoms to form an Al(n-1)OAl motif, of which the Al(n-1) part retains the stable structure of pure aluminum clusters.     

Growth behavior of La @Si n (n=1-21) metal-encapsulated clusters

Density functional theory involving generalized gradient approximation correlation functional is used to investigate the cluster series La @Si n (n=1-21). We find that the growth process of La @Si n (n=1-21) could be divided into three stages: First, La atom adheres to other Si atoms in the size range of 1相似文献   

Probing the electronic structure of early transition-metal oxide clusters: polyhedral cages of (V2O5)n(-) (n = 2-4) and (M2O5(2)(-) (M = Nb, Ta)

Vanadium oxide clusters, (V2O5)n, have been predicted to possess interesting polyhedral cage structures, which may serve as ideal molecular models for oxide surfaces and catalysts. Here we examine the electronic properties of these oxide clusters via anion photoelectron spectroscopy for (V2O5)n(-) (n = 2-4), as well as for the 4d/5d species, Nb4O10(-) and Ta4O10(-). Well-resolved photoelectron spectra have been obtained at 193 and 157 nm and used to compare with density functional calculations. Very high electron affinities and large HOMO-LUMO gaps are observed for all the (V2O5)n clusters. The HOMO-LUMO gaps of (V2O5)n, all exceeding that of the band gap of the bulk oxide, are found to increase with cluster size from n = 2-4. For the M4O10 clusters, we find that the Nb/Ta species yield similar spectra, both possessing lower electron affinities and larger HOMO-LUMO gaps relative to V4O10. The structures of the anionic and neutral clusters are optimized; the calculated electron binding energies and excitation spectra for the global minimum cage structures are in good agreement with the experiment. Evidence is also observed for the predicted trend of electron delocalization versus localization in the (V2O5)n(-) clusters. Further insights are provided pertaining to the potential chemical reactivities of the oxide clusters and properties of the bulk oxides.     

Theoretical study on (Al2O3)n (n = 1-10 and 30) fullerenes and H2 adsorption properties

The structures and stabilities of (Al2O3)n (n = 1-10 and 30) clusters were studied by means of first principles calculations. The calculated results reveal that the global minima of small (Al2O3)n (n = 1-5) clusters are cage structures with high symmetries, in which Al and O atoms are three- and two-coordinated, respectively, and are linked to neighbors via single bonds. Beyond (Al2O3)5, we calculated both cage and cage-dimer structures for (Al2O3)n (n = 6-10), and the results show that, at this size range, cage-dimer structures are more stable than cage structures. Furthermore, an onion-like motif for (Al2O3)10 was studied, and it is interesting to find that, at this size, the onion structure is more favorable than cage and cage-dimer structures. For large clusters, a shell structure of Al60O90 is suggested. Electronic properties and calculations on hydrogen adsorption of these aluminum oxide structures are reported, and we discuss their possible use as hydrogen storage materials.     

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.     

Mid-infrared characterization of the NH4 +(H2O)n clusters in the neighborhood of the n=20 "magic" number

Vibrational predissociation spectra are reported for size-selected NH4+ (H2O)n clusters (n=5-22) in the 2500-3900 cm(-1) region. We concentrate on the sharp free OH stretching bands to deduce the local H-bonding configurations of water molecules on the cluster surface. As in the spectra of the protonated water clusters, the free OH bands in NH4+ (H2O)n evolve from a quartet at small sizes (n<7), to a doublet around n=9, and then to a single peak at the n=20 magic number cluster, before the doublet re-emerges at larger sizes. This spectral simplification at the magic number cluster mirrors that found earlier in the H+(H2O)n clusters. We characterize the likely structures at play for the n=19 and 20 clusters with electronic structure calculations. The most stable form of the n=20 cluster is predicted to have a surface-solvated NH4+ ion that lies considerably lower in energy than isomers with the NH4+ in the interior.     

Stabilization of fully reduced iron-sulfur clusters by carbene ligation: the [FenSn]0 oxidation levels (n = 4, 8)

The all-ferrous [Fe4S4](0) state has been demonstrated in the fully reduced Fe protein of the Azotobacter vinelandii nitrogenase complex. We seek synthetic analogues of this state more tractable than the recently prepared but highly unstable cluster [Fe4S4(CN)4](4-) (Scott, Berlinguette, Holm, and Zhou, Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 9741). The N-heterocyclic carbene 1,3-diisopropyl-4,5-dimethylimidazol-2-ylidene (Pr(i)2NHCMe2) has been found to stabilize the fully reduced clusters [Fe8S8(Pr(i)2NHCMe2)6] (4) and [Fe4S4(Pr(i)2NHCMe2)4] (5), which are prepared by cluster assembly or phosphine substitution of FenSn (n = 8, 16) clusters. Cluster 4 is also obtained by reaction of the carbene with all-ferrous [Fe7S6(PEt3)5Cl2] (3) and cluster 5 by carbene cleavage of 4. Detailed structures of 3 (monocapped prismatic), 4, and 5 are described; the latter two are the first iron-sulfur clusters with Fe-C sigma bonds. Cluster 4 possesses the [Fe8(mu3-S) 6(mu4-S)2] edge-bridged double cubane structure and 5 the cubane-type [Fe4(mu3-S)4] stereochemistry. The all-ferrous formulations of the clusters are confirmed by X-ray structure parameters and (57)Fe isomer shifts. Both clusters are stable under conventional aprotic anaerobic conditions, enabling further study of reactivity. The collective properties of 5 indicate that it is a meaningful synthetic analogue of the core of the fully reduced protein-bound cluster.     

Oxidation pattern of small silicon oxide clusters: structures and stability of Si6On (n = 1-12)

We have performed systematic ab initio calculations to study the structures and stability of Si(6)O(n)() clusters (n = 1-12) in order to understand the oxidation process in silicon systems. Our calculation results show that oxidation pattern of the small silicon cluster, with continuous addition of O atoms, extends from one side to the entire Si cluster. Si atoms are found to be separated from the pure Si cluster one-by-one by insertion of oxygen into the Si-O bonds. From fragmentation energy analyses, it is found that the Si-rich clusters usually dissociate into a smaller pure Si clusters (Si(5), Si(4), Si(3), or Si(2)), plus oxide fragments such as SiO, Si(2)O(2), Si(3)O(3), Si(3)O(4), and Si(4)O(5). We have also studied the structures of the ionic Si(6)O(n)(+/-) (n = 1-12) clusters and found that most of ionic clusters have different lowest-energy structures in comparison with the neutral clusters. Our calculation results suggest that transformation Si(6)O(n)+(a) + O --> Si(6)O(n+1)+(a) should be easier.     

Global optimization of ionic Mg(n)F(2n) (n=1-30) clusters

The global optimization basin-hopping (BH) method has been used to locate the global minima (GM) of Mg(n)F(2n) (n=1-30) clusters using a Born-Mayer-type potential. Some of the GM were particularly difficult to find, requiring more than 1.5 x 10(4) BH steps. We have found that both the binding energy per MgF2 unit and the effective volume of the GM isomers increase almost linearly with n, and that cluster symmetry decreases with cluster size. The data derived from the BH runs reveal a growing density of local minima just above the GM as n increases. Despite this, the attraction basin around each GM is relatively large, since after all their atomic coordinates are randomly displaced by values as high as 2.0 bohrs, the perturbed structures, upon reoptimization, relax back to the GM in more than 50% of the cases (except for n=10 and 11). The relative stabilities derived from energy second differences suggest that n=8,10,13,15, and 20 are probably the magic numbers for these systems. Mass spectrum experiments would be very useful to clarify this issue.     

Infrared spectra and ab initio calculations for the Cl--(CH4)n (n = 1-10) anion clusters

In an effort to elucidate their structures, mass-selected Cl--(CH4)n (n = 1-10) clusters are probed using infrared spectroscopy in the CH stretch region (2800-3100 cm(-1)). Accompanying ab initio calculations at the MP2/6-311++G(2df,2p) level for the n = 1-3 clusters suggest that methane molecules prefer to attach to the chloride anion by single linear H-bonds and sit adjacent to one another. These conclusions are supported by the agreement between experimental and calculated vibrational band frequencies and intensities. Infrared spectra in the CH stretch region for Cl--(CH4)n clusters containing up to ten CH4 ligands are remarkably simple, each being dominated by a single narrow peak associated with stretching motion of hydrogen-bonded CH groups. The observations are consistent with cluster structures in which at least ten equivalent methane molecules can be accommodated in the first solvation shell about a chloride anion.     

Synthesis and Characterization of Four Consecutive Members of the Five-Member [Fe(6)S(8)(PEt(3))(6)](n)()(+) (n = 0-4) Cluster Electron Transfer Series

The clusters [Fe(6)S(8)(PEt(3))(6)](+,2+) have been shown by other investigators to be formed by the reaction of [Fe(OH(2))(6)](2+) and H(2)S, to contain face-capped octahedral Fe(6)S(8) cores, and to be components of the five-membered electron transfer series [Fe(6)S(8)(PEt(3))(6)](n)()(+) (n = 0-4) estalished electrochemically. We have prepared two additional series members. Reaction of [Fe(6)S(8)(PEt(3))(6)](2+) with iodine in dichloromethane affords [Fe(6)S(8)(PEt(3))(6)](3+), isolated as the perchlorate salt (48%). Reduction of [Fe(6)S(8)(PEt(3))(6)](2+) with Na(Ph(2)CO) in acetonitrile/THF produces the neutral cluster [Fe(6)S(8)(PEt(3))(6)] (65%). The structures of the four clusters with n = 0, 1+, 2+, 3+ were determined at 223 K. The compounds [Fe(6)S(8)(PEt(3))(6)](ClO(4))(3), [Fe(6)S(8)(PEt(3))(6)] crystallize in trigonal space group R&thremacr;c with a = 21.691(4), 16.951(4) ?, c = 23.235(6), 19.369(4) ?, and Z = 6, 3. The compounds [Fe(6)S(8)(PEt(3))(6)](BF(4))(2), [Fe(6)S(8)(PEt(3))(6)](BF(4)).2MeCN were obtained in monoclinic space groups P2(1)/c, C2/c with a = 11.673(3), 16.371(4) ?, b = 20.810(5), 16.796(4) ?, c = 12.438(4), 23.617(7) ?, beta = 96.10(2), 97.98(2) degrees, and Z = 2, 4. [Fe(6)S(8)(PEt(3))(6)](BPh(4))(2) occurred in trigonal space group P&onemacr; with a = 11.792(4) ?, b = 14.350(5) ?, c = 15.536(6) ?, alpha = 115.33(3) degrees, beta = 90.34(3) degrees, gamma = 104.49(3) degrees, and Z = 1. Changes in metric features across the series are slight but indicate increasing population of antibonding Fe(6)S(8) core orbitals upon reduction. Zero-field M?ssbauer spectra are consistent with this result, isomer shifts increasing by ca. 0.05 mm/s for each electron added, and indicate a delocalized electronic structure. Magnetic susceptibility measurements together with previously reported results established the ground states S = (3)/(2) (3+), 3 (2+), (7)/(2) (1+), 3 (0). The clusters [Fe(6)S(8)(PEt(3))(6)](n)()(+) possess the structural and electronic features requisite to multisequential electron transfer reactions. This work provides the first example of a cluster type isolated over four consecutive oxidation states. Note is also made of the significance of the [Fe(6)S(8)(PEt(3))(6)](n)()(+) cluster type in the development of iron-sulfur-phosphine cluster chemistry.     

Rydberg states of small NaAr(n)* clusters

The 4s and 5s Rydberg excited states of NaAr(n)* clusters are investigated using a pseudopotential quantum-classical method. While NaAr(n) clusters in their ground state are known to be weakly bound van der Waals complexes with Na lying at the surface of the argon cluster, isomers in 4s or 5s electronically excited states of small NaAr(n)* clusters (n< or =10) are found to be stable versus dissociation. The relationship between electronic excitation and cluster geometry is analyzed as a function of cluster size. For both 4s and 5s states, the stable exciplex isomers essentially appear as sodium-centered structures with similar topologies, converging towards those of the related NaAr(n)+ positive ions when the excitation level is increased. This is consistent with a Rydberg-type picture for the electronically excited cluster, described by a central sodium ion solvated by an argon shell, and an outer diffuse electron orbiting around this NaAr(n)+ cluster core.     

Simulated annealing and density functional theory calculations of structural and energetic properties of the ammonium chloride clusters (NH4Cl)n, (NH4+)(NH4Cl)n, and (Cl-)(NH4Cl)n, n = 1-13

Simulated annealing Monte Carlo conformer searches using the "mag-walking" algorithm are employed to locate the global minima of molecular clusters of ammonium chloride of the types (NH(4)Cl)(n), (NH(4)(+))(NH(4)Cl)(n), and (Cl(-))(NH(4)Cl)(n) with n = 1-13. The M06-2X density functional theory method is used to refine and predict the structures, energies, and thermodynamic properties of the neutral, cation, and anion clusters. For selected small clusters, the resulting structures are compared to those obtained from a variety of models and basis sets, including RI-MP2 and B3LYP calculations. M06-2X calculations predict enhanced stability of the (NH(4)(+))(NH(4)Cl)(n) clusters when n = 3, 6, 8, and 13. This prediction corresponds favorably to anomalies previously observed in thermospray mass spectroscopy experiments. The (NH(4)Cl)(n) clusters show alternations in stability between even and odd values of n. Clusters of the type (Cl(-))(NH(4)Cl)(n) display a magic number distribution different from that of the cation clusters, with enhanced stability predicted for n = 2, 6, and 11. None of the observed cluster structures resemble the room-temperature CsCl structure of NH(4)Cl(s), which is consistent with previous work. Numerous clusters have structures reminiscent of the higher-temperature, rock-salt phase of the solid ammonium halides.     

Theoretical study of oxygen adsorption on pure Au(n+1)+ and doped MAu(n)+ cationic gold clusters for M = Ti, Fe and n = 3-7

A comparative study of the adsorption of an O2 molecule on pure Au(n+1)+ and doped MAu(n)+ cationic gold clusters for n = 3-7 and M = Ti, Fe is presented. The simultaneous adsorption of two oxygen atoms also was studied. This work was performed by means of first principles calculations based on norm-conserving pseudo-potentials and numerical basis sets. For pure Au4 +, Au6+, and Au7+ clusters, the O2 molecule is adsorbed preferably on top of low coordinated Au atoms, with an adsorption energy smaller than 0.5 eV. Instead, for Au5+ and Au8+, bridge adsorption sites are preferred with adsorption energies of 0.56 and 0.69 eV, respectively. The ground-state geometry of Au(n)+ is almost unperturbed after O2 adsorption. The electronic charge flows towards O2 when the molecule is adsorbed in bridge positions and towards the gold cluster when O2 is adsorbed on top of Au atoms, and both the adsorption energy and the O-O bond length of adsorbed oxygen increase when the amount of electronic charge on O2 increases. On the other hand, we studied the adsorption of an O2 molecule on doped MAu(n)+ clusters, leading to the formation of (MAu(n)O2+) ad complexes with different equilibrium configurations. The highest adsorption energy was obtained when both atoms of O2 bind on top of the M impurity, and it is larger for Ti doped clusters than for Fe doped clusters, showing an odd-even effect trend with size n, which is opposite for Ti as compared to Fe complexes. For those adsorption configurations of (MAu(n)O2+) ad involving only Au sites, the adsorption energy is similar to or smaller than that for similar configurations of Au(n)+1O2 + complexes. However, the highest adsorption energy of (MAu(n)O2+) ad is higher than that for (Au(n)+1O2+) ad by a factor of approximately 4.0 (1.2) for M = Ti (M = Fe). The trends with size n are rationalized in terms of O-O and O-M bond distances, as well as charge transfer between oxygen and cluster substrates. The spin multiplicity of those (MAu(n)O2+) ad complexes with the highest O2 adsorption energy is a maximum (minimum) for M = Fe (Ti), corresponding to parallel (anti-parallel) spin coupling of MAu(n)+ clusters and O2 molecules. Finally, we obtained the minimum energy equilibrium structure of complexes (Au(n)O2+) dis and (MAu(n)O2+) dis containing two separated O atoms bonded at different sites of Au(n)+ and MAu(n)+ clusters, respectively. For (MAu(n)O2 (+)) dis, the equilibrium configuration with the highest adsorption energy is stable against separation in MAu(n)+ and O2 fragments, respectively. Instead, for (Au(n)O2+) dis, only the complex n = 6 is stable against separation in Au(n)+ and O2 fragments. The maximum separation energy of (MAu(n)O2+) dis is higher than the O2 adsorption energy of (MAu(n)O2+) ad complexes by factors of approximately 1.6 (2.5), 1.6 (1.7), 1.5 (2.4), 1.5 (1.3), and 1.6 (1.8) for M = Ti (Fe) complexes in the range n = 3-7, respectively.     

Size- and shape-dependent polarizabilities of sandwich and rice-ball Co(n)Bz(m) clusters from density functional theory

The dipole polarizabilities of Co(n)Bz(m), (n, m = 1-4, m = n, n + 1) clusters are studied by means of an all-electron gradient-corrected density functional theory and finite field method. The dipole moments are relatively large for most of the clusters, implying their asymmetric structures. The total polarizability increases rapidly as cluster size, whereas the average polarizability shows "odd-even" oscillation with relatively large values at (n, n + 1). The polarizabilities exhibit clear shape-dependent variation, and the sandwich structures have systematically larger polarizability and anisotropy than the rice-ball isomers. The dipole polarizabilities are further analyzed in terms of the highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap, ionization potential, and electron delocalization volume. We conclude that the polarizability variations are determined by the interplay between the geometrical and electronic properties of the clusters.     

Density functional study of CO adsorption on Sc(n) (n=2-13) clusters

The adsorption properties of a single CO molecule on Sc(n) (n=2-13) clusters are studied by means of a density functional theory with the generalized gradient approximation. Two adsorption patterns are identified. Pattern a (n=3, 4, 6, 8, 11, and 12), CO binds to hollow site while Pattern b (n=5, 7, 9, 10, and 13), CO binds to bridge site accompanied by significantly lengthening of the Sc-Sc bond. The adsorption energy exhibits clear size-dependent variation and odd-even oscillation for n<10 and reach the peak at n=5, 7, and 9, implying their high chemical reactivity. Similar variations are noted in C-O bond length, vibrational frequency, and charge transferred between CO and the clusters. This can be understood in light of the adsorption pattern, the atomic motif, and the relative stability of the bare Sc clusters. Compared with the free Sc clusters, the magnetic nature remains upon adsorption except n=2, 4, 12, and 13. Particularly, the moments of n=13 reduce significantly from 19 to 5 micro(B), implying the adsorption plays an attenuation influence on the magnetism of the cluster.     

Dynamics and fragmentation of van der Waals clusters: (H2O)n, (CH3OH)n, and (NH3)n upon ionization by a 26.5 eV soft x-ray laser

A tabletop soft x-ray laser is applied for the first time as a high energy photon source for chemical dynamics experiments in the study of water, methanol, and ammonia clusters through time of flight mass spectroscopy. The 26.5 eV/photon laser (pulse time duration of approximately 1 ns) is employed as a single photon ionization source for the detection of these clusters. Only a small fraction of the photon energy is deposited in the cluster for metastable dissociation of cluster ions, and most of it is removed by the ejected electron. Protonated water, methanol, and ammonia clusters dominate the cluster mass spectra. Unprotonated ammonia clusters are observed in the protonated cluster ion size range 2< or =n< or =22. The unimolecular dissociation rate constants for reactions involving loss of one neutral molecule are calculated to be (0.6-2.7)x10(4), (3.6-6.0)x10(3), and (0.8-2.0)x10(4) s(-1) for the protonated water (9< or =n< or =24), methanol (5< or =n< or =10), and ammonia (5< or =n< or =18) clusters, respectively. The temperatures of the neutral clusters are estimated to be between 40 and 200 K for water clusters (10< or =n< or =21), and 50-100 K for methanol clusters (6< or =n< or =10). Products with losses of up to five H atoms are observed in the mass spectrum of the neutral ammonia dimer. Large ammonia clusters (NH(3))(n) (n>3) do not lose more than three H atoms in the photoionization/photodissociation process. For all three cluster systems studied, single photon ionization with a 26.5 eV photon yields near threshold ionization. The temperature of these three cluster systems increases with increasing cluster size over the above-indicated ranges.     

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.     

Density-functional study of small neutral and cationic bismuth clusters Bi(n) and Bi(n) (+)(n=2-24)

Density-functional theory with scalar-relativistic pseudopotential and a generalized gradient correction is used to calculate the neutral and cationic Bi(n) clusters (2< or =n< or =24), with the aim to elucidate their structural evolution, relative stability, and magnetic property. The structures of neutral Bi clusters are found to be similar to that of other group-V elemental clusters, with the extensively studied sizes of n=4 and 8 having a tetrahedron and wedgelike structure, respectively. Generally, larger Bi clusters consist of a combination of several stable units of Bi(4), Bi(6), and Bi(8), and they have a tendency to form an amorphous structure with the increase of cluster sizes. The curves of second order energy difference exhibit strong odd-even alternations for both neutral and cationic Bi clusters, indicating that even-atom (odd-atom) sizes are relatively stable in neutral clusters (cationic clusters). The calculated magnetic moments are 1micro (B) for odd-atom clusters and zero for even-atom clusters. We propose that the difference in magnetism between experiment and theory can be greatly improved by considering the orbital contribution. The calculated fragmentation behavior agrees well with the experiment, and for each cationic cluster the dissociation into Bi(4) or Bi(7) (+) subclusters confirms the special stability of Bi(4) and Bi(7) (+). Moreover, the bond orders and the gaps between the highest occupied molecular orbital and the lowest unoccupied molecular orbital show that small Bi clusters would prefer semiconductor characters to metallicity.     

Comparison of the growth patterns of Si(n) and Ge(n) clusters (n = 25-33)

We performed an unbiased search for low-energy structures of medium-sized neutral Si n and Ge n clusters ( n = 25-33) using a genetic algorithm (GA) coupled with tight-binding interatomic potentials. Structural candidates obtained from our GA search were further optimized by first-principles calculations using density functional theory (DFT). Our approach reproduces well the lowest-energy structures of Si n and Ge n clusters of n = 25-29 compared to previous studies, showing the accuracy and reliability of our approach. In the present study, we pay more attention to determine low-lying isomers of Si n and Ge n ( n = 29-33) and study the growth patterns of these clusters. The B3LYP calculations suggest that the growth pattern of Si n ( n = 25-33) clusters undergoes a transition from prolate to cage at n = 31, while this transition appears at n = 26 from the PBE-calculated results. In the size range of 25-33, the corresponding Ge n clusters hold the prolate growth pattern. The relative stabilities and different structural motifs of Si n and Ge n ( n = 25-33) clusters were studied, and the changes of small cluster structures, when acting as building blocks of large clusters, were also discussed.