Origin of the size-dependence of the polarizability per atom in heterogeneous clusters: The case of AlP clusters

An analysis of the atomic polarizabilities α in stoichiometric aluminum phosphide clusters, computed at the MP2 and density functional theory (DFT) levels, the latter using the B3LYP functional, and partitioned using the classic and iterative versions of the Hirshfeld method, is presented. Two sets of clusters are examined: the ground-state Al(n)P(n) clusters (n=2-9) and the prolate clusters (Al(2)P(2))(N) and (Al(3)P(3))(N) (N≤6). In the ground-state clusters, the mean polarizability per atom, i.e., α/2n, decreases with the cluster size but shows peaks at n=5 and at n=7. We demonstrate that these peaks can be explained by a large polarizability of the Al atoms and by a low polarizability of the P atoms in Al(5)P(5) and Al(7)P(7) due to the presence of homopolar bonds in these clusters. We show indeed that the polarizability of an atom within an Al(n)P(n) cluster depends on the cluster size and the heteropolarity of the bonds it forms within the cluster, i.e., on the charges of the atoms. The polarizabilities of the fragments Al(2)P(2) and Al(3)P(3) in the prolate clusters were found to depend mainly on their location within the cluster. Finally, we show that the iterative Hirshfeld method is more suitable than the classic Hirshfeld method for describing the atomic polarizabilities and the atomic charges in clusters with heteropolar bonds, although both versions of the Hirshfeld method lead to similar conclusions.     

The structural and electronic properties of Ag-adsorbed (SiO2)n (n=1-7) clusters

Equilibrium geometries, charge distributions, stabilities, and electronic properties of the Ag-adsorbed (SiO(2))(n) (n=1-7) clusters have been investigated using density functional theory with generalized gradient approximation for exchange-correlation functional. The results show that the Ag atom preferably binds to silicon atom with dangling bond in nearly a fixed direction, and the incoming Ag atoms tend to cluster on the existing Ag cluster leading to the formation of Ag islands. The adsorbed Ag atom only causes charge redistributions of the atoms near itself. The effect of the adsorbed Ag atom on the bonding natures and structural features of the silica clusters is minor, attributing to the tendency of stability order of Ag(SiO(2))(n) (n=1-7) clusters in consistent with silica clusters. In addition, the energy gaps between the highest occupied and lowest unoccupied molecular orbitals remarkably decrease compared with the pure (SiO(2))(n) (n=1-7) clusters, eventually approaching the near infrared radiation region. This suggests that these small clusters may be an alternative material which has a similar functionality in treating cancer to the large gold-coated silica nanoshells and the small Au(3)(SiO(2))(3) cluster.     

Cluster size selectivity in the product distribution of ethene dehydrogenation on niobium clusters

Ethene reactions with niobium atoms and clusters containing up to 25 constituent atoms have been studied in a fast-flow metal cluster reactor. The clusters react with ethene at about the gas-kinetic collision rate, indicating a barrierless association process as the cluster removal step. Exceptions are Nb8 and Nb10, for which a significantly diminished rate is observed, reflecting some cluster size selectivity. Analysis of the experimental primary product masses indicates dehydrogenation of ethene for all clusters save Nb10, yielding either Nb(n)C2H2 or Nb(n)C2. Over the range Nb-Nb6, the extent of dehydrogenation increases with cluster size, then decreases for larger clusters. For many clusters, secondary and tertiary product masses are also observed, showing varying degrees of dehydrogenation corresponding to net addition of C2H4, C2H2, or C2. With Nb atoms and several small clusters, formal addition of at least six ethene molecules is observed, suggesting a polymerization process may be active. Kinetic analysis of the Nb atom and several Nb(n) cluster reactions with ethene shows that the process is consistent with sequential addition of ethene units at rates corresponding approximately to the gas-kinetic collision frequency for several consecutive reacting ethene molecules. Some variation in the rate of ethene pick up is found, which likely reflects small energy barriers or steric constraints associated with individual mechanistic steps. Density functional calculations of structures of Nb clusters up to Nb(6), and the reaction products Nb(n)C2H2 and Nb(n)C2 (n = 1...6) are presented. Investigation of the thermochemistry for the dehydrogenation of ethene to form molecular hydrogen, for the Nb atom and clusters up to Nb6, demonstrates that the exergonicity of the formation of Nb(n)C2 species increases with cluster size over this range, which supports the proposal that the extent of dehydrogenation is determined primarily by thermodynamic constraints. Analysis of the structural variations present in the cluster species studied shows an increase in C-H bond lengths with cluster size that closely correlates with the increased thermodynamic drive to full dehydrogenation. This correlation strongly suggests that all steps in the reaction are barrierless, and that weakening of the C-H bonds is directly reflected in the thermodynamics of the overall dehydrogenation process. It is also demonstrated that reaction exergonicity in the initial partial dehydrogenation step must be carried through as excess internal energy into the second dehydrogenation step.     

Binding energies of small lithium clusters (Li(n)) and hydrogenated lithium clusters (Li(n)H)

Large coupled cluster computations utilizing the Dunning weighted correlation-consistent polarized core-valence (cc-pwCVXZ) hierarchy of basis sets have been conducted, resulting in a panoply of internally consistent geometries and atomization energies for small Li(n) and Li(n)H (n=1-4) clusters. In contrast to previous ab initio results, we predict a monotonic increase in atomization energies per atom with increasing cluster size for lithium clusters, in accordance with the historical Knudsen-effusion measurements of Wu. For hydrogenated lithium clusters, our results support previous theoretical work concerning the relatively low atomization energy per atom for Li(2)H compared to LiH and Li(3)H. The CCSD(T)/cc-pwCVQZ atomization energies for LiH, Li(2)H, Li(3)H, and the most stable isomer of Li(4)H, including zero-point energy corrections, are 55.7, 79.6, 113.0, and 130.6 kcal/mol, respectively. The latter results are not consistent with the most recent experiments of Wu.     

Structures and energetics of hydrated oxygen anion clusters

Hydration of the atomic oxygen radical anion is studied with computational electronic structure methods, considering (O(-))(H(2)O)(n) clusters and related proton-transferred (OH(-))(OH)(H(2)O)(n)(-)(1) clusters having n = 1-5. A total of 67 distinct local-minimum structures having various interesting hydrogen bonding motifs are obtained and analyzed. On the basis of the most stable form of each type, (O(-))(H(2)O)(n)) clusters are energetically favored, although for n > or = 3, there is considerable overlap in energy between other members of the (O(-))(H(2)O)(n) family and various members of the (OH(-))(OH)(H(2)O)(n)(-)(1) family. In the lower-energy (O(-))(H(2)O)(n) clusters, the hydrogen bonding arrangement about the oxygen anion center tends to be planar, leaving the oxygen anion p-like orbital containing the unpaired electron uninvolved in hydrogen bonding with any water molecule. In (OH(-))(OH)(H(2)O)(n)(-)(1) clusters, on the other hand, nonplanar arrangements are the rule about the anionic oxygen center that accepts hydrogen bonds. No instances are found of OH(-) acting as a hydrogen bond donor. Those OH bonds that form hydrogen bonds to an anionic O(-) or OH(-) center are significantly stretched from their equilibrium value in isolated water or hydroxyl. A quantitative inverse correlation is established for all hydrogen bonds between the amount of the OH bond stretch and the distance to the other oxygen involved in the hydrogen bond.     

Negative ion clusters in self-condensation of GeH4.

Formation of negative ion clusters from GeH4 has been studied as a function of germane pressure, in the 25-450 mTorr range, by chemical ionisation mass spectrometry. At the lowest pressures, only the GeHn- (n = 0-3) ion family is formed, whilst at increasing pressures GemHn- (m = 1-9) ion clusters of increasing size are observed in the mass spectra. A variable contribution of the ions with different hydrogen content is observed as a function of the pressure of germane in all the GemHn- (m = 1-9) clusters. Increasing pressures induce a general increase of ion species with a low content of hydrogen atoms. In fact, at 450 mTorr, 38% of the ion current is due to the bare Gem- (m = 2-5) clusters and 83% to the sum of abundances of the GemHn- ions without hydrogen (n = 0) and with a number of hydrogen atoms not higher than the number of germanium atoms (n = 0-m). This trend suggests that a contribution of negative clusters to the deposition of the amorphous solid a-Ge:H from gaseous systems containing GeH4, activated by radiolytic methods, can enhance the formation of solids with a low hydrogen content, which show better photoelectrical properties.     

The structural and electronic properties of In(n)N(n = 1-13) clusters

The structural and electronic properties of In(n)N(n=1-13) clusters have been investigated by density-functional theory with the generalized gradient approximation. The results indicate that the equilibrium structures of In(n)N are linear for n=1,2, planar for n=3-5, and three dimensional for n=6-13. Maximum peaks were observed for In(n)N clusters at n=3,7,9 on the size dependence for second-order energy difference. These imply that these clusters possess relatively higher stability, which is consistent with the case of binding energy per atom. Moreover, the results show that the bonding in small In(n)N clusters has a little ionic character by Mulliken population analysis. The energy gap between the highest occupied and lowest unoccupied molecular orbitals, the vertical ionization potential and electron vertical affinity (VIP and VEA) form an even-odd alternating pattern with increasing cluster size. In general, the VIP tends to lower as the cluster size increases, while the VEA tends to increase as the cluster size increases.     

Single photon ionization of van der Waals clusters with a soft x-ray laser: (CO2)n and (CO2)n(H2O)m

Pure neutral (CO2)n clusters and mixed (CO2)n(H2O)m clusters are investigated employing time of flight mass spectroscopy and single photon ionization at 26.5 eV. The distribution of pure (CO2)n clusters decreases roughly exponentially with increasing cluster size. During the ionization process, neutral clusters suffer little fragmentation because almost all excess cluster energy above the vertical ionization energy is taken away by the photoelectron and only a small part of the photon energy is deposited into the (CO2)n cluster. Metastable dissociation rate constants of (CO2)n+ are measured in the range of (0.2-1.5) x 10(4) s(-1) for cluster sizes of 5< or =n< or =16. Mixed CO2-H2O clusters are studied under different generation conditions (5% and 20% CO2 partial pressures and high and low expansion pressures). At high CO2 concentration, predominant signals in the mass spectrum are the (CO2)n+ cluster ions. The unprotonated cluster ion series (CO2)nH2O+ and (CO2)n(H2O)2+ are also observed under these conditions. At low CO2 concentration, protonated cluster ions (H2O)nH+ are the dominant signals, and the protonated CO2(H2O)nH+ and unprotonated (H2O)n+ and (CO2)(H2O)n+ cluster ion series are also observed. The mechanisms and dynamics of the formation of these neutral and ionic clusters are discussed.     

Comparison of hydrated hydroperoxide anion (HOO-)(H2O)n clusters with alkaline hydrogen peroxide (HOOH)(OH-)(H2O)(n-1) clusters, n = 1-8, 20: an ab initio study

Hydroperoxide anion (HOO(-)), the conjugate base of hydrogen peroxide (HOOH), has been relatively little studied despite the importance of HOOH in commercial processes, atmospheric science, and biology. The anion has been shown to exist as a stable species in alkaline water. This project explored the structure of gas phase (HOO(-))(H(2)O)(n) clusters and identified the lowest energy configurations for n ≤ 8 at the B3LYP/6-311++G** level of theory and for n ≤ 6 at the MP2/aug-cc-pVTZ level of theory. As a start toward understanding equilibration between HOO(-) and HOOH in an alkaline environment, (HOOH)(OH(-))(H(2)O)(n-1) clusters were likewise examined, and the lowest energy configurations were determined for n ≤ 8 (B3LYP/6-311++G**) and n ≤ 6 (MP2/aug-cc-pVTZ). Some studies were also done for n = 20. The two species have very different solvation behaviors. In low energy (HOOH)(OH(-))(H(2)O)(n-1) clusters, HOOH sits on the surface of the cluster, is 4-coordinated (each O is donor once and acceptor once), and donates to the hydroxide ion. In contrast, in low energy (HOO(-))(H(2)O)(n) clusters, (HOO(-)) takes a position in the cluster center surrounded on all sides by water molecules, and its optimum coordination number appears to be 7 (one O is donor-acceptor-acceptor while the other is a 4-fold acceptor). For n ≤ 6 the lowest (HOOH)(OH(-))(H(2)O)(n-1) cluster lies 1.0-2.1 kcal/mol below the lowest (HOO(-))(H(2)O)(n) cluster, but the lowest clusters found for n = 20 favor (HOO(-))(H(2)O)(20). The results suggest that ambient water could act as a substantial kinetic brake that slows equilibration between (HOOH)(OH(-)) and (HOO(-))(H(2)O) because extensive rearrangement of solvation shells is necessary to restabilize either species after proton transfer.     

Enhancement of a Lewis acid-base interaction via solvation: ammonia molecules and the benzene radical cation

The interaction between ammonia and the benzene radical cation has been investigated by gas-phase studies of mass selected ion clusters {C(6)H(6)-(NH(3))(n=0-8)}(+) via tandem quadrupole mass spectrometry and through calculations. Experiments show a special stability for the cluster ion that contains four ammonias: {C(6)H(6)(NH(3))(4)}(+). Calculations provide evidence that the first ammonia forms a weak dative bond to the cyclohexadienyl radical cation, {C(6)H(6)-NH(3)}(+), where there is a transfer of electrons from ammonia to benzene. Additional solvating ammonia molecules form stabilizing hydrogen bonds to the ring-bound ammonia {C(6)H(6)-NH(3)}(+).(NH(3))(n), which cause cooperative changes in the structure of the cluster complex. Free ammonia is a weak hydrogen bond donor, but electron transfer from NH(3) to the benzene ring that strengthens the dative bond will increase the hydrogen acidity and the strength of the cluster hydrogen bonds to the added ammonia. A progressive "tightening" of this dative bond is observed upon addition of the first, second, and third ammonia to give a cluster stabilized by three N-(+)H x N hydrogen bonds. This shows that the energetic cost of tightening the dative bond is recovered with dividends in the formation of stable cluster hydrogen bonds.     

The effect of alloying on the H-atom adsorption on the (100) surfaces of Pd-Ag,Pd-Pt,Pd-Au,Pt-Ag,and Pt-Au. A theoretical study

The effect of alloying on the adsorption of atomic hydrogen was studied using density functional theory (DFT). In the study the (100) surfaces of Pd-Ag, Pd-Pt, Pd-Au, Pt-Ag, and Pt-Au alloys were considered by means of a cluster model. The structural and energetic properties of the H atom adsorbed on the Pd₄Me (Me = Ag, Pt, Au) and Pt₄Me (Me = Pd, Ag, Au) clusters were calculated and compared with the H-atom adsorption on monometallic clusters. The effect of alloying on the H-atom adsorption is evident for all the investigated bimetallic systems. However, it strongly depends on the second metal atom, Me, is placed in the surface layer or in the subsurface one. In general, the H atom adsorbed in a site containing the second metal exhibits different properties from those characteristic of its adsorption on Pd(100) and Pt(100). Hence, the modified interaction between atomic hydrogen and the alloyed surfaces may increase the selectivity of the catalytic hydrogenation reactions on such surfaces.     

Grotthus-type and diffusive proton transfer in 7-hydroxyquinoline.(NH(3))(n) clusters.

Proton translocation along ammonia wires is investigated in 7-hydroxyquinoline.(NH(3))(n) clusters, both experimentally by laser spectroscopy and theoretically by Hartree-Fock and density functional (DFT) calculations. These clusters serve as realistic finite-size models for proton transfer along a chain of hydrogen-bonded solvent molecules. In the enol tautomer of 7-hydroxyquinoline (7-HQ), the OH group acts as a proton injection site into the (NH(3))(n)cluster. Proton translocation along a chain of three NH(3) molecules within the cluster can take place, followed by reprotonation of 7-HQ at the quinolinic N atom, forming the 7-ketoquinoline tautomer. Exoergic proton transfer from the OH group of 7-HQ to the closest NH(3) molecule within the cluster giving a zwitterion 7-HQ-.(NH(3))(6)H+ (denoted PT-A) occurs at a threshold cluster size of n = 6 in the DFT calculations and at n = 5 or 6 experimentally. Three further locally stable zwitterion clusters denoted PT-B, PT-B', and PT-C, the keto tautomer, and several transition structures along the proton translocation path were characterized theoretically. Grotthus-type proton-hopping mechanisms occur for three of the proton transfer steps, which have low barriers and are exoergic or weakly endoergic. The step with the highest barrier involves a complex proton transfer mechanism, involving structural reorganization and large-scale diffusive motions of the cluster.     

Magic number silicon dioxide-based clusters: laser ablation-mass spectrometric and density functional theory studies

The magic number silica clusters [(SiO(2))(n)O(2)H(3)](-) with n = 4 and 8 have been observed in the XeCl excimer laser (308 nm) ablation of various porous siliceous materials. The structural origin of the magic number clusters has been studied by the density functional theoretical calculation at the B3LYP/6-31G** level, with a genetic algorithm as a supplementary tool for global structure searching. The DFT results of the first magic number cluster are parallel to the corresponding Hartree-Fock results previously reported with only small differences in the structural parameters. Theoretical calculation predicts that the first magic number cluster (SiO(2))(4)O(2)H(4) and its anion [(SiO(2))(4)O(2)H(3)](-) will most probably take pseudotetrahedral cage-like structures. To study the structural properties of the second magic number cluster, geometries of the bare cluster (SiO(2))(8), the neutral complex cluster (SiO(2))(8)O(2)H(4), and the anionic cluster [(SiO(2))(8)O(2)H(3)](-) are fully optimized at the B3LYP/6-31G** level, and the corresponding vibrational frequencies are calculated. The DFT calculations predict that the ground state of the bare silica octamer (SiO(2))(8) has a linear chain structure, whereas the second magic number complex cluster (SiO(2))(8)O(2)H(4) and its anion [(SiO(2))(8)O(2)H(3)](-) are most probably a mixture of cubic cage-like structural isomers with an O atom inside the cage and several quasi-bicage isomers with high intercage interactions. The stabilization of these structures can also be attributed to the active participation of the group of atoms 2O and 4H (3H for the anion) in chemical bonding during cluster formation. Our theoretical calculation gives preliminary structural interpretation of the presence of the first and second magic number clusters and the absence of higher magic numbers.     

Theoretical study on the small clusters of LiH, NaH, BeH(2), and MgH(2)

High-level ab initio molecular orbital theory is used to calculate the geometries, vibrational frequencies, atomic charges, and binding energies of the small clusters (LiH)(n), (NaH)(n), (BeH(2))(n), and (MgH(2))(n) (n = 1-4). For (LiH)(n) and (NaH)(n), there are planar cyclic structures when n = 2, 3. We have found the cubic structure T(d) in addition to the planar cyclic D(4)(h) when n = 4. The D(4)(h) is less stable than the T(d) geometry. For (BeH(2))(n) and (MgH(2))(n), when n = 3, there are three kinds of structures: chain C(2)(v), planar cyclic D(3)(h), and hat-like C(2)(v). The C(2)(v) geometry is more stable than the others. When n = 4, there are four kinds of structures: chain D(2)(h), cubic T(d), string-like C(2), and cubic transformation C(1). The most stable compounds in the families of (LiH)(n), (NaH)(n), (BeH(2))(n), and (MgH(2))(n) are cubic T(d), cubic T(d), chain D(2)(h), and string-like C(2) geometries, respectively, when n = 4. Calculated binding energies range from -24 to -37 kcal/mol for (LiH)(n) and --19 to -30 kcal/mol for (NaH)(n), (BeH(2))(n), and (MgH(2))(n). The hydrogen atoms in hydride clusters always have negative charges. The atomic charges of planar cyclic structures are weaker than those of cubic structures, and there is a tendency of reducing along with the increase of the cluster size. The vibrational frequencies of planar cyclic structures have consistent tendency, too. It indicates that the bond distance increases with the ionic character of the bond.     

Hydrogen dissociative chemisorption and desorption on saturated subnano palladium clusters (Pdn, n = 2-9)

H(2) sequential dissociative chemisorption on small palladium clusters was studied using density functional theory. The chosen clusters Pd(n) (n = 2-9) are of the lowest energy structures for each n. H(2) dissociative chemisorption and subsequent H atom migration on the bare Pd clusters were found to be nearly barrierless. The dissociative chemisorption energy of H(2) and the desorption energy of H atom in general decrease with the coverage of H atoms and thus the catalytic efficiency decreases as the H loading increases. These energies at full cluster saturation were identified and found to vary in small energy ranges regardless of cluster size. As H loading increases, the clusters gradually change their bonding from metallic character to covalent character. For the selected Pd clusters, the capacity to adsorb H atoms increases almost proportionally with cluster size; however, it was found that the capacity of Pd clusters to adsorb H atoms is, on average, substantially smaller than that of small Pt clusters, suggesting that the catalytic efficiency of Pt nanoparticles is superior to Pd nanoparticles in catalyzing dissociative chemisorption of H(2) molecules.     

Single photon ionization of van der Waals clusters with a soft x-ray laser: (SO2)n and (SO2)n(H2O)m

van der Waals cluster (SO2)n is investigated by using single photon ionization of a 26.5 eV soft x-ray laser. During the ionization process, neutral clusters suffer a small fragmentation because almost all energy is taken away by the photoelectron and a small part of the photon energy is deposited into the (SO2)n cluster. The distribution of (SO2)n clusters decreases roughly exponentially with increasing cluster size. The photoionization dissociation fraction of I[(SO2)(n-1)SO+] / I[(SO2)n+] decreases with increasing cluster size due to the formation of cluster. The metastable dissociation rate constants of (SO2)n+ are measured in the range of (0.6-1.5) x 10(4) s(-1) for cluster sizes 5< or =n< or =16. Mixed SO2-H2O clusters are studied at different experimental conditions. At the condition of high SO2 concentration (20% SO2 partial pressure), (SO2)n+ cluster ions dominate the mass spectrum, and the unprotonated mixed cluster ions (SO2)nH2O+ (1< or =n< or =5) are observed. At the condition of low SO2 concentration (5% SO2 partial pressure) (H2O)nH+ cluster ions are the dominant signals, and protonated cluster ions (SO2)(H2O)nH+ are observed. The mixed clusters, containing only one SO2 or H2O molecule, SO2(H2O)nH+ and (SO2)nH2O+ are observed, respectively.     

A theoretical study on structural, spectroscopic and energetic properties of acetamide clusters [CH3CONH2] (n=1-15)

Insights into the formation of hydrogen bonded clusters are of outstanding importance and quantum chemical calculations play a pivotal role in achieving this understanding. Structure and energetic comparison of linear, circular and standard forms of (acetamide)(n) clusters (n = 1-15) at the B3LYP/D95** level of theory including empirical dispersion correction reveals significant cooperativity of hydrogen bonding and size dependent structural preference. A substantial amount of impact of BSSE is observed in these calculations as the cluster size increases irrespective of the kind of arrangement. The interaction energy per monomer increases from dimer to 15mer by 90% in the case of the circular arrangement, by 76% in the case of the linear arrangement and by 34% in the case of the standard arrangement respectively. The cooperativity in hydrogen bonding is also manifested by a regular decrease in average OH and C-N bond distances, while average C=O and N-H bond lengths increase with increasing cluster size. Atoms-In-Molecules (AIM) analysis is used to characterize the nature of hydrogen bonding between the acetamide molecules in the cluster on the basis of electron density (ρ) values obtained at the bond critical point. An analysis of N-H bond stretching frequencies as a function of the cluster size shows a marked red shift as the cluster size increases from 1 to 15.     

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.     

Structural evolution and stability of hydrogenated Li(n) (n = 1-30) clusters: a density functional study

The structure and electronic and optical properties of hydrogenated lithium clusters Li(n)H(m) (n = 1-30, m ≤ n) have been investigated by density functional theory (DFT). The structural optimizations are performed with the Becke 3 Lee-Yang-Parr (B3LYP) exchange-correlation functional with 6-311G++(d, p) basis set. The reliability of the method employed has been established by excellent agreement with computational and experimental data, wherever available. The turn over from two- to three-dimensional geometry in Li(n)H(m) clusters is found to occur at size n = 4 and m = 3. Interestingly, a rock-salt-like face-centered cubic structure is seen in Li(13)H(14). The sequential addition of hydrogen to small-sized Li clusters predicted regions of regular lattice in saturated hydrogenated clusters. This led us to focus on large-sized saturated clusters rather than to increase the number of hydrogen atoms monotonically. The lattice constants of Li(9)H(9), Li(18)H(18), Li(20)H(20), and Li(30)H(30) calculated at their optimized geometry are found to gradually approach the corresponding bulk values of 4.083. The sequential addition of hydrogen stabilizes the cluster, irrespective of the cluster size. A significant increase in stability is seen in the case of completely hydrogenated clusters, i.e., when the number of hydrogen atoms equals Li atoms. The enhanced stability has been interpreted in terms of various electronic and optical properties like adiabatic and vertical ionization potential, HOMO-LUMO gap, and polarizability.     

Molecular-dynamics simulation of the structural stability,energetics, and melting of Cu n(n = 13–135) clusters

Cluster properties of copper have been investigated using the Molecular-Dynamics md technique. The structural stability and energetics of spherical Cu_n (n = 13–135) clusters have been investigated at temperatures T = 1 K and T = 300 K. It has been found that the average interaction energy per atom in the cluster decreases and reaches an asymptotic value as cluster size increases. The melting behaviour of clusters n = 13 and n = 55 have been investigated. It has been found that the melting temperature decreases as cluster size increases, and for clusters with multishell structures melting starts from the outermost shell. In the simulation an emprical potential energy function (PEF) proposed by Erkoç has been used, which contains two-body atomic interactions.