A DFT study of Se n Te n clusters.

First principles calculations have been performed to study the characteristic properties of Se n Te n (n = 5-10) clusters. The present study reveals that the properties of these small clusters are consistent with the properties of Se-Te glassy systems. Several hundred equilibrium structures obtained from a genetic algorithm based USPEX code are relaxed to their minimum energy using the VASP code. Most of the lowest energy buckled ring-like structures are formed from Se-Te heteropolar bonds. Detailed structural analysis and distance energy plots unveil that many equilibrium structures are close in energy to their global minimum. The computed Raman and IR spectra show the dominance of Se-Te heteropolar bonds, consistent with earlier simulation and experimental findings in Se1-x Te x glass materials. Low frequency vibrational modes observed in small clusters are characteristic features of amorphous materials. Non-bonding orbitals (lone pair) are observed in the HOMO, whereas the LUMO is formed from purely antibonding orbitals. The dielectric functions corroborate the bonding mechanism and slightly polar nature of Se n Te n clusters. The energy loss and absorption coefficient indicate the presence of π-plasmons in the UV-visible region. Furthermore, it is ascertained that the use of a hybrid functional (B3LYP) does not affect the properties of small clusters appreciably, except causing a blue shift in the optical spectra. Hence, we find that the small clusters have bearing on the formation of glassy Se-Te systems.

Thermodynamic properties of Ga27Si3 cluster using density functional molecular dynamics.

Density functional molecular dynamical calculations have been carried out to explore the effect of silicon impurities on thermodynamic properties of Ga(30). We have obtained 500 distinct low energy equilibrium geometries of Ga(27)Si(3) in order to obtain reliable ground state geometry. The specific heat has been calculated using multiple histogram techniques and compared with that of Ga(30). We demonstrate that silicon impurities have a dramatic effect on the thermodynamic properties of the host cluster. In contrast to Ga(30), the specific heat of Ga(27)Si(3) shows a clear melting peak at ≈500 K, changing the character of Ga(30) from a nonmelter to a melter.

Growth and structural properties of Mg(N) (N = 10-56) clusters: density functional theory study.

Using the minima hopping global geometry optimization method on density functional potential energy surface, we have studied the structural and electronic properties of magnesium clusters for a size range of Mg(N) where N = 10-56. Our exhaustive search reveals that most of our global minima are nonsymmetric in the size range above N = 20. We elucidate the evolutionary trend of the entire series and present more details about the peculiar growth of the clusters. For N > 20, it is possible to divide the cluster into two regions: the core region and the surface region. It turns out that the growth follows a peculiar cyclic pattern where the core and surface grow alternatively. The surface energy, as a function of number of atoms shows a clear signature as the number of atoms in the core increases by one. We have also carried out stability analysis and the stable sizes(magic numbers) agree very well with the experimental magic numbers reported by Diederich [J. Chem. Phys. 2011, 134, 124302]. We point out the similarities and differences between our results and sodium clusters.

Density functional investigations on structural and electronic properties of anionic and neutral sodium clusters Na(N) (N = 40-147): comparison with the experimental photoelectron spectra.

Density functional calculations have been carried out to obtain low energy equilibrium geometries of anionic and neutral sodium clusters over a wide range of sizes 40 ≤ N ≤ 147, where N is the number of atoms. An exhaustive search for the low energy equilibrium geometries has been carried out. The density of states of the lowest energy geometries are compared with the experimental photoelectron spectra (Huber et al 2009 Phys. Rev. B 80 235425; Kostko et al 2007 Phys. Rev. Lett.98 043401) for N > 41. The agreement between theory and experiment is good for almost all the clusters and the changes in the spectrum with size correlate very well with the changes in the shapes as observed in the evolutionary trend of the ground state geometries.

Ferromagnetism in carbon-doped zinc oxide systems.

We report spin-polarized density functional calculations of ferromagnetic properties for a series of ZnO clusters and ZnO solid containing one or two substitutional carbon impurities. We analyze the eigenvalue spectra, spin densities, molecular orbitals, and induced magnetic moments for ZnC, Zn(2)C, Zn(2)OC, carbon-substituted Zn(n)O(n) (n = 3-10, 12) clusters and the bulk ZnO. The results show that the doping induces magnetic moment of approximately 2 mu(B) in all the cases. All systems with two carbon impurities show ferromagnetic interaction, except when carbon atoms share the same zinc atom as the nearest neighbor. This ferromagnetic interaction is predominantly mediated via pi-bonds in the ring structures and through pi- and sigma-bonds in the three-dimensional structure. The calculations also show that the interaction is significantly enhanced in the solid, bringing out the role of dimensionality of the Zn-O network connecting two carbon atoms.

A systematic study of electronic structure from graphene to graphane.

While graphene is a semi-metal, a recently synthesized hydrogenated graphene called graphane is an insulator. We have probed the transformation of graphene upon hydrogenation to graphane within the framework of density functional theory. By analysing the electronic structure for 18 different hydrogen concentrations, we bring out some novel features of this transition. Our results show that the hydrogenation favours clustered configurations leading to the formation of compact islands. The analysis of the charge density and electron localization function (ELF) indicates that, as hydrogen coverage increases, the semi-metal turns into a metal, showing a delocalized charge density, then transforms into an insulator. The metallic phase is spatially inhomogeneous in the sense it contains islands of insulating regions formed by hydrogenated carbon atoms and metallic channels formed by contiguous bare carbon atoms. It turns out that it is possible to pattern the graphene sheet to tune the electronic structure. For example, removal of hydrogen atoms along the diagonal of the unit cell, yielding an armchair pattern at the edge, gives rise to a bandgap of 1.4 eV. We also show that a weak ferromagnetic state exists even for a large hydrogen coverage whenever there is a sublattice imbalance in the presence of an odd number of hydrogen atoms.

Building clusters atom-by-atom: from local order to global order.

We have carried out extensive density functional calculations for series of sodium clusters NaN ranging from N = 10 to 147 and have obtained approximately 13000 distinct isomers. We unravel a number of striking features of the growth characteristics. The growth shows an order-disorder-order pattern of cyclic nature. Between two ordered clusters, the growth proceeds via disordered clusters having multicentered icosahedral local order. The global order emerges suddenly with the addition of one or two atoms only. The clusters around N = 92, the electronically closed shell system, behave completely differently and do not show the favored icosahedral local order. It is the absence of icosahedral local order that is responsible for the rather low melting temperatures observed in the experiments.

Enhanced magnetic moment in Fe-doped Pd(n) clusters (n = 1-13): a density functional study.

Here we report a systematic theoretical study of the equilibrium structures, electronic and magnetic properties of FePd(n-1) clusters with n = 1-13, within the framework of density functional theory. The results show that the doping of a single Fe impurity enhances the binding energies as well as the magnetic moment of the Pd(n) clusters. Interestingly, in the mid-size region (n = 5-7), Fe substitution in Pd(n) clusters results in a three fold enhancement in the magnetic moment. We find that the geometries of the host clusters do not change significantly after the addition of an Fe atom, except for n = 6, 7, 11, 12. In the lowest energy configurations, the Fe atom tries to increase its coordination number by moving from the convex to the interior site as the number of Pd atoms varies from 2 to 12.

Electronic and structural investigations of gold clusters doped with copper: Aun-1Cu- (n=13-19).

We have obtained the ground state and the equilibrium geometries of Au(n) (-) and Au(n-1)Cu(-) in the size range of n=13-19. We have used first principles density functional theory within plane wave and Gaussian basis set methods. For each of the cluster we have obtained at least 100 distinct isomers. The anions of gold clusters undergo two structural transformations, the first one from flat cage to hollow cage and the second one from hollow cage to pyramidal structure. The Cu doped clusters do not show any flat cage structures as the ground state. The copper doped systems evolve from a general 3D structure to hollow cage with Cu trapped inside the cage at n=16 and then to pyramidal structure at n=19. The introduction of copper atom enhances the binding energy per atom as compared to gold cluster anions.

Far-infrared absorption of water clusters by first-principles molecular dynamics.

Based on first-principle molecular dynamic simulations, we calculate the far-infrared spectra of small water clusters (H(2)O)(n) (n = 2, 4, 6) at frequencies below 1000 cm(-1) and at 80 K and at atmospheric temperature (T>200 K). We find that cluster size and temperature affect the spectra significantly. The effect of the cluster size is similar to the one reported for confined water. Temperature changes not only the shape of the spectra but also the total strength of the absorption, a consequence of the complete anharmonic nature of the classical dynamics at high temperature. In particular, we find that in the frequency region up to 320 cm(-1), the absorption strength per molecule of the water dimer at 220 K is significantly larger than that of bulk liquid water, while tetramer and hexamer show bulklike strengths. However, the absorption strength of the dimer throughout the far-infrared region is too small to explain the measured vapor absorption continuum, which must therefore be dominated by other mechanisms.

The effects of electronic structure and charged state on thermodynamic properties: an ab initio molecular dynamics investigations on neutral and charged clusters of Na(39), Na(40), and Na(41).

In this paper we explore the effects of the electronic structure, the charge state, and the nature of energy distribution of isomers on the thermodynamic properties of sodium clusters. The focus of the work is to isolate the effects of these ingredients on thermodynamic behavior by choosing specific clusters. Toward this end we investigate Na(39) (-), Na(40), and Na(41) (+), which are the electronic closed shell systems which differ in number of atoms and charge state. We also examine Na(39), Na(39) (+), Na(40) (+), and Na(41) clusters having different charges of these clusters. Our density functional molecular dynamics simulations show that all electronic shell-closing clusters have similar melting temperature of approximately 310 K. Remarkably, it is observed that an addition of even one electron to Na(39) increases the melting temperature by about 40 K and makes the specific heat curve sharper. All the cationic clusters show broadened specific heat curves.

Ab initio molecular dynamical investigation of the finite temperature behavior of the tetrahedral Au19 and Au20 clusters.

Density functional molecular dynamics simulations have been carried out to understand the finite temperature behavior of Au19 and Au20 clusters. Au20 has been reported to be a unique molecule having tetrahedral geometry, a large HOMO-LUMO energy gap, and an atomic packing similar to that of the bulk gold (Li, J.; et al. Science 2003, 299, 864). Our results show that the geometry of Au19 is exactly identical with that of Au20 with one missing corner atom (called a vacancy). Surprisingly, our calculated heat capacities for this nearly identical pair of gold clusters exhibit dramatic differences. Au20 undergoes a clear and distinct solid-like to liquid-like transition with a sharp peak in the heat capacity curve around 770 K. On the other hand, Au19 has a broad and flat heat capacity curve with continuous melting transition. This continuous melting transition turns out to be a consequence of a process involving a series of atomic rearrangements along the surface to fill in the missing corner atom. This results in a restricted diffusive motion of atoms along the surface of Au19 between 650 to 900 K during which the shape of the ground state geometry is retained. In contrast, the tetrahedral structure of Au20 is destroyed around 800 K, and the cluster is clearly in a liquid-like state above 1000 K. Thus, this work clearly demonstrates that (i) the gold clusters exhibit size sensitive variations in the heat capacity curves and (ii) the broad and continuous melting transition in a cluster, a feature that has so far been attributed to the disorder or absence of symmetry in the system, can also be a consequence of a defect (absence of a cap atom) in the structure.

Electronic structure of spherical quantum dots using coupled cluster method.

2, 6, 12, and 20 electron quantum dots have been studied using coupled cluster at singles and doubles level and extensive multireference coupled cluster (MRCC) method. A Fock-space version of MRCC (FSMRCC) containing single hole-particle excited determinants has been used to calculate low-lying excited states of the above system. The ionization potential and electron affinity are also calculated. The effect of correlation energy on excitation energy and charge density is shown by calculating them at the high density region (low value of density parameter rs) and at the low density region (high value of density parameter rs).

Density functional analysis of the structural evolution of Gan (n=30-55) clusters and its influence on the melting characteristics.

Recent experimental results have reported surprising variations in the shapes of the heat capacity curves and melting temperatures of gallium clusters in the size range of 30-55 atoms [G. A. Breaux et al., J. Am. Chem. Soc. 126, 8628 (2004)]. In the present work, we have carried out an extensive density functional investigation on ten selected clusters in the above mentioned size range. In particular, we have analyzed the ground state geometry and the nature of bonding in these clusters using electron localization function. We demonstrate that the existence or otherwise of a large island of atoms bonded with similar strength (i.e., the local order) in the ground state geometry is responsible for the variation in the shape of the heat capacity curve. We attribute the observed higher melting temperatures of some of the clusters (viz., Ga45-Ga48) to the presence of a distinct core and strong covalent bonds between the core and surface atoms. The present work clearly demonstrates that it is possible to understand the general trends observed in the heat capacity curves across the entire series on the basis of the analysis of their ground state.

Density functional investigation of the interaction of acetone with small gold clusters.

The structural evolution of Au(n) (n=2, 3, 5, 7, 9, and 13) clusters and the adsorption of organic molecules such as acetone, acetaldehyde, and diethyl ketone on these clusters are studied using a density functional method. The detailed study of the adsorption of acetone on the Au(n) clusters reveals two main points. (1) The acetone molecule interacts with one gold atom of the gold clusters via the carbonyl oxygen. (2) This interaction is mediated through back donation mainly from the spd-hybridized orbitals of the interacting gold atom to the oxygen atom of the acetone molecule. In addition, a hydrogen bond is observed between a hydrogen atom of the methyl group and another gold atom (not involved in the bonding with carbonyl oxygen). Interestingly, the authors notice that the geometries of Au(9) and Au(13) undergo a significant flattening due to the adsorption of an acetone molecule. They have also investigated the role of the alkyl chain attached to the carbonyl group in the adsorption process by analyzing the interaction of Au(13) with acetaldehyde and diethyl ketone.

"Magic melters" have geometrical origin.

Recent experimental reports bring out extreme size sensitivity in the heat capacities of gallium and aluminum clusters. In the present work we report results of our extensive ab initio molecular dynamical simulations on Ga30 and Ga31, the pair which has shown rather dramatic size sensitivity. We trace the origin of this size sensitive heat capacities to the relative order in their respective ground state geometries. Such an effect of nature of the ground state on the characteristics of heat capacity is also seen in case of small gallium and sodium clusters, indicating that the observed size sensitivity is a generic feature of small clusters.

Structural and electronic properties of neutral and ionic Ga(n)On clusters with n = 4-7.

We report the results of a theoretical study of neutral, anionic, and cationic Ga(n)On clusters (n = 4-7), focusing on their ground-state configurations, stability, and electronic properties. The structural motif of these small gallium oxide clusters appears to be a rhombus or a hexagonal ring with alternate gallium and oxygen atoms. With the increase in the cluster size from Ga4O4 to Ga7O7, the ground-state configurations show a transition from planar to quasi-planar to three-dimensional structure that maximizes the number of ionic metal-oxygen bonds in the cluster. The ionization-induced distortions in the ground state of the respective neutral clusters are small. However, the nature of the LUMO orbital of the neutral isomers is found to be a key factor in determining the ordering of the low-lying isomers of the corresponding anionic clusters. A sequential addition of a GaO unit to the GaO monomer initially increases the binding energy, though values of the ionization potential and the electron affinity do not show any systematic variation in these clusters.

First-principles investigation of finite-temperature behavior in small sodium clusters.

A systematic and detailed investigation of the finite-temperature behavior of small sodium clusters, Na(n), in the size range of n=8-50 are carried out. The simulations are performed using density-functional molecular dynamics with ultrasoft pseudopotentials. A number of thermodynamic indicators such as specific heat, caloric curve, root-mean-square bond-length fluctuation, deviation energy, etc., are calculated for each of the clusters. Size dependence of these indicators reveals several interesting features. The smallest clusters with n=8 and 10 do not show any signature of melting transition. With the increase in size, broad peak in the specific heat is developed, which alternately for larger clusters evolves into a sharper one, indicating a solidlike to liquidlike transition. The melting temperatures show an irregular pattern similar to the experimentally observed one for larger clusters [Schmidt et al., Nature (London) 393, 238 (1998)]. The present calculations also reveal a remarkable size-sensitive effect in the size range of n=40-55. While Na(40) and Na(55) show well-developed peaks in the specific-heat curve, Na(50) cluster exhibits a rather broad peak, indicating a poorly defined melting transition. Such a feature has been experimentally observed for gallium and aluminum clusters [Breaux et al., J. Am. Chem. Soc. 126, 8628 (2004); Breaux et al., Phys. Rev. Lett. 94, 173401 (2005)].

Why do gallium clusters have a higher melting point than the bulk?

Density functional molecular dynamical simulations have been performed on Ga17 and Ga13 clusters to understand the recently observed higher-than-bulk melting temperatures in small gallium clusters [Phys. Rev. Lett. 91, 215508 (2003)]]. The specific-heat curve, calculated with the multiple-histogram technique, shows the melting temperature to be well above the bulk melting point of 303 K, viz., around 650 and 1400 K for Ga17 and Ga13, respectively. The higher-than-bulk melting temperatures are attributed mainly to the covalent bonding in these clusters, in contrast with the covalent-metallic bonding in the bulk.