Session N27: Focus Session: Computational Nanoscience IV - Nanoparticles

Evolution of Magnetism from Atoms to Crystals

The existence of spontaneous magnetization in metallic systems is an intriguing problem because of the extensive technological applications of magnetic phenomena and an incomplete theory of its fundamental mechanisms. Clusters of metallic atoms are important in this respect as they serve as a bridge between the atomic limit and the bulk, and they can form a basis for understanding the emergence of magnetization as a function of size. In solids, ferromagnetism is understood in terms of the exchange interaction and the formation of distinct energy bands for the majority spin and minority spin channels. In clusters, energy bands are replaced with dellocalized electronic orbitals, whose properties are affected by the finite size and the presence of a surface. Therefore, the size and shape of a cluster play important role in its magnetic properties. Indeed, direct measurements have indicated a strong dependence of magnetic moment with the size of the cluster, especially in iron clusters but also nickel and cobalt. Taking advantage of recent developments in computational methods for the electronic structure of nanosystems, we can now investigate in greater detail the magnetic properties of metallic clusters containing several hundreds of atoms and understand the role of size and shape. This analysis is based on first-principles density-functional theory, within the generalized gradient approximation. Numerical calculations were done in clusters containing up to 400 atoms (iron, nickel, and cobalt). Calculations are done using the PARSEC code ( www.ices.utexas.edu/parsec ). We also discuss some of the recently developed capabilities of PARSEC.   

Electronic and structural properties of binary Pt-Ni nanoclusters

The lowest energy structures of binary (PtNi$_{3})_{n}$, (Pt$_{3}$Ni)$_{n}$, and (PtNi)$_{m}$ nanoclusters, with n=3-10 and m=3-20, modeled by the many-body Gupta potential, were obtained by using a genetic-symbiotic algorithm. These structures were further relaxed with DFT-GGA. In agreement with the experimental evidence, segregation is observed in these clusters, where the Ni atoms are mainly found in the cluster core and the Pt atoms on the cluster surface. Furthermore, it has been experimentally found that the (Pt$_{3}$Ni)$_{n}$ nanoalloys present a higher catalytic activity for the N$_{2}$O + H$_{2}$ reaction at low temperatures than the other compositions [1], while the contrary trend is observed in the case of the oxidation of carbon monoxide in the presence of hydrogen, where the (PtNi$_{3})_{n}$ nanoparticles present a higher catalytic activity than the other ones. In order to understand these tendencies in the catalytic activity, we performed an analysis of the surface electronic structure of the bimetallic Pt-Ni nanoclusters with the mentioned compositions, by means of first-principles density functional calculations. Acknowledgments: This work was supported by CONACyT No. 43414-F. [1] Arenas-Alatorre J, Avalos-Borja M, Diaz G J. Phys. Chem. B \textbf{109}, 2371 (2005).   

First principles studies of the geometric and electronic structure of nanoalloy Ag$_{27}$Cu$_{7}$.

We present first-principles calculations of the structure and electronic density of states (DOS) for the perfect core-shell Ag$_{27}$Cu$_{7}$ nanocluster. Our results show an expansion of 0.4 A in the \textit{diameter} of the cluster compared with previous results$^{\ast }$. From the projected DOS we conclude that the 34-atom cluster has only 2 non-equivalent Cu atoms (core) and 4 non-equivalent Ag atoms (shell), confirming that this finite-size structure has D$_{5}$h symmetry. The HOMO-LUMO gap is found to be 0.77 eV, in agreement with previous results$^{\ast }$. Comparing with Ag bulk, the valence band centroid of Ag$_{27}$Cu$_{7}$ presents shift of $\sim $1.0 eV towards the Fermi energy, but a 0.5 eV shift away from it, compared with Cu bulk. The total DOS of the structure as a whole does not present valence band narrowing when compared to the bulk of either species. Individual Ag atoms show band narrowing, a positive centroid shift to lower binding energies, and a very small enhancement of the DOS at the top of the band. Electronic states of Cu atoms are greatly concentrated in two sharp peaks in the top region of their valence band. In the bottom of the band, however, copper and silver atoms hybridize in spite of their short d-wavefunctions. Charge density plots give some insight about the hybridization of electronic states between atoms. $^{ \ast }$G. Rossi et al. Phys. Rev. Lett. \textbf{93,} 105503 (2004).   

Bond Stiffening in Small Clusters, and its Consequences

We have used density functional theory and density functional perturbation theory to compute the interatomic force constant tensors for small clusters of Si, Sn and Pb; these results have important implications for the size dependence of the elastic and thermal properties of nanosized objects. We find a clear sequence of relationships: as the size of the cluster is decreased, bonds get shorter and stiffer and vibrational frequencies higher; however the behaviour relative to the bulk depends on the coordination number of the latter. Though all the clusters we have studied are softer than the corresponding bulk, vibrational amplitudes may be enhanced or damped relative to the bulk values, and vary non-monotonically with size. Scaling relations connect results for varying sizes and different elements. These results also provide a framework for understanding recent results showing that, surprisingly, some clusters have melting temperatures that are much higher than that of the corresponding bulk material.   

Structural Properties of Small Pd Clusters

The properties of small Pd clusters ($2\leq N \leq 21$) are computed by means of the most common phenomenological many body potentials, and also by {\it ab initio} methods. The lowest energy configuration is found by means of an unbiased search using computational space annealing (CSA). Satisfactory agreement between the results of the several methods implemented is achieved. Of special interest is the fact that different phenomenological potentials yield the same symmetry group for the lowest energy cluster geometries. Moreover, they are in general compatible with {\it ab initio} results both of our own and other already published data.   

Efficient method to calculate total energies of large nanoclusters

We present a computationally efficient method to calculate total energies of very large nanoclusters based on first principles electronic structure techniques. The total energy of a cluster with well-defined facets can be separated into surface, edge, and corner energies, each a function of the chemical potentials, in addition to bulk contributions. Using density functional calculations we have verified that this separation describes the total energies of fcc $Cu$ and zincblende $CdSe$ polyhedral clusters with up to $256$ atoms. The calculated energies are then used to estimate the shapes of stable structures for large polyhedral nanoclusters. For sufficiently large clusters, only the surface and bulk terms survive. This method has been shown to be applicable to stoichiometric as well as non-stoichiometric clusters, containing polar or non-polar surfaces, and we are in the process of calculating the energies of various surfaces using total energy and energy density methods in order to predict equilibrium shapes of clusters as a function of size and chemical potentials.   

First principles study of coulombic correlation effect on lithium doped zinc oxide nanocrystals

We examine the role of quantum confinement for impurities in zinc oxide nanocrystals. The electronic gap between the highest occupied level and the lowest unoccupied level for these systems will be larger than the band gap of bulk ZnO crystal owing to quantum confinement. We also expect quantum confinement to enhance correlation effects from on-site coulombic interactions, which will occur for lithium doped zinc oxide nanocrystals. We investigate the ionization energy for lithium impurities in ZnO nanocrystals and characterize the properties of the impurity levels. We assess the validity of arguments from recent experimental studies in which lithium impurities are expected to form shallow donors and acceptors in ZnO. We use a real-space ab initio pseudopotential method to obtain the ground state properties of an isolated nanocrystal. We use a rotationally invariant ``LDA+U'' scheme to model the on-site coulombic interaction of the zinc d-levels. The Hubbard U potential is rescaled for each nanocrystal using the static dielectric constant to reflect the reduced screening in a nanocrystal.   

Excitonic effects and optical properties of passivated CdSe clusters

We calculate the optical properties of a series of passivated non-stoichiometric CdSe clusters using two first-principles approaches: time-dependent density functional theory within the local density approximation, and many-body methods, based on computing the self-energy in the GW approximation and solving the Bethe-Salpeter equation for optical excitations. We analyze the character of optical excitations leading to the first low-energy peak in the absorption cross-section of these clusters. Within time-dependent density functional theory, we find that the lowest-energy excitation is mostly a single-level to single-level transition. In contrast, many-body methods predict a strong mixture of several different transitions, which is a signature of excitonic effects. We also find that the majority of the clusters have a series of dark transitions before the first bright transition. This may explain the long radiative lifetimes observed experimentally for these clusters. Reference: PRL 97, 096401 (2006).   

Structure and Dynamics of Silicon Carbide Clusters: A Tight-Binding Adaptive Monte Carlo Application

A tight-binding parametrization for silicon carbide nanoclusters was developed based on the electronic energy surface of small clusters calculated within the generalized gradient approximation of density functional theory. This parametrization includes s and p angular momentum symmetries and parameters for the on-site, hopping and overlap matrix elements. With the aid of these new parameters, the global minima of silicon carbide clusters in the range of 10-30 atoms were discovered with the adaptive Monte Carlo Method [1]. The ATMC optimization process is fast and drives the system across configuration space very effectively reaching the global minimum in a small number of tempering events. Growth sequence, stability patterns, and temperature behavior were also obtained. [1] X. Dong and E. Blaisten-Barojas, J. of Comp. {\&} Theor. Nanoscience, 3, 118-127 (2006).   

First-principles studies of isomerization processes of silicon clusters

Nanoclusters typically exhibit a large number of isomers, often with strikingly different structural and electronic properties. Controlled growth and use of these ultrasmall particles depends, therefore, on an understanding of the atomic-scale details of inter-isomer conversions. Here we use first-principles calculations to study the isomerization kinetics of silicon clusters. Based on the results on activation energies, we infer a classification scheme for the complex phase of isomers in domains which are delineated by bond-breaking events at the outer cluster shells. Our findings are consistent with experimental measurements and they have implications for theoretical searches of low-energy cluster structures. We also present results on hydrogenation and oxidation kinetics and we discuss their relevance for pristine and functionalized silicon clusters. This work was supported in part by DOE Grant DEFG0203ER46096.   

Investigation of the structure and properties of vacancies in Si and Ge nano-crystals by \textit{ab initio} methods

The production of nano-scale devices requires the ability to selectively dope nano-structures either n-type or p-type. The functionality of such devices demands that the dopant species remains in the nano-structure, and not diffuse into neighboring regions or to surfaces. The diffusivity of impurities in a crystal depends explicitly upon the self-diffusion of the host species. Understanding this requires understanding the modes of self-diffusion, and the mobility of intrinsic defects in the host crystal. Here we investigate the structure and properties of vacancies in Si and Ge nano-crystals. Using a real space pseudopotential method we study the energy of vacancies within 2 nm diameter crystals. It is observed that vacancies are naturally pulled toward the surfaces; however, in highly symmetric crystals, it is possible to trap vacancies in the center of the crystal. Once a vacancy is within 0.4 nm of the surface a bucking effect occurs, which indicates that a surface reaction will probably act to pull the vacancy to the surface.   

Self-purification in semiconductor nanostructures

Doping semiconductors is an important process in order to develop functional devices with them. This suggests that, when dealing with semiconductor nanostructures, they should also be doped in order to broaden their possible applications. Experimentally this shows to be a very difficult task. ``Self-purification'' mechanisms are often claimed to make this task even more difficult, as the distance a defect or impurity must move to reach the surface of a nanocrystal is very small. Kinetic effects like this are usually invoked in order to explain this difficulty. Here we show that self-purification can be explained through energetic arguments and is an intrinsic property of defects in semiconductor nanocrystals. We find the formation energies of defects increases as the size of the nanocrystal decreases. This is due to the pinning of the impurity levels as the size of the nanocrystal decreases and experimental evidences support our argumentation. We analyze the case of Mn-doped CdSe nanocrystals and compare our results to experimental findings, proposing ways to improve their dopability.