Force field for copper clusters and nanoparticles

An atomic force field for simulating copper clusters and nanoparticles is developed. More than 2000 cluster configurations of varying size and shape are used to constrain the parametrization of the copper force field. Binding energies for these training clusters were computed using density functional theory. Extensive testing shows that the copper force field is fast and reliable for near‐equilibrium structures of clusters, ranging from only a few atoms to large nanoparticles that approach bulk structure. Nonequilibrium dissociation and compression structures that are included in the training set are also well described by the force field. Implications for molecular dynamics simulations and extensions to other metallic and covalent systems are discussed. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Force fields for metallic clusters and nanoparticles

Atomic force fields for simulating copper, silver, and gold clusters and nanoparticles are developed. Potential energy functions are obtained for both monatomic and binary metallic systems using an embedded atom method. Many cluster configurations of varying size and shape are used to constrain the parametrization for each system. Binding energies for these training clusters were computed using density functional theory (DFT) with the Perdew-Wang exchange-correlation functional in the generalized gradients approximation. Extensive testing shows that the many-body potentials are able to reproduce the DFT energies for most of the structures that were included in the training set. The force fields were used to calculate surface energies, bulk structures, and thermodynamic properties. The results are in good agreement with the DFT values and consistent with the available experimental data.     

Modeling the sorption dynamics of NaH using a reactive force field

We have parametrized a reactive force field for NaH, ReaxFF(NaH), against a training set of ab initio derived data. To ascertain that ReaxFF(NaH) is properly parametrized, a comparison between ab initio heats of formation of small representative NaH clusters with ReaxFF(NaH) was done. The results and trend of ReaxFF(NaH) are found to be consistent with ab initio values. Further validation includes comparing the equations of state of condensed phases of Na and NaH as calculated from ab initio and ReaxFF(NaH). There is a good match between the two results, showing that ReaxFF(NaH) is correctly parametrized by the ab initio training set. ReaxFF(NaH) has been used to study the dynamics of hydrogen desorption in NaH particles. We find that ReaxFF(NaH) properly describes the surface molecular hydrogen charge transfer during the abstraction process. Results on heat of desorption versus cluster size shows that there is a strong dependence on the heat of desorption on the particle size, which implies that nanostructuring enhances desorption process. To gain more insight into the structural transformations of NaH during thermal decomposition, we performed a heating run in a molecular dynamics simulation. These runs exhibit a series of drops in potential energy, associated with cluster fragmentation and desorption of molecular hydrogen. This is consistent with experimental evidence that NaH dissociates at its melting point into smaller fragments.     

Tight binding molecular dynamics studies of GamAsn and AlmAsn clusters

The parametrized tight binding molecular dynamics method is used to study the structures and properties of small GaAs and AlAs clusters. Relative stabilities and ground state properties of GaAs clusters consisting of up to 4 atoms agree with those obtained in previous studies. Similar properties are found for small AlAs clusters. The present study of microclusters of both GaAs and AlAs revealed that the icosahedral structure is unstable for the binary clusters. Stability of such clusters increases monatomically as a function of As to Ga or As to Al ratio.     

Electronic structure and magnetic properties of small manganese oxide clusters

To investigate the electronic structure and magnetic properties of manganese oxide clusters, we carried out first-principles electronic structure calculations for small MnO clusters. Among various structural and magnetic configurations of the clusters, the bulklike [111]-antiferromagnetic ordering is found to be favored energetically, while the surface atoms of the clusters exhibit interesting electronic and magnetic characteristics which are different from their bulk ones. The distinct features of the surface atoms are mainly attributed to the reduction of Mn coordination numbers and the bond-length contractions in the clusters, which may serve as a key factor for the understanding of physical and chemical properties of magnetic oxide nanoparticles.     

Structure,stability, and vibrational properties of small silver cluster

The ground state geometries and binding energies of small silver clusters were found using Density Functional Theory (DFT) methods. We have compared various non local corrections for exchange and correlation energies, with or without treating explicitely all the electrons. The transferability of standard effective core potentials (ECP) is good, as far as their core size is small enough. From these results, and after comparison with ab initio CI one electron- ECP calculations, we have concluded to the ability of describing small silver clusters as one-electron systems. Thus, we have parametrized our distance-dependent tight- binding hamiltonian (DDTB), previously applied to alkali clusters. The geometries and energies provided by the model are very close to those found in ab initio calculations when available, that is, up to Ag₉. We have also computed the harmonic frequencies of small silver clusters.     

Semiempirical self-consistent polarization description of bulk water, the liquid-vapor interface, and cubic ice

We have applied an efficient electronic structure approach, the semiempirical self-consistent polarization neglect of diatomic differential overlap (SCP-NDDO) method, previously parametrized to reproduce properties of water clusters by Chang, Schenter, and Garrett [ J. Chem. Phys. 2008 , 128 , 164111 ] and now implemented in the CP2K package, to model ambient liquid water at 300 K (both the bulk and the liquid-vapor interface) and cubic ice at 15 and 250 K. The SCP-NDDO potential retains its transferability and good performance across the full range of conditions encountered in the clusters and the bulk phases of water. In particular, we obtain good results for the density, radial distribution functions, enthalpy of vaporization, self-diffusion coefficient, molecular dipole moment distribution, and hydrogen bond populations, in comparison to experimental measurements.     

Moderately and strongly supercooled liquids: a temperature-derivative study of the primary relaxation time scale

The primary relaxation time scale tau(T) derived from the glass forming supercooled liquids (SCLs) is discussed within ergodic-cluster Gaussian statistics, theoretically justified near and above the glass-transformation temperature T(g). An analysis is given for the temperature-derivative data by Stickel et al. on the steepness and the curvature of tau(T). Near the mode-coupling-theory (MCT) crossover T(c), these derivatives separate by a kink and a jump, respectively, the moderately and strongly SCL states. After accounting for the kink and the jump, the steepness remains a piecewise conitnuous function, a material-independent equation for the three fundamental characteristic temperatures, T(g), T(c), and the Vogel-Fulcher-Tamman (VFT) T(0), is found. Both states are described within the heterostructured model of solidlike clusters parametrized in a self-consistent manner by a minimum set of observable parameters: the fragility index, the MCT slowing-down exponent, and the chemical excess potential of Adam and Gibbs model (AGM). Below the Arrhenius temperature, the dynamically and thermodynamically stabilized clusters emerge with a size of around of seven to nine and two to three molecules above and close to T(g) and T(c), respectively. On cooling, the main transformation of the moderately into the strongly supercooled state is due to rebuilding of the cluster structure, and is attributed to its rigidity, introduced through the cluster compressibility. It is shown that the validity of the dynamic AGM (dynamically equivalent to the standard VFT form) is limited by the strongly supercooled state (T(g) < T < T(c)) where the superrigid cooperative rearranging regions are shown to be well-chosen parametrized solidlike clusters. Extension of the basic parameter set by the observable kinetic and diffusive exponents results in prediction of a subdiffusion relaxation regime in SCLs that is distinct from that established for amorphous polymers.     

Constitution and Properties of Nanocomposites Prepared by Thermal Decomposition of Silver Salts Sorbed by Polyacrylate Matrix

Constitution and dispersity of the products of thermal decomposition of silver nitrate ammonia complex sorbed by polyacrylate matrix are studied by the methods of small- and wide-angle X-ray scattering, optical, photoelectron and Auger-electron spectroscopies. It is shown that, at temperatures of 140–150°C, the complete decomposition of the complex occurs with the formation of nanoparticles and charged silver clusters in polymer bulk. No initial or intermediate products were observed. The average size of obtained nanoparticles is equal to 5 nm. The particles with the size less than 5 nm are amorphous according to X-ray data. The stabilization of nanoparticles occurs due to the adsorption of acrylic copolymer (presumably, via oxygen atoms) on their surfaces. Upon long-term storage in air, the self-diffusion of silver particles and clusters takes place from the surface to composite bulk caused by the detachment of oxygen-containing groups occurring at the metal–polymer interface.     

Thermodynamic equilibrium compositions, structures, and reaction energies of Pt(x)O(y) (x = 1-3) clusters predicted from first principles

As synthetic nanocatalysis strives to create and apply well-defined catalytic centers containing as few as a handful of active metal atoms, it becomes particularly important to understand the structures, compositions, and reactivity of small metal clusters as a function of size and chemical environment. As a part of our effort to better understand the oxidation chemistry of Pt clusters, we present here a comprehensive set of density functional theory simulations combined with thermodynamic modeling that allow us to map out the T-p(O)2 phase diagrams and predict the oxygen affinity of Pt(x)O(y) clusters, x = 1-3. We find that the Pt clusters have a much stronger tendency to form oxides than does the bulk metal, that these oxides persist over a wide range of oxygen chemical potentials, and that the most stable cluster stoichiometry varies with size and may differ from the stoichiometry of the stable bulk oxide in the same environment. Further, the facility with which the clusters are reduced depends both on size and on composition. These models provide a systematic framework for understanding the compositions and energies of redox reactions of discrete metal clusters of interest in supported and gas-phase nanocatalysis.     

多体展开势能函数在碳族元素原子簇研究中的应用III. 锗原子族的结构和相对稳定性

基于从晶体锗确立的多体展开势能函数, 本文通过坐标完全优化, 发现小的锗原子簇分子(Ge~2~Ge~14)倾向于形成密堆积结构, 表面原子分布以蝶形四元环(D~2d)为主; 常见立方晶体“微观晶体碎片”的分层优化结果表明, 在Ge~15~Ge~100范围内, 多数壳层的原子到分子中心的距离均受到压缩, 且以畸变的简单立方、面心立方及体心立方较为稳定; 在这些畸变密堆积结构中, 表面原子向内压缩最为严重, 使整个分子趋于球形化。较为开放的金刚石类层状原子族只有当所含原子数达数百以上时才可能相对更为稳定。     

Effect of grafting on nanoparticle segregation in polymer/nanoparticle blends near a substrate

Nanoparticles in polymer films have shown the tendency to migrate to the substrate due to an entropic-based attractive depletion interaction between the particles and the substrate. It is also known that polymer-grafted nanoparticles show better dispersion in a polymer matrix. Here, molecular dynamics simulations are employed to study the effect of grafting on the nanoparticle segregation to the substrate. The nanoparticles were modeled as spheres and the polymers as bead-spring chains. The polymers of the grafts and the matrix are identical in nature. For a purely repulsive system, the nanoparticle density near the surface was found to decrease as the length of grafted chains and the number of grafts increased and in the bulk, the nanoparticles are well-dispersed. Whereas, in case of attractive systems with interparticle interactions on the order of thermal energy, the nanoparticles segregated to the substrate even more strongly, essentially forming clusters on the wall and in the bulk. However, due to the presence of grafted chains on the nanoparticles, the clusters formed in the bulk are structurally anisotropic. The effect of grafts on nanoparticle segregation to the surface was found to be qualitatively similar to the purely repulsive case.     

锡原子簇的结构和相对稳定性

基于从固体锡确立的多体展开势能函数, 采用座标直接优化方法预测了锡原子簇分子(Sn_2-Sn_(300))的结构和相对稳定性, 并用蒙特卡罗方法验证了有关小的原子簇(Sn_2-Sn_(15))的所有结果. 优化结果表明: (1)小的锡原子簇分子(Sn_2-Sn_(15))倾向于密堆积结构, 与锡晶体结构无关; (2)中等大小的簇分子, 如Sn_(47), Sn_(71), Sn_(87)及Sn_(147)等, 则呈α-Sn晶体的畸变结构, 其外围各层原子到中心原子的距离受到压缩, 且某些层被劈裂为两层或多层; (3)随着原子簇尺寸的进一步增大, 结构畸变逐渐减弱, 簇分子的单原子平均结合能缓慢增大, 其外椎值大约在Sn_(740)处趋近于α-Sn的结合能.     

Simulation of ab initio results for palladium and rhodium clusters by tight‐binding calculations*

The study of metal clusters is nowadays a very active field of research using both experimental and theoretical techniques. Regular trends as well as unexpected behaviors have been observed regarding size‐dependent properties such as ionization potentials and atomization energies. Palladium and rhodium clusters of small size have been extensively studied at various semiempirical and ab initio levels of the theory, but the achievement and the interpretation of these calculations are generally difficult to be performed because of the incomplete shell structure of transition metal clusters. So we have tried to mimic the most important conclusions of the ab initio results available for Pd and Rh clusters by means of tight‐binding calculations, in the original Wolfsberg–Helmholz form, with appropriate parametrized repulsion terms. The occupation numbers of the one‐electron energy levels have been determined by taking into account some predictions of the graph theory. This enables us to study the variation of the atomization energies per atom for these clusters and to derive a bond‐energy systematics for Pd–Pd, Rh–Rh, and Pd–Rh linked atoms. Magic clusters with 13 atoms are considered. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 26–33, 2001     

Structural and electric field effects of ions in aqueous nanodrops

Ensemble infrared photodissociation (IRPD) spectra in the hydrogen stretch region (～2950-3800 cm(-1)) are reported for M(H(2)O)(35-37), with M = I(-), Cl(-), HCO(3)(-), OH(-), tetrabutyl-, tetrapropyl-, and tetramethylammonium, Cs(+), Na(+), Li(+), H(+), Ba(2+), Ca(2+), Co(2+), Mg(2+), La(3+), and Tm(3+), at 133 K. A single, broad feature is observed in the bonded-OH region of the spectra that indicates that the water network in these clusters is bulk-like and likely resembles liquid water more strongly than ice. The free-OH region for all of these clusters is dominated by peaks corresponding to water molecules that accept two and donate one hydrogen bond (AAD water molecules), indicating that AAD water molecules are more abundant at the surface of these ions than AD water molecules. A-only water molecules are present in significant abundance only for the trivalent metal cations. The frequency of the AAD free-OH stretch band shifts nearly linearly with the charge state of the ion, consistent with a Stark shift attributable to the ion's electric field. From these data, a frequency range of 3704.9-3709.7 cm(-1) is extrapolated for the free-OH of AAD water molecules at the (uncharged) bulk liquid water surface, consistent with sum-frequency generation spectroscopy experiments. Differences in both the bonded- and the free-OH regions of the spectra for these ions are attributable to ion-induced patterning of the water network that extends to the surface of the clusters, which includes water molecules in the third and fourth solvation shells; that is, these ions pattern water molecules at long distance to various extents. These spectra are simulated using two different electrostatic models previously used to calculate OH-stretch spectra of bulk water and aqueous solutions and parametrized for bonded-OH frequencies. These models qualitatively reproduce a number of features in the experimental spectra, although it is evident that more sophisticated treatment of water molecule and ion polarizability and vibrational coupling is necessary for more quantitative comparisons.     

ReaxFF(MgH) reactive force field for magnesium hydride systems

We have developed a reactive force field (ReaxFF(MgH)) for magnesium and magnesium hydride systems. The parameters for this force field were derived from fitting to quantum chemical (QM) data on magnesium clusters and on the equations of states for condensed phases of magnesium metal and magnesium hydride crystal. The force field reproduces the QM-derived cell parameters, density, and the equations of state for various pure Mg and MgH(2) crystal phases as well as and bond dissociation, angle bending, charge distribution, and reaction energy data for small magnesium hydride clusters. To demonstrate one application of ReaxFF(MgH), we have carried out MD simulations on the hydrogen absorption/desorption process in magnesium hydrides, focusing particularly on the size effect of MgH(2) nanoparticles on H(2) desorption kinetics. Our results show a clear relationship between grain size and heat of formation of MgH(2); as the particle size decreases, the heat of formation increases. Between 0.6 and 2.0 nm, the heat of formation ranges from -16 to -19 kcal/Mg and diverges toward that of the bulk value (-20.00 kcal/Mg) as the particle diameter increases beyond 2 nm. Therefore, it is not surprising to find that Mg nanoparticles formed by ball milling (20-100 nm) do not exhibit any significant change in thermochemical properties.     

A pseudoatom approach to molecular truncation: application in ab initio MBPT methods

In this paper, we test the performance of the molecular truncation method of Mallik et al., which was originally applied at the semiempirical NDDO level, in ab initio MBPT methods. Pseudoatoms developed for the replacement of -OCH(3) and -OCH(2)CH(3) functional groups are used in optimizations of selected clusters, and the resulting geometries are compared to reference values taken from the full molecules. It is shown that the pseudoatoms, which consist of parametrized effective core potentials for the nearest neighbor interactions and an external charge field for long-range Coulomb effects, perform well at the MP2 and CCSD levels of theory for the suite of molecules to which they were applied. Representative timings for some of the pseudoatom-terminated clusters are presented, and it is seen that there is a significant reduction in computational time, yet the geometric configurations and deprotonation energies of the pseudoatom-terminated clusters are comparable to the more computationally expensive all-atom molecules.     

Dynamical mean-field theory for molecules and nanostructures

Dynamical mean-field theory (DMFT) has established itself as a reliable and well-controlled approximation to study correlation effects in bulk solids and also two-dimensional systems. In combination with standard density-functional theory (DFT), it has been successfully applied to study materials in which localized electronic states play an important role. It was recently shown that this approach can also be successfully applied to study correlation effects in nanostructures. Here, we provide some details on our recently proposed DFT+DMFT approach to study the magnetic properties of nanosystems [V. Turkowski, A. Kabir, N. Nayyar, and T. S. Rahman, J. Phys.: Condens. Matter 22, 462202 (2010)] and apply it to examine the magnetic properties of small FePt clusters. We demonstrate that DMFT produces meaningful results even for such small systems. For benchmarking and better comparison with results obtained using DFT+U, we also include the case of small Fe clusters. As in the case of bulk systems, the latter approach tends to overestimate correlation effects in nanostructures. Finally, we discuss possible ways to further improve the nano-DFT+DMFT approximation and to extend its application to molecules and nanoparticles on substrates and to nonequilibrium phenomena.     

Comparison between selenium and tellurium clusters

Selenium and tellurium clusters are produced by the inert gas condensation technique. The mass spectra of both species are completely different and reveal different properties. In selenium, a periodicity of 6–7 is observed and may be interpreted by the binding energy between small cyclic molecules. Moreover, it was very difficult to obtained large clusters probably because the binding energy between these molecules is very small. In tellurium, these periodic structures do not exist and large clusters are easily obtained in nucleation conditions where only small selenium clusters are present. These results are discussed and a simple nucleation model is used to illustrate this different behavior. Finally these clusters properties are correlated to the bulk structure of both materials.     

Origin of bulklike structure and bond length disorder of Pt37 and Pt6Ru31 clusters on carbon: comparison of theory and experiment

We describe a theoretical analysis of the structures of self-organizing nanoparticles formed by Pt and Ru-Pt on carbon support. The calculations provide insights into the nature of these metal particle systems-ones of current interest for use as the electrocatalytic materials of direct oxidation fuel cells-and clarify complex behaviors noted in earlier experimental studies. With clusters deposited via metallo-organic Pt or PtRu(5) complexes, previous experiments [Nashner et al. J. Am. Chem. Soc. 1997, 119, 7760; Nashner et al. J. Am. Chem. Soc. 1998, 120, 8093; Frenkel et al. J. Phys. Chem. B 2001, 105, 12689] showed that the Pt and Pt-Ru based clusters are formed with fcc(111)-stacked cuboctahedral geometry and essentially bulklike metal-metal bond lengths, even for the smallest (few atom) nanoparticles for which the average coordination number is much smaller than that in the bulk, and that Pt in bimetallic [PtRu(5)] clusters segregates to the ambient surface of the supported nanoparticles. We explain these observations and characterize the cluster structures and bond length distributions using density functional theory calculations with graphite as a model for the support. The present study reveals the origin of the observed metal-metal bond length disorder, distinctively different for each system, and demonstrates the profound consequences that result from the cluster/carbon-support interactions and their key role in the structure and electronic properties of supported metallic nanoparticles.