Real space pseudopotential calculations for copper clusters

Neutral and anion clusters of copper, Cu(n) (n=3-11), are examined using real space pseudopotentials constructed within the local spin density approximation. We predict the ground state structure for each cluster, the binding energy, and the corresponding photoelectron spectra, which we compare to experiment. We find strong final state effects in the photoelectron spectra, especially for the smaller clusters. The binding energy as a function of cluster size tracks well with the measured values, although the magnitude of the binding energy exceeds the experimental values by approximately 20%, as expected for the local spin density approximation.     

Ab initio SCF molecular dynamics: Exploring the potential energy surface of small silicon clusters

A few classical nuclear trajectories at finite temperature have been calculated from ab initio SCF energy gradients. They have been used as an alternative means to search for local minimum energy structures on the Born–Oppenheimer surfaces for some elemental silicon clusters. The approach is found to be beneficial in yielding different structures of silicon clusters. In other cases, the trajectories stay trapped in only one region of the phase space.     

Density functional calculation of transition metal cluster energy surfaces

A quantum field mechanics of an electron subsystem in 3D physical space as the topology of compact atomic clusters with spontaneously broken local canonical symmetry is used for investigation of different types of microdefects in the condensed state of transition metals. The theory is illustrated with results of calculation of small compact Fe_n clusters (n = 2, 6, 14).     

A dynamic lattice searching method for fast optimization of Lennard-Jones clusters

A highly efficient unbiased global optimization method called dynamic lattice searching (DLS) was proposed. The method starts with a randomly generated local minimum, and finds better solution by a circulation of construction and searching of the dynamic lattice (DL) until the better solution approaches the best solution. The DL is constructed adaptively based on the starting local minimum by searching the possible location sites for an added atom, and the DL searching is implemented by iteratively moving the atom located at the occupied lattice site with the highest energy to the vacant lattice site with the lowest energy. Because the DL can greatly reduce the searching space and the number of the time-consuming local minimization procedures, the proposed DLS method runs at a very high efficiency, especially for the clusters of larger size. The performance of the DLS is investigated in the optimization of Lennard-Jones (LJ) clusters up to 309 atoms, and the structure of the LJ(500) is also predicted. Furthermore, the idea of dynamic lattice can be easily adopted in the optimization of other molecular or atomic clusters. It may be a promising approach to be universally used for structural optimizations in the chemistry field.     

Spatial localization and dynamics of water molecules with good tetrahedral surroundings

The local structure of the molecular- dynamic model of water (729 particles at 300 K) is analyzed by isolating molecules whose surroundings differ slightly in configuration from a regular tetrahedron. These molecules are not randomly distributed in space but form nanometer clusters having a fractal structure. In these clusters, molecules are less mobile than the model molecules in general;their self- correlation function of rate and the density of vibrational states also differ from the average characteristics of the system. Translated fromZhumal Strukturnoi Khimii, Vol. 38, No. 4, pp. 713–722, July–August, 1997.     

Combining smart darting with parallel tempering using Eckart space: application to Lennard-Jones clusters

The smart-darting algorithm is a Monte Carlo based simulation method used to overcome quasiergodicity problems associated with disconnected regions of configurations space separated by high energy barriers. As originally implemented, the smart-darting method works well for clusters at low temperatures with the angular momentum restricted to zero and where there are no transitions to permutational isomers. If the rotational motion of the clusters is unrestricted or if permutational isomerization becomes important, the acceptance probability of darting moves in the original implementation of the method becomes vanishingly small. In this work the smart-darting algorithm is combined with the parallel tempering method in a manner where both rotational motion and permutational isomerization events are important. To enable the combination of parallel tempering with smart darting so that the smart-darting moves have a reasonable acceptance probability, the original algorithm is modified by using a restricted space for the smart-darting moves. The restricted space uses a body-fixed coordinate system first introduced by Eckart, and moves in this Eckart space are coupled with local moves in the full 3N-dimensional space. The modified smart-darting method is applied to the calculation of the heat capacity of a seven-atom Lennard-Jones cluster. The smart-darting moves yield significant improvement in the statistical fluctuations of the calculated heat capacity in the region of temperatures where the system isomerizes. When the modified smart-darting algorithm is combined with parallel tempering, the statistical fluctuations of the heat capacity of a seven-atom Lennard-Jones cluster using the combined method are smaller than parallel tempering when used alone.     

Surveying a potential energy surface by eigenvector-following

We have developed a method to search potential energy surfaces which avoids some of the difficulties associated with trapping in local minima. Steps are directly taken between minima using eigenvector-following. Exploration of this space by low temperature Metropolis Monte Carlo is a useful global optimisation tool. This method successfully finds the lowest energy icosahedral minima of Lennard- Jones clusters from random starting configurations, but cannot find the global minimum in a reasonable time for difficult cases such as the 38-atom Lennard-Jones cluster where the face-centred-cubic truncated octahedron is lowest in energy. However, by performing searches at higher temperatures, we have found a pathway between the truncated octahedron and the lowest energy icosahedral minima. Such a pathway may be illustrative of some of the structural transformations that are observed for supported metal clusters by electron microscopy.     

Computer optimization of small atomic clusters

We have successfully identified stable configurations of both rare-gas and NaCl clusters with a new optimization procedure. An initial cluster configuration is prepared in a so-called shoot-and-stay process. Its total energy is then minimized with respect to the atomic coordinates. To prevent the system from being locked in local minima, the step size of each move is chosen as the width of the energy well at a higher level. As the system evolves, the global minimum is contained in the volume bounded by the decreasing value of step sizes. We have also carried out the optimization of NaCl clusters by the simulated annealing technique, for comparison. The results show that for such heterogeneous systems, the latter method cannot always find the global minimum, because of large energy gaps between different catchment regions in phase space.     

An O(N3) implementation of Hedin's GW approximation for molecules

We describe an implementation of Hedin's GW approximation for molecules and clusters, the complexity of which scales as O(N(3)) with the number of atoms. Our method is guided by two strategies: (i) to respect the locality of the underlying electronic interactions and (ii) to avoid the singularities of Green's functions by manipulating, instead, their spectral functions using fast Fourier transform methods. To take into account the locality of the electronic interactions, we use a local basis of atomic orbitals and, also, a local basis in the space of their products. We further compress the screened Coulomb interaction into a space of lower dimensions for speed and to reduce memory requirements. The improved scaling of our method with respect to most of the published methodologies should facilitate GW calculations for large systems. Our implementation is intended as a step forward towards the goal of predicting, prior to their synthesis, the ionization energies and electron affinities of the large molecules that serve as constituents of organic semiconductors.     

Efficient statistical mapping of energy surfaces of nanoclusters and molecules

A statistical technique to efficiently map out the energy surfaces of nanoclusters and molecules is described. Global energy minimizations are performed to reach of the catchment basins of the lowest energy stationary points. Saddle points are located by using a large value of the iterative energy change as the stopping criterion of a final local relaxation. Minima are derived from saddle points by simply tightening the stopping criterion and continuing the relaxation. A statistical approximation to the widths of the paths in phase space between saddle points and minima is obtained. Application is made to argon clusters of 7 and 38 atoms.     

Some aspects of dynamic chaos in small Lennard-Jones clusters

For the purpose of studying stochastic phenomena in the clusters due to an instability of their trajectories in phase space, an evolution of ensembles of the clusters with the representative points initially located in small regions of phase space is investigated using the molecular dynamics method. A path of a cloud of the representative points through the subspace of phase space available for the clusters, and cloud growth in size and in volume are considered. Specific results are presented for Ar₄. A “cold” cluster (subjected to neither an isomerization nor an evaporation) is examined in details. A brief comparison with a “hot” cluster (both the phenomena are available) is given.     

Ar n HF van der Waals clusters revisited. I. New low-energy isomeric structures for n=6-13

New low-lying isomeric structures of Ar(n)HF clusters are reported for n=6-13. They were determined using simulated annealing and evolutionary programming, for pairwise additive intermolecular potential energy surfaces. New global minima were found for the clusters with n=7, 10, 11. The new lowest-energy structure of Ar(7)HF and several new local minima for n=6, 7 clusters have the HF bound on a threefold surface site, consistent with the recent spectroscopic data for Ar(n)HF clusters in helium nanodroplets. A new type of low-energy local minima were determined for n=9-13 clusters.     

Magic Clusters PtMg2,3H5− Facilitated by Local σ-Aromaticity

The concept of local aromaticity has been successfully utilized in understanding the stability of certain atomic clusters. However, all the skeleton atoms in these clusters are covered by at least one local aromatic feature, collectively making the multiple local aromaticities coexist globally. Herein we show the robustness of local aromaticity as a tool for the discovery of novel magic clusters: not all of the skeleton atoms need to be covered by an aromatic feature to make the cluster magic. In this study, the PtMg_2,3H₅⁻ cluster anions are generated by a unique high-current pulsed discharge ion source and found to be magic numbers using mass spectrometry. Photoelectron spectroscopy and calculations confirm that only the PtH₄²⁻ kernels in these clusters are locally aromatic. Based on these results, we propose that local aromaticity can be gainfully utilized as a new potential magic rule in the search for magic numbers.     

More on the melting of Lennard-Jones clusters

The melting of 13-atom clusters interacting via Lennard-Jones potentials has been revisited using molecular dynamics coupled to steepest descent quenches. A procedure was devised to account for the fraction of times the global and local minima of the potential energy surface are accessed during a long trajectory. This quantity presents a sigmoid shape. A phenomenological model of melting is given in terms of a correlated walk that maps the short time excursions among the global and local minima in configuration space. Comparison between the simulation results and the theoretical model shows that the melting transition is well described in terms of the temperature changes of the fraction of high energy minima accessed during the cluster trajectory. Cooperativity is clear from the S shape of this quantity, i.e., the access to a local minimum favours the access to other local minima.     

Defect clustering and local ordering in rare earth co-doped ceria

Defect clustering and local ordering in rare earth co-doped ceria were studied by computer simulation and electron diffraction, respectively. The simulation of electrically neutral defect clusters containing up to four oxygen vacancies revealed that the permutation of different dopant cations in a co-doped cluster could have a significant influence on the binding energy of the cluster. Moreover, the growth of larger clusters (number of oxygen vacancies ≥ 3) could be restrained by a co-doping effect. The selected area electron diffraction study indicated that the restrained growth of larger clusters will further lead to a suppression of the local ordering of oxygen vacancies in co-doped ceria. The correlation between defect clustering, local ordering of oxygen vacancies and ionic conduction in co-doped ceria was discussed.     

聚乙烯单链松驰过程的分子模拟

利用分子模拟方法研究了不同链长聚乙烯单链折叠过程和相关的松弛和坍塌机理．发现在链长短于１０００ＣＨ２单元时,聚乙烯的链段主要通过整体塌缩机理进行折叠和取向;而链长超过１０００ＣＨ２单元时,可以明显地观察到局部取向团簇的形成,聚乙烯单链通过局部塌缩机理进行折叠和取向．通过对各阶段团簇数目,体系取向链段长度的表征,说明体系在模拟时间范围内表现了很强的松驰特性．     

Clusters in expanding plasma

An analysis is given of processes in a weakly ionized vapor expanding in a space and condensing on ions as nuclei of condensation. Processes including the growth and evaporation of clusters, mutual neutralization of clusters of different charges and coagulation are considered. Evolution of a laser plasma resulting from irradiation of a copper surface is analyzed. In the end a vapor of the plasma is transformed to charged clusters.     

The local electronic and magnetic properties of Fe impurity in Al clusters

The local magnetic property,d electronic structure and the charge transfer effect of Fe impurity in Al clusters have been studied by using a tight-binding model Hamiltonian in the unrestricted Hartree-Fock approximation, which includes intra-atomic and interatomic Coulomb interactions. We have obtained that local magnetic moment of Fe impurity in FeAl _N clusters decreases with increasing cluster size and convergences to zero (that of bulk given by Anderson) withN larger than 12, meanwhile, the local magnetic moment for smaller clusters depends on the clusters size and it is a monotonous descent function of cluster size. We have also found that the spin splitting of the localizedd states decreases as the cluster size increases, which mainly results from the interaction between the localized electrons of Fe atom and the delocalized electrons of Al atoms.     

(CoMn)n(n=1～5)合金团簇的结构和磁性

All geometry structures of (CoMn)n (n=1-5) clusters were optimized, and the energy, frequence and magnetism of (CoMn)n (n=1-5) clusters were calculated by using the local spin density approximation and generalized gradient approximation of density functional theory. The same ground state structures of CoMn alloy clusters were confirmed in two methods, and magnetism of CoMn alloy ground state clusters was studied systemically. In order to understand structure and magnetism of CoMn alloy clusters better, Co2n (n=1-5) and Mn2n (n=1-5) clusters were calculated by the same method as alloy clusters, whose ground state structure and magnetism were confirmed. Moreover, the ground state structure and magnetism of clusters with the corresponding CoMn alloy clusters was compared. Results indicated that for (CoMn)n (n=1-4) clusters, geometry structures of CoMn alloy clusters are the same as the corresponding pure clusters still, (CoMn)3 and (CoMn)4 exhibit magnetic bistability, show ferromagnetic and anti-ferromagnetic coupling, local magnetic moment of Co, Mn atoms in CoMn alloy clusters almost preserves magnetism of pure clusters still.