Partial optimization of large molecules and clusters

By examining the displacement coordinate metric three modes of constrained optimization for large molecules and clusters are suggested. The first method corresponds to a conventional optimization using internal coordinates. The second mode has applications with respect to both internal and cartesian coordinates. The final mode is particularly interesting because it can result in computational savings. A mixture of both internal and cartesian coordinates is specified where these coordinates are usually a subset of the molecules or clusters total coordinate set. In the optimization only a subset of the energy derivatives need be evaluated reducing the computational effort associated with the gradient calculation.     

Structures of large transition metal clusters

The present review surveys the results of X-ray diffraction studies of large stoichiometric transition metal clusters containing from 20 to 145 atoms in metal cores surrounded by ligand shells (72 compounds). Structures of such clusters have fragments of close packings (face-centered cubic (f.c.c.), hexagonal close (h.c.p.), and body-centered cubic (b.c.c.) packings) characteristic of crystalline bulk metals as well as mixed packings (f.c.c./h.c.p.), local close packings with pentagonal symmetry, and strongly distorted amorphous packings. The observed packing types, their distortions, and the relationship between the atomic structures of metal cores and the atomic radial distribution functions (RDF) are discussed. The structural principles established for the large clusters are applied to analysis of the experimental RDF for metal nanoparticles determined by X-ray diffraction and EXAFS spectroscopy.     

Fragmentation channels of large multicharged clusters

We address unifying features of fragmentation channels driven by long-range Coulomb or pseudo-Coulomb forces in clusters, nuclei, droplets, and optical molasses. We studied the energetics, fragmentation patterns, and dynamics of multicharged (A+)n (n=55, 135, 321) clusters. In Morse clusters the variation of the range of the pair-potential induced changes in the cluster surface energy and in the fissibility parameter X=E(Coulomb)2E(surface). X was varied in the range of X=1-8 for short-range interactions and of X=0.1-1.0 for long-range interactions. Metastable cluster configurations were prepared by vertical ionization of the neutral clusters and by subsequent structural equilibration. The energetics of these metastable ionic clusters was described in terms of the liquid drop model, with the coefficients of the volume and surface energies depending linearly on the Morse band dissociation energy. Molecular-dynamics simulations established two distinct fragmentation patterns of multicharged clusters that involve cluster fission into a small number of large, multicharged clusters for X<1 and Coulomb explosion into a large number of individual ions and small ionic fragments for X>1. The Rayleigh instability limit X=1 separates between spatially anisotropic fission and spatially isotropic Coulomb explosion. Distinct features of the fragmentation energetics and dynamics were unveiled. For fission of n=55 clusters, large kinetic and internal energies of the large fragments are exhibited and the characteristic fragmentation time is approximately 700 fs, while for Coulomb explosion the major energy content of the small fragments involves kinetic energy and the characteristic fragmentation time of approximately 300 fs is shorter. The Rayleigh (X=1) limit, leading to isotropic Coulomb explosion, is transcended by a marked enhancement of the Coulomb energy, which is realized for extremely ionized clusters in ultraintense laser fields, or by a dramatic reduction of the surface energy as is the case for the expansion of optical molasses.     

Semiclassical description of large multipole-deformed metal clusters

We use the semiclassical periodic orbit theory to describe large metal clusters with axial quadrupole, octupole, or hexadecapole deformations. The clusters are regarded as cavities with ideally reflecting walls. We start from the case of spherical symmetry and then apply a perturbative approach for calculating the oscillating part of the level density in the deformed case. The advantage of this approach is that one only has to know the periodic orbits of the spherical cavity, which makes the calculation very simple. This perturbative method is a priori restricted to small deformations. However, the results agree quite well with those of quantum-mechanical calculations for deformations that are not too large, such as typically occur for the ground states of metal clusters. We also calculate shell-correction energies. With this, it becomes possible to predict at least qualitatively the deformation energy of metal clusters.     

Icosahedral structure of large charged argon clusters

Measurements of the mass distribution of large argon clusters formed about positive ions in a free jet expansion are reported. The results support an icosahedrally derived shell model of cluster structure through completion of the fourth shell (N = 309 atoms), but significant differences are found near the completion of the fifth shell (N = 561).     

Magic numbers of large rare gas clusters

The superior stability of closed-shell icosahedral structures is evident from size distributions of argon, krypton and xenon cluster ions in the size range 100?n?1000.     

Analytical approach to very large benzenoid polymers

We consider rigorous evaluation of conjugated-circuit resonance energies for families of structurally related benzenoid hydrocarbons of increasing size. Local and global aromatic properties of such molecules are investigated with particular interest in modeling high polymers. Using the algebra of large numbers, exact formulas for contributions from individual benzene rings of polymers with up to 25,000 repeating units (close to half a million carbon atoms) were derived. All arithmetic procedures were carried out in terms of whole numbers retaining all digits, of which there were sometimes more than 10⁵. © 1995 by John Wiley & Sons, Inc.     

Drag reduction experiments with very large pipes

Various substances have been tested in the laboratory for their suitability as flow enhancers in aqueous solutions. The following maximum drag reductions (%) were obtained with pipes of 14 mm diameter and a Reynolds number of 10⁵: Na-carboxy methylcellulose (32), hydroxyethyl cellulose (42), cetyltrimethylammonium chloride/-naphthol (74; Re=10⁴), polyethylene oxide (76), K-polyphosphate/Na-pyrophosphate (77), polyacrylamide (80). The tested, partially hydrolysed polyacrylamide which was produced by a special process was found to be not only extremely effective and highly resistant to shear degradation but also unaffected by the salt content, the temperature and the water spoilage. Experiments were therefore made with this material on an industrial scale, that is to say with pipes up to 750 mm in diameter and 3200m in length. Whilst in the laboratory (pipes up to 14 mm in diameter) drag reductions were measured according to the Virk asymptote, the results obtained with large pipe diameters were lower. At diameters ranging from 300 to 750 mm a maximum drag reduction of 65% (at a concentration of 30 ppm PAAM and a constant wall shear stress of 50 Pa) has been obtained independently of the diameter.Symbols c concentration - d diameter - FE (as index) flow enhancer - k roughness - l length - n degree of polymerization - p pressure drop - r radius - Re Reynolds number - T temperature - v velocity - w (as index) water - drag reduction - friction factor - kinematic viscosity - density - wall shear stress Dedicated to Prof. Dr. R. Bonart on the occasion of his 60th birthday     

Resonance energy of very large benzenoid hydrocarbons

The resonance energy of conjugated benzenoid systems is expressed as contributions arising from independent conjugated circuits. The scheme has been applied to numerous very large conjugated systems. In many cases, it was possible to find regularities in the increments for the resonance energy within a family of benzenoid systems as the number of benzene rings is increased.     

A review of very large scale chromatography

Summary The relative merits of large scale gas chromatography (GC) and high performance liquid chromatography (HPLC) have not been reviewed for some considerable time. Although methodologies capable of manufacturing high efficiency (and hence cost effective) plant have existed for over a decade, commercial introduction has been remarkably slow. This has primarily been caused by confidentiality restrictions placed on equipment manufacturers, in turn severely limiting wide ranging applications data. These are necessary to raise potential end users confidence that both techniques offer viable large scale routes to separation and purification of mixtures as analysed by laboratory chromatographic methods. Considerable recent progress has been made with large scale HPLC plant, which has led to sufficient published data to make both technical and economic comparisons against GC possible.     

Modified Nilsson model for large sodium clusters

We propose a modified Nilsson model for spheroidal sodium clusters and investigate the modification of shell structure by deformation for sizes up toN=850. For spherical clusters, our potential is fitted to the single-particle spectra obtained from microscopically selfconsistent Kohn-Sham calculations using the jellium model and the local density approximation. Employing Strutinsky's shell-correction method, the surface energy of the jellium model is renormalized to its experimental value. We find good agreement between our theoretically predicted deformed magic numbers and the experimentally observed ones extracted from recent sodium mass abundance spectra.     

Binding energy of large icosahedral and cuboctahedral Lennard-Jones clusters

It is widely believed that the lowest energy configurations for small rare gas clusters have icosahedral symmetry. This contrasts with the bulk crystal structures which have cuboctahedral fcc symmetry. It is of interest to understand the transition between this finite and bulk behavior. To model this transition in rare gas clusters we have undertaken optimization studies within the Lennard-Jones pair potential model. Using a combination of Monte Carlo and Partan Search optimization methods, the lowest energy relaxed structures of Lennard-Jones clusters having icosahedral and cuboctahedral symmetry were found. Studies were performed for complete shell clusters ranging in size from one shell having 13 atoms to 14 shells having 10,179 atoms. It was found that the icosahedral structures are lower in energy than the cuboctahedral structures for cluster sizes having 13 shells or fewer. Additional studies were performed using the more accurate Aziz-Chen [HFD-C] pair potential parameterized for argon. The conclusions appear to be relatively insensitive to the form of the potential.     

On the Lindemann criterion for quantum clusters at very low temperature

The Lindemann criterion to discern the solid-like or liquid-like nature of a quantum cluster at T = 0 is discussed. A critical analysis of current Lindemann parameters is presented and a new parameter is proposed that is appropriate to study quantum clusters made of identical particles. A simple model wave function is introduced to fix the range of variation of these parameters. The model presents two extreme limits that correspond to either a liquid-like or a solid-like system; besides, it fulfills the Bose symmetry and also permits evaluations without symmetrization. Variational and diffusion Monte Carlo calculations are also performed for clusters of spinless bosons interacting through Lennard-Jones potentials. It is shown that the liquid-like or solid-like character of quantum clusters at zero temperature cannot be simply established in terms of a single parameter.     

Investigation of large electronic shells in Cs-compound clusters

Magic numbers in cluster mass spectra can be caused by either geometric or electronic structure. The study of metallic compound clusters allows the number of atoms and the number of electrons in clusters to be controlled independently. We report magic numbers in the mass spectra of Cs-compound clusters containing up to 700 free electrons.     

Interaction energies of large clusters from many-body expansion

In the canonical supermolecular approach, calculations of interaction energies for molecular clusters involve a calculation of the whole cluster, which becomes expensive as the cluster size increases. We propose a novel approach to this task by demonstrating that interaction energies of such clusters can be constructed from those of small subclusters with a much lower computational cost by applying progressively lower-level methods for subsequent terms in the many-body expansion. The efficiency of such "stratified approximation" many-body approach (SAMBA) is due to the rapid convergence of the many-body expansion for typical molecular clusters. The method has been applied to water clusters (H(2)O)(n), n = 6, 16, 24. For the hexamer, the best results that can be obtained with current computational resources in the canonical supermolecular method were reproduced to within about one tenth of the uncertainty of the canonical approach while using 24 times less computer time in the many-body expansion calculations. For (H(2)O)(24), SAMBA is particularly beneficial and we report interaction energies with accuracy that is currently impossible to obtain with the canonical supermolecular approach. Moreover, our results were computed using two orders of magnitude smaller computer resources than used in the previous best calculations for this system. We also show that the basis-set superposition errors should be removed in calculations for large clusters.     

Spectroscopy of large molecules in inert gas clusters

Aromatic hydrocarbons provide nucleation centers for the formation of clusters of inert gases in high-flow supersonic beams. Large clusters of Ar, each containing a single tetracene (T) molecule, were prepared by supersonic expansion of the seeded gas at pressures p = 3000–13000 Torr and interrogated by laser-induced fluorescence spectroscopy Evidence is reported for homogeneous line broadening of large TAr_n clusters prepared at p? 8000 Torr.     

Quantum Monte Carlo with very large multideterminant wavefunctions

An algorithm to compute efficiently the first two derivatives of (very) large multideterminant wavefunctions for quantum Monte Carlo calculations is presented. The calculation of determinants and their derivatives is performed using the Sherman–Morrison formula for updating the inverse Slater matrix. An improved implementation based on the reduction of the number of column substitutions and on a very efficient implementation of the calculation of the scalar products involved is presented. It is emphasized that multideterminant expansions contain in general a large number of identical spin‐specific determinants: for typical configuration interaction‐type wavefunctions the number of unique spin‐specific determinants ( ) with a non‐negligible weight in the expansion is of order . We show that a careful implementation of the calculation of the N_det ‐dependent contributions can make this step negligible enough so that in practice the algorithm scales as the total number of unique spin‐specific determinants, , over a wide range of total number of determinants (here, N_det up to about one million), thus greatly reducing the total computational cost. Finally, a new truncation scheme for the multideterminant expansion is proposed so that larger expansions can be considered without increasing the computational time. The algorithm is illustrated with all‐electron fixed‐node diffusion Monte Carlo calculations of the total energy of the chlorine atom. Calculations using a trial wavefunction including about 750,000 determinants with a computational increase of ～400 compared to a single‐determinant calculation are shown to be feasible. © 2016 Wiley Periodicals, Inc.     

Ionization potentials of large sodium doped ammonia clusters

In a continuous neat supersonic expansion ammonia clusters are generated and doped with sodium atoms in a pickup cell. Thus clusters of the form Na(NH(3))(n) are produced that are photoionized by a tunable dye laser system. The ions are mass analyzed in a reflectron time-of-flight mass spectrometer, and the wavelength dependent ion signals serve for the determination of the ionization potentials (IP) of the different clusters in the size range 10< or =n< or =1500. Aside from a plateau for 10< or =n< or =17 and smaller steps at n=24, 35, and 59 on the average a continuous decrease of the IP with cluster size is observed. The IPs in this size range are linear with (n+1)(-13) and extrapolate to IP(n=infinity)=1.66+/-0.01 eV. The slope is consistent with a dielectric continuum model of the solvated electron and the dielectric constant of the solid. The extrapolated IPs are compared with results obtained for negative ammonia cluster ions and metallic solutions in liquid ammonia. Differences are explained by the presence of counterions and their various distances from the solvated electron.