Counting chemical compositions using Ehrhart quasi-polynomials

To count the number of chemical compositions of a particular mass, we consider an alphabet ${\mathop{\bf a}}$ with a mass function which assigns a mass to each letter in ${\mathop{\bf a}}$ . We then compute the mass of a word (an ordered sequence of letters) by adding the masses of the constituent letters. Our main interest is to count the number of words that have a particular mass, where we ignore the order of the letters within the word. We show first that counting the number of words of a given mass has a geometric interpretation, whose solutions are called Ehrhart quasi-polynomials, a class of functions defined on integers. These special functions are “periodic” in the sense that they use the same polynomial every λ steps. In addition to discovering the connection between counting compositions and Ehrhart quasi-polynomials, we also find number theoretic results that greatly reduce the number of candidates for the period, λ. Finally, we illustrate the usefulness of these results and the use of a software library named barvinok (by Verdoolaege et?al.) by applying them to eight different classes of chemical compositions, including organic molecules, peptides, DNA, and RNA.     

Electron impact ionization efficiency curves of van der Waals clusters

The study of van der Waals clusters is an area of growing interest and is being widely studied for a number of reasons. The measurement of the ionization efficiency (IE) curves have yielded a wealth of information by enabling ionization and appearance energies of ions to be determined which are essential for the calculation of thermochemical data. In the case of van der Waals clusters, the measurement ofIE curves enables one to determine the qualitative trends in the ionization potentials as a function of cluster size. In additionIE curves have also offered valuable insight into ionization related processes occurring in clusters. This paper will cover some of the more recent studies of Penning ionization, exciton induced decay and Coulomb explosion in van der Waals clusters through the use of electron impactIE curves.     

Thermodynamics of atomic clusters using variational quantum hydrodynamics

Small clusters of rare-gas atoms are ideal test cases for studying how quantum delocalization affects both the thermodynamics and the structure of molecular scale systems. In this paper, we use a variational quantum hydrodynamic approach to examine the structure and dynamics of (Ne)n clusters, with n up to 100 atoms, at both T = 0 K and for temperatures spanning the solid-to-liquid transition in bulk Ne. Finite temperature contributions are introduced to the grand potential in the form of an "entropy" potential. One surprising result is the prediction of a negative heat capacity for very small clusters that we attribute to the nonadditive nature of the total free-energy for very small systems.     

Global optimization of clusters using electronic structure methods

Over the past decade, there has been a significant growth in the development and application of methods for performing global optimization (GO) of cluster and nanoparticle structures using first‐principles electronic structure methods coupled to sophisticated search algorithms. This has in part been driven by the desire to avoid the use of empirical potentials (EPs), especially in cases where no reliable potentials exist to guide the search toward reasonable regions of configuration space. This has been facilitated by improvements in the reliability of the search algorithms, increased efficiency of the electronic structure methods, and the development of faster, multiprocessor high‐performance computing architectures. In this review, we give a brief overview of GO algorithms, though concentrating mainly on genetic algorithm and basin hopping techniques, first in combination with EPs. The major part of the review then deals with details of the implementation and application of these search methods to allow exploration for global minimum cluster structures directly using electronic structure methods and, in particular, density functional theory. Example applications are presented, ranging from isolated monometallic and bimetallic clusters to molecular clusters and ligated and surface supported metal clusters. Finally, some possible future developments are highlighted. © 2013 Wiley Periodicals, Inc.     

Comparison of calibration curves using the L p norm

Interlaboratory comparisons are a fundamental task in order to provide measurements with traceability. The simplest possible scenario implies that a single traveling standard of a quantity is measured at various laboratories. A more complex scenario arises when the laboratories measure a large set of standard values pertaining to a given physical quantity or when the traveling standard is not a realization of the quantity of interest but a measuring instrument. In the last case, it might be convenient to globally compare the calibration curves provided by the laboratories. We will introduce a distance between two generic analytical curves based on the Least Power L _p norm of their difference. The properties of such distance will be presented, with particular attention to its dependence on the parameter p.     

Photoionization mass spectrometry of molecular clusters using synchrotron radiation

The photoionization and dissociative ionization of molecular aggregates using synchrotron radiation is reported. The main objective of the review is to consider the intracluster relaxation processes after ionization. For hydrogen-bonded systems proton transfer is dominant. For small clusters (n<4) appearance potentials, ionization potentials, absolute proton affinities, proton solvation energies and intermolecular bond energies in the ionic clusters are deduced. For van der Waals aggregates proton transfer can also be used to characterize the intermolecular bond in the ionic cluster. Aggregates of CH₄, SiH₄, CH₃F show proton transfer in contrast to simple aromatic compounds, which reveal no proton transfer. From the fragmentation pattern and appearance potentials relaxation by intracluster ion molecule reactions is discussed. In heterogeneous clusters intracluster Penning ionization is observed. The shift of the charge transfer resonances depends on the π-electron density in the aromatic system. The width and spectral position of these resonances are influenced by the cluster size.     

Single-photon double ionization of mercury clusters using synchrotron radiation

Single-photon doublet-ionization experiments have been carried out on mercury resulting in the formation of doubly charged clusters. The efficiency is very high and similar to that obtained by electron impact. The mechanism of double ionization is discussed and our results favor a two-step process both in photon and electron impact ionization.     

Preparation of submicrometer-sized clusters from polymer spheres using ultrasonication

The fabrication of small assemblies of spherical colloidal particles is presented. Basic principles of the preparation of miniemulsions were combined with the concept originally described by Pine and co-workers for the preparation of clusters from microspheres. The application of ultrasonic emulsification limits the size distribution of the emulsion droplets and thus the statistical distribution of the number of particles per droplet. The small droplet sizes together with the use of building blocks in the submicrometer range leads to large yields of well-defined small clusters with diameters below 300 nm. Such clusters might serve to build novel promising materials that demand high complexity or special symmetries.     

Stability and structure of rare-gas ionic clusters using density functional methods: A study of helium clusters

Several modelings of exchange and correlation forces which can be carried out using density functional theory (DFT) methods have been analyzed to study their efficiency and reliability when evaluating possible competing structures of helium ionic clusters of increasing size. This study examines He_n⁺systems with n from 1 to 7 and compares the present calculations with earlier evaluations that used more conventional, and more computationally intensive, methods with configuration interaction (CI) approaches. The present results indicate that it is indeed possible to strike a fruitful balance between reduction of computational times and quality of the ensuing structural information. © 1996 John Wiley & Sons, Inc.     

Area determination under chromatographic curves using the Monte Carlo method

Summary A rapid method is described for the determination of the areas under chromatographic curves (peaks). The method is based on the application of the Monte Carlo procedure, and its advantage lies in its successful application to irregular curves.     

Enhancement of magnetic resonance contrast effect using ionic magnetic clusters

Precise diagnosis by magnetic resonance imaging (MRI) requires sensitive magnetic resonance probes to detect low concentrations of magnetic substances. Ionic magnetic clusters (IMCs) as versatile magnetic probes were successfully synthesized for enhancing the magnetic resonance (MR) contrast effect as well as ensuring high water solubility. IMCs with various sizes were prepared by assembly of MNCs using cationic cetyltrimethylammonium bromide (CTAB) and anionic sodium dodecyl sulfate (SDS). To synthesize IMCs in the aqueous phase, magnetic nanocrystals in an organic solvent were assembled with CTAB and SDS using the nanoemulsion method, to fabricate cationic magnetic clusters (CMCs) and anionic magnetic clusters (AMCs), respectively. IMCs demonstrated ultrasensitivity by MR imaging and sufficient magnetic mobility under an external magnetic field.     

Geometry optimization of bimetallic clusters using an efficient heuristic method

In this paper, an efficient heuristic algorithm for geometry optimization of bimetallic clusters is proposed. The algorithm is mainly composed of three ingredients: the monotonic basin-hopping method with guided perturbation (MBH-GP), surface optimization method, and iterated local search (ILS) method, where MBH-GP and surface optimization method are used to optimize the geometric structure of a cluster, and the ILS method is used to search the optimal homotop for a fixed geometric structure. The proposed method is applied to Cu(38-n)Au(n) (0 ≤ n ≤ 38), Ag(55-n)Au(n) (0 ≤ n ≤ 55), and Cu(55-n)Au(n) (0 ≤ n ≤ 55) clusters modeled by the many-body Gupta potential. Comparison with the results reported in the literature indicates that the present method is highly efficient and a number of new putative global minima missed in the previous papers are found. The present method should be a promising tool for the theoretical determination of ground-state structure of bimetallic clusters. Additionally, some key elements and properties of the present method are also analyzed.     

Geometry optimizations of benzene clusters using a modified genetic algorithm

A modified genetic algorithm with real-number coding, non-uniform mutation and arithmetical crossover operators was described in this paper. A local minimization was used to improve the final solution obtained by the genetic algorithm. Using the exp-6-1 interatomic energy function, the modified genetic algorithm with local minimization (MGALM) was applied to the geometry optimization problem of small benzene clusters (C6H6)N(N = 2-7) to obtain the global minimum energy structures. MGALM is simple but the structures optimized are comparable to the published results obtained by parallel genetic algorithms.     

Photoionisation studies of homogeneous argon and krypton clusters using TPEPICO

The photoionisation threshold region of homogeneous Argon and Krypton clusters Ar _n and Kr _n forn up to 24 formed in a free jet expansion has been studied in detail, using the threshold photoelectron photoion coincidence (TPEPICO) time of flight technique. Measurements performed at a variety of different expansion conditions (nozzle temperature and stagnation pressure) demonstrate that fragmentation of larger clusters contributes substantially to the shape of the TPEPICO spectra even for the smallest clusters and at all photon energies higher than about 200 meV to 400 meV above the ionisation threshold. The determination of ionisation potentials for these cluster ions is discussed and careful estimates are given and compared with recent theoretical values.     

Laser chemical synthesis of clusters and ultrafine particles using organometallics

Gas-phase synthesis of clusters and ultrafine particles using lasers and organometallics is reviewed. The general field of laser chemistry is introduced in the context of using organometallics as reactants. Examples of particle and cluster synthesis in flowing gases and in bulk gases, and during laser chemical vapor deposition, are given. A brief introduction to the general field of random irreversible fractal coagulation provides a basis for describing how powders, clusters and ultrafine particles are synthesized. References to applications and characterization methods are given.     

Exploring the free energy surfaces of clusters using reconnaissance metadynamics

A new approach is proposed for exploring the low-energy structures of small to medium-sized aggregates of atoms and molecules. This approach uses the recently proposed reconnaissance metadynamics method [G. A. Tribello, M. Ceriotti, and M. Parrinello. Proc. Natl. Acad. Sci. U.S.A. 107(41), 17509 (2010)] in tandem with collective variables that describe the average structure of the coordination sphere around the atoms/molecules. We demonstrate this method on both Lennard-Jones and water clusters and show how it is able to quickly find the global minimum in the potential energy surface, while exploring the finite temperature free energy surface.