Designing stable binary endohedral fullerene lattices.

Nanoparticle lattices and endohedral fullerenes have both been identified as potential building blocks for future electronic, magnetic and optical devices; here it is proposed that it could be possible to combine those concepts and design stable nanoparticle lattices composed from binary collections of endohedral fullerenes. The inclusion of an atom, for example Ca or F, within a fullerene cage is known to be accompanied by a redistribution of surface charge, whereby the cage can acquire either a negative (Ca) or positive (F) charge. From calculations involving a combination of van der Waals and many-body electrostatic interactions, it is predicted that certain binary combinations, for example a metal (A) and a halogen (B), could result in the formation of stable nanoparticle lattices with the familiar AB and AB2 stoichiometries. Much of the stability is due to Coulomb interactions, however, charge-induced and van der Waals interactions, which always enhance stability, are found to extend the range of charge on a cage over which lattices are stable. Some lattice types are shown to be three or four times more stable than an equivalent neutral C60 structure. An extension of the calculations to the fabrication of structures involving endohedral C84 is also discussed.

Self-Assembly Behavior of Oppositely Charged Inverse Bipatchy Microcolloids.

A directed attractive interaction between predefined "patchy" sites on the surfaces of anisotropic microcolloids can provide them with the ability to self-assemble in a controlled manner to build target structures of increased complexity. An important step toward the controlled formation of a desired superstructure is to identify reversible electrostatic interactions between patches which allow them to align with one another. The formation of bipatchy particles with two oppositely charged patches fabricated using sandwich microcontact printing is reported. These particles spontaneously self-aggregate in solution, where a diversity of short and long chains of bipatchy particles with different shapes, such as branched, bent, and linear, are formed. Calculations show that chain formation is driven by a combination of attractive electrostatic interactions between oppositely charged patches and the charge-induced polarization of interacting particles.

Electrostatic interactions between spheroidal dielectric particles.

Theory is developed to address the significant problem of electrostatic interactions between charged polarizable dielectric spheroids. The electrostatic force is defined by particle dimensions and charge, dielectric constants of the interacting particles and medium, and the interparticle separation distance; and it is expressed in the form of an integral over the particle surface. The switching behavior between like charge repulsion and attraction is demonstrated as depending on the ratio of the major and minor axes of spheroids. When the major and minor axes are equal, the theory yields a solution equivalent to that obtained for spherical particles. Limiting cases are presented for nonpolarizable spheroids, which describe the electrostatic behavior of charged rods, discs, and point charges. The developed theory represents an important step toward comprehensive understanding of direct interactions and mechanisms of electrostatically driven self-assembly processes.

Electrostatic interactions between charged dielectric particles in an electrolyte solution: constant potential boundary conditions.

The problem of electrostatic interactions between colloidal particles in an electrolyte solution has been solved within the Debye-Hückel approximation using the boundary condition of constant potential. The model has been validated in two independent ways - by considering the limiting cases obtained from DLVO theory and comparison with the available experimental data. The presented methodology provides the final part of a complete theory of pairwise electrostatic interactions between spherical colloidal particles; one that embraces all possible chemical scenarios within the boundary conditions of constant potential and constant charge.

Coulomb Fission in Multiply-Charged Ammonia Clusters: Accurate Measurements of the Rayleigh Instability Limit from Fragmentation Patterns.

A series of experiments have been undertaken on the fragmentation of multiply charged ammonia clusters, (NH3) nz+, where z ≤ 8 and n ≤ 850, to establish Rayleigh instability limits, whereby clusters at certain critical sizes become unstable due to Coulomb repulsion between the resident charges. Experimental results on size-selected clusters are found to be in excellent agreement with theoretical predictions of Rayleigh instability limits at all values of the charge. Electrostatic theory has been used to help identify fragmentation patterns on the assumption that the clusters separate into two dielectric spheres, and the predicted Coulomb repulsion energies used to establish pathways and the sizes of cluster fragments. The results show that fragmentation is very asymmetric in terms of both the numbers of molecules involved and the amount of charge each fragment accommodates. For clusters carrying a charge ≤+4, the results show that fragmentation proceeds via the loss of small, singly charged clusters. When clusters carry a charge of +5 or more, the experimental observations suggest a marked switch in behavior. Although the laboratory measurements equate to fragmentation via the loss of a large dication cluster, electrostatic theory supports an interpretation that involves the sequential loss of two smaller, singly charged clusters possibly accompanied by the extensive evaporation of neutral molecules. It is suggested that this change in fragmentation pattern is driven by the channelling of Coulomb repulsion energy into intermolecular modes within these larger clusters. Overall, the results appear to support the ion evaporation model that is frequently used to interpret electrospray experiments.

Coulomb fission in multiply charged molecular clusters: Experiment and theory.

A series of three multiply charged molecular clusters, (C6H6)nz+ (benzene), (CH3CN)nz+ (acetonitrile), and (C4H8O)nz+ (tetrahydrofuran), where the charge z is either 3 or 4, have been studied for the purpose of identifying the patterns of behaviour close to the charge instability limit. Experiments show that on a time scale of ∼10-4 s, ions close to the limit undergo Coulomb fission where the observed pathways exhibit considerable asymmetry in the sizes of the charged fragments and are all associated with kinetic (ejection) energies of between 1.4 and 2.2 eV. Accurate kinetic energies have been determined through a computer simulation of peak profiles recorded in the experiments and the results modelled using a theory formulated to describe how charged particles of dielectric materials interact with one another [E. Bichoutskaia et al., J. Chem. Phys. 133, 024105 (2010)]. The calculated electrostatic interaction energy between separating fragments gives an accurate account for the measured kinetic energies and also supports the conclusion that +4 ions fragment into +3 and +1 products as opposed to the alternative of two +2 fragments. This close match between the theory and experiment reinforces the assumption that a significant fraction of excess charge resides on the surfaces of the fragment ions. It is proposed that the high degree of asymmetry seen in the fragmentation patterns of the multiply charged clusters is due, in part, to limits imposed by the time window during which observations are made.

Progress in the theory of electrostatic interactions between charged particles.

In this perspective we examine recent theoretical developments in methods for calculating the electrostatic properties of charged particles of dielectric materials. Particular attention is paid to the phenomenon of like-charge attraction and we investigate the specific conditions under which particles carrying the same sign of charge can experience an attractive interaction. Given favourable circumstances, it is shown that even weakly polarisable materials, such as oil droplets and polymer particles, can experience like-charge attraction. Emphasis is also placed on the numerical accuracy of the multipole approach adopted in many electrostatic solutions and on the importance of establishing strict convergence criteria when addressing problems involving particulate materials with high dielectric constants.

Electrostatic interactions between charged dielectric particles in an electrolyte solution.

Theory is developed to address a significant problem of how two charged dielectric particles interact in the presence of a polarizable medium that is a dilute solution of a strong electrolyte. The electrostatic force is defined by characteristic parameters for the interacting particles (charge, radius, and dielectric constant) and for the medium (permittivity and Debye length), and is expressed in the form of a converging infinite series. The limiting case of weak screening and large inter-particle separation is considered, which corresponds to small (macro)ions that carry constant charge. The theory yields a solution in the limit of monopole and dipole terms that agrees exactly with existing analytical expressions, which are generally used to describe ion-ion and ion-molecular interactions in a medium. Results from the theory are compared with DLVO theory and with experimental measurements for the electrostatic force between two PMMA particles contained in a nonpolar solvent (hexadecane) with an added charge control agent.

Metastable Aluminum Atoms Floating on the Surface of Helium Nanodroplets.

Metal atoms have proved to be sensitive probes of the properties of superfluid helium nanodroplets. To date, all experiments on the doping of helium droplets have concentrated on the attachment of metal atoms in their ground electronic states. Here we report the first examples of metal atoms in excited states becoming attached to helium nanodroplets. The atoms in question are aluminum, and they have been generated by laser ablation in a metastable quartet state, which attaches to and remains on the surface of helium droplets. Evidence for a surface location comes from electronic spectra, which consist of very narrow absorption profiles that show very small spectral shifts. Supporting ab initio calculations show there to be an energy incentive for a metastable Al atom to remain on the surface of a helium droplet rather than move to the interior. The results suggest that helium droplets may provide a method for the capture and transport of metastable excited atomic and molecular species.

Molecular dynamic simulations of the elastic and inelastic surface scattering of nanoparticles.

Molecular dynamics calculations have been undertaken to simulate the collision of a solid, rotating nanoparticle with a planar, two-dimensional surface at thermal velocities (linear and rotational) equivalent to 500 K. During the course of a collision, mechanisms have been introduced into the simulation process that allows for the dissipation of kinetic energy and for components of linear and angular velocity to couple. Although previous studies of particle-particle collisions have used a similar energy dissipation procedure, in these first calculations on particle-surface collisions, it is found that the mechanism actually facilitates the movement of particles across a surface. It is also shown that the direction of travel of particles on a surface is strongly influenced by their rotational motion.

Gas phase UV spectrum of a Cu(II)-bis(benzene) sandwich complex: experiment and theory.

Photofragmentation with tunable UV radiation has been used to generate a spectrum for the copper-bis(benzene) complex, [Cu(C6H6)2](2+), in the gas phase. The ions were held in an ion trap where their temperature was reduced to ∼150 K, whereby the spectrum revealed two broad features at ∼38,200 and ∼45,700 cm(-1). Detailed calculations using density functional theory (DFT) show the complex can occupy three minimum energy structures with C2v and C2 (staggered and eclipsed) symmetries. Adiabatic time-dependent DFT (TDDFT) has been used to identify electronic transitions in [Cu(benzene)2](2+), and the calculations show these to fall into two groups that are in excellent agreement with the experimental data. However, the open-shell electronic configuration of Cu(2+) (d(9)) may give rise to excited states with double-excitation character, and the single-excitation adiabatic TDDFT treatment leads to extensive spin contamination. By quantifying the extent of spin contamination and allowing for the inclusion of a small percentage (∼10%), the theory can provide quantitative agreement with the experimental data.

Electrostatic force between a charged sphere and a planar surface: a general solution for dielectric materials.

Using the bispherical coordinate system, an analytical solution describing the electrostatic force between a charged dielectric sphere and a planar dielectric surface is presented. This new solution exhibits excellent numerical convergence, and is sufficiently general as to allow for the presence of charge on both the sphere and the surface. The solution has been applied to two examples of sphere-plane interactions chosen from the literature, namely, (i) a charged lactose sphere interacting with a neutral glass surface and (ii) a charged polystyrene sphere interacting with a neutral graphite surface. Theory suggests that in both cases the electrostatic force makes a major contribution to the experimentally observed attraction at short sphere-plane separations, and that the force is much longer ranged than previously suggested.

The significance of multipole interactions for the stability of regular structures composed from charged particles.

Identifying the forces responsible for stabilising binary particle lattices is key to the controlled fabrication of many new materials. Experiments have shown that the presence of charge can be integral to the formation of ordered arrays; however, a complete analysis of the forces responsible has not included many of the significant lattice types that may form during fabrication. A theory of many-body electrostatic interactions has been applied to six lattice stoichiometries, AB, AB2, AB3, AB4, AB5 and AB6, to show that induced multipole interactions can make a very significant (>80 %) contribution to the total lattice energy of arrays of charged particles. Particle radii ratios which favour global minima in electrostatic energy are found to be the same or a close match to those observed by experiment. Although certain lattice types exhibit local energy minima, the calculations show that many-body rather than two-body interactions are ultimately responsible for the structures observed by experiment. For a lattice isostructural with CFe4, a particle size ratio not previously observed is found to be particularly stable due to many-body effects.

Surface-charge distribution on a dielectric sphere due to an external point charge: examples of C60 and C240 fullerenes.

An analytical solution for the distribution of surface charge on a dielectric sphere due to the presence of an external point charge is presented. This solution describes how charge on the surface of the sphere is polarised in the electric field into regions of negative and positive charge. The polarisation effect (distribution of surface charge) generally varies with the separation between the sphere and the charge, and it is particularly significant at very short separations. Results obtained from the classical electrostatic model are in qualitative agreement with density functional theory calculations of charge separation in C60 and C240 fullerenes in the presence of an external point charge. This suggests that, from an electrostatic point of view, in the static electric field of external charges these molecules exhibit dielectric behaviour.

Gas phase measurements of the stabilization and solvation of metal dications in clusters of ammonia and methanol.

An experimental study has been undertaken of the ability of small numbers of either ammonia or methanol molecules (XH) to form stable solvated complexes with each of nine metal dications, M(2+). Complexes have been generated using a combination of the pick-up technique and electron impact ionization, and individual ions were monitored for evidence of metastability in the form of Coulomb fission or charge separation: [M(XH)n](2+) → [M(+)X](XH)n-m + H2X(+)(XH)m-2. Values have been assigned to a quantity ns, which is identified as the minimum number of molecules required to suppress the above reaction. These values were found to range from 3 for Sr(2+) complexed with methanol to 19 for Sn(2+) complexed with ammonia. Comparisons are made with results published previously for the same metal dications complexed with water (Chen, X.; Stace, A. J. Chem. Commun.2012, 10292), and for the most part, it is found that ions solvated with either ammonia or methanol are less stable than their water counterparts. To account for differences in stability, several criteria have been examined, and of those, the most satisfactory correlation is between ns and M(2+)-XH bond strength; the stronger the bond, the larger ns has to be in order for a complex to be stable. However, for complexes where ns is large, such as those involving Zn(2+), Cu(2+), and especially Sn(2+) and Pb(2+), it is proposed that the geometry adopted by solvent molecules also has a significant influence on proton transfer. By comparing the ease with which proton transfer occurs for the three protic solvents, water, ammonia, and methanol, it is possible to comment on metal ion acidity in nonaqueous solutions, for which condensed phase data are nonexistent; the results suggest that most of the nine metals would be stronger Lewis acids in ammonia than in water.

Coulomb fission in dielectric dication clusters: experiment and theory on steps that may underpin the electrospray mechanism.

A series of five molecular dication clusters, (H2O)n(2+), (NH3)n(2+), (CH3CN)n(2+), (C5H5N)n(2+), and (C6H6)n(2+), have been studied for the purpose of identifying patterns of behavior close to the Rayleigh instability limit where the clusters might be expected to exhibit Coulomb fission. Experiments show that the instability limit for each dication covers a range of sizes and that on a time scale of 10(-4) s ions close to the limit can undergo either Coulomb fission or neutral evaporation. The observed fission pathways exhibit considerable asymmetry in the sizes of the charged fragments, and are associated with kinetic (ejection) energies of ~0.9 eV. Coulomb fission has been modeled using a theory recently formulated to describe how charged particles of dielectric materials interact with one another (Bichoutskaia et al. J. Chem. Phys. 2010, 133, 024105). The calculated electrostatic interaction energy between separating fragments accounts for the observed asymmetric fragmentation and for the magnitudes of the measured ejection energies. The close match between theory and experiment suggests that a significant fraction of excess charge resides on the surfaces of the fragment ions. The experiments provided support for a fundamental step in the electrospray ionization (ESI) mechanism, namely the ejection from droplets of small solvated charge carriers. At the same time, the theory shows how water and acetonitrile may behave slightly differently as ESI solvents. However, the theory also reveals deficiencies in the point-charge image-charge model that has previously been used to quantify Coulomb fission in the electrospray process.

Conformation-resolved UV spectra of Pb(II) complexes: a gas phase study of the sandwich structures [Pb(toluene)2]2+ and [Pb(benzene)2]2+.

Toxic heavy metals, such as Pb(2+), have become important targets for the development of efficient receptors that are capable of recognizing their presence as environmental and biological pollutants, and an important part of that receptor-metal characterization process is the provision of spectral evidence that identifies the presence of a metal ion. From results reported here on a combined experimental and theoretical study it is shown that, when complexed with aromatic ligands, Pb(2+) is capable of yielding structured UV spectra, which: (i) exhibit discrete electronic transitions that include significant contributions from the metal ion; (ii) are very sensitive to the electronic properties of coordinating ligands; and (iii) are sensitive to subtle changes in coordination geometry. Two aromatic sandwich complexes, [Pb(benzene)2](2+) and [Pb(toluene)2](2+) have been prepared in the gas phase and their UV action spectra recorded from ions held and cooled in an ion trap. Whilst [Pb(benzene)2](2+) exhibits a spectrum with very little detail, that recorded for [Pb(toluene)2](2+) reveals a rich structure in the wavelength range 220-280 nm. Theory in the form of density functional theory (DFT) shows that both types of complex take the form of hemidirected structures, and that [Pb(toluene)2](2+) can adopt three distinct conformers depending upon the relative positions of the two methyl groups. Further calculations, using adiabatic time-dependent DFT to assign electronic transitions, provide evidence of individual [Pb(toluene)2](2+) conformers having been resolved in the experimental spectrum. Of particular significance for the development of methods for identifying Pb(2+) as an environmental or biological pollutant, is the observation that there are distinct ligand-to-metal charge transfer transitions in the UV that are sensitive to both the geometry and the electronic characteristics of molecules that accommodate the metal ion.

Moderating the acidity of Pb(II)-water complexes through the coordination of nonaqueous ligands: a computational study.

The metal dication Pb(II) is known to promote catalytic cleavage of the sugar-phosphate backbone in tRNA. The mechanism proposed to achieve this step requires that the [Pb(II)OH(-)](+) moiety act as a nucleophile and alter the local acidity of surrounding water molecules. MP2 calculations investigating the effect that nonaqueous bases have on the stability of dihydrated-Pb(II) show that the height and position of the proton-transfer barrier are sensitive to the presence of a single N- or O-coordinating "spectator" ligand and that, with the addition of two ligands coordinated directly to the Pb(II) center, the equilibrium for the hydrolysis reaction can shift to the left, thus making the Pb(II)-hydrate complex more stable than the Pb(II)-hydroxide complex. The calculations reveal a good correlation between the gas-phase basicities of nonaqueous ligands coordinated to the metal center and the barriers to proton transfer in [Pb(H(2)O)(2)](2+). In terms of the Pb(II)-induced hydrolysis of tRNA, these results indicate that the coordination of [Pb(II)-OH(-)](+) to uracil and cytosine in tRNA increases the basicity of the hydroxyl group and promotes nucleophilic attack of H(+).

Manipulating Interactions between Dielectric Particles with Electric Fields: A General Electrostatic Many-Body Framework.

We derive a rigorous analytical formalism and propose a numerical method for the quantitative evaluation of the electrostatic interactions between dielectric particles in an external electric field. This formalism also allows for inhomogeneous charge distributions, and, in particular, for the presence of pointlike charges on the particle surface. The theory is based on a boundary integral equation framework and yields analytical expressions for the interaction energy and net forces that can be computed in linear scaling cost, with respect to the number of interacting particles. We include numerical results that validate the proposed method and show the limitations of the fixed dipole approximation at small separation between interacting particles. The proposed method is also applied to study the stability and melting of ionic colloidal crystals in an external electric field.