Limit Of Large Clusters Research Articles

Cluster Size Effects in the Surface-Enhanced Raman Scattering Response of Ag and Au Nanoparticle Aggregates: Experimental and Theoretical Insight

In this work we report the spectral evolution of the surface-enhanced Raman scattering (SERS) response of biotin molecules that generate the assembly of Ag and Au nanospheres (NSs) into clusters with controlled interparticle gaps during the aggregation process. The experiments are analyzed using rigorous near-field electrodynamic calculations of the enhancement produced in a close-packed cluster with a different number of NSs. Two kinetic mechanisms during the NS aggregation were identified which give rise to a different cluster size distribution and as a consequence to a different SERS response. It is found that during NS aggregation there is an initial fast growth of the SERS signals followed by a decay that reaches an almost constant value at relatively long times. These results are qualitatively explained by the trends observed in the electrodynamics calculations of the near-field enhancement as a function of the cluster size, which highlights the critical role played by radiation damping as the size of the cluster increases for small clusters (dimers and trimers), in contrast with the behavior observed for clusters with a relative greater number of particles where the decrease of the near-field enhancement is less significant. In addition, a general procedure is presented that makes it possible to perform a suitable comparison of the SERS response for tight-compact clusters, in the limit of large clusters, as long as the wavelength range of the SERS response is almost size independent. This procedure is tested for Ag and Au nanoaggregates generated in solution formed by spheres of different size, at an almost constant interparticle separation. It was found that even there are differences between the analytic enhancement factor and the calculated enhancement predicted by the electrodynamic theory in the large cluster size limit, and the trends in the SERS response of the biotin molecules are qualitatively explained by the electromagnetic (EM) mechanism for both Ag and Au clusters. These discrepancies could be indicative of a chemical contribution to the global SERS response, but a rigorous assessment of this mechanism would require additional theoretical calculations supported by experiments. Notwithstanding, the SERS enhancement results obtained with noncovalent bonded dye molecules (Coumarin 440 and Rhodamine B) that are randomly distributed in the clusters as Raman reporters, using the same large clusters as substrates (linked by biotin molecules), are in fairly good quantitative agreement with the electrodynamics model of the average SERS enhancement.

Theoretical Study of Rb2 in HeN: Potential Energy Surface and Monte Carlo Simulations

An analytical potential energy surface for a rigid Rb₂ in the ³Σ(u)⁺ state interacting with one helium atom based on accurate ab initio computations is proposed. This 2-dimensional potential is used, together with the pair approximation approach, to investigate Rb₂ attached to small helium clusters He(N) with N = 1-6, 12, and 20 by means of quantum Monte Carlo studies. The limit of large clusters is approximated by a flat helium surface. The relative orientation of the dialkali axis and the helium surface is found to be parallel. Dynamical investigations of the pendular and of the in-plane rotation of the rigid Rb₂ molecule on the surface are presented.

Extension of molecular electronic structure methods to the solid state: computation of the cohesive energy of lithium hydride

We describe a simple strategy for calculating the cohesive energy of certain kinds of crystal using readily available quantum chemistry techniques. The strategy involves the calculation of the electron correlation energies of a hierarchy of free clusters, and the cohesive energy E(coh) is extracted from the constant of proportionality between these correlation energies and the number of atoms in the limit of large clusters. We apply the strategy to the LiH crystal, using the MP2 and CCSD(T) schemes for the correlation energy, and show that for this material E(coh) can be obtained to an accuracy of approximately 30 meV per ion pair. Comparison with the experimental value, after correction for zero-point energy, confirms this accuracy.

Density-Functional Theory of Polar Insulators

We examine the density-functional theory of macroscopic insulators, obtained in the large-cluster limit or under periodic boundary conditions. For polar crystals, we find that the two procedures are not equivalent. In a large-cluster case, the exact exchange-correlation potential acquires a homogeneous ``electric field'' which is absent from the usual local approximations, and the Kohn-Sham electronic system becomes metallic. With periodic boundary conditions, such a field is forbidden, and the polarization deduced from Kohn-Sham wave functions is incorrect even if the exact functional is used.

Rate Equations for Clusters in Rare Earth-Doped Fibers

We present two rate equation models describing the effects of clusters on rare earth-doped silica fibers. The first one, valid for my cluster size, describes the interaction between clustered ions (cross relaxation) as a nonradiative process. The second model, valid only for large clusters, describes it as a cooperative upconversion process. These models are applied to both Nd- and Er-doped fibers. In the limit of large clusters, the two models predict comparable behavior, which provides the heretofore missing relationship between these two formalisms. Increasing the cluster size is found to significantly reduce the steady-state population of the metastable level and to introduce an increasingly faster and stronger fast component in its relaxation. The model is used to quantify the effect of clusters on the gain of fiber amplifiers and the threshold of fiber lasers. These results can be directly applied to study the impact of clusters of any size on doped fiber devices, as well as cooperative upconversion in highly doped materials.

Photodissociation of sulfur dioxide cluster anions

Photodissociation of negatively charged sulfur dioxide clusters (SO2)n−, 2≦n≦11, was investigated in the wavelength range between 458 nm and 600 nm using a tandem mass spectrometer. The spectral position of the absorption band remains unchanged, however it exhibits narrowing with increasing cluster size. The smooth evolution of the spectra shows that the clusters are composed of a dimer anion core surrounded by neutral molecules. The analysis of the fragmentation products reveals that the absorption of a photon is followed by statistical evaporation of neutrals with a mean energy loss of 0.28±0.05 eV per evaporated monomer in the large cluster limit.

Finite-size effects in ionization potentials and electron affinities of metal clusters

Experimental ionization potentials (I) and electron affinities (A) of metal clusters MeN are compiled for a variety of systems and their size dependence is analyzed. In the theoretical part, we perform semiclassical density variational calculations using the spherical jellium model and the local density approximation. For alkali systems and, to some extent, also for some nonalkali systems, the calculated values of I and A reproduce very well the average size dependence of the measured quantities, if their common bulk limit W is adjusted to the experimental bulk work function. This holds even for rather small systems where I and A are no longer linear in N−1/3. We discuss the extent to which classical models for the energetics of charged metal spheres can account for the correct size dependence in the large-cluster limit. We point out that the deviation of the slope parameters α and β in the asymptotic expressions I∼W+α(e2/rs)N−1/3, A∼W−β(e2/rs)N−1/3 from the values (1)/(2) , which depends on the material via the Wigner–Seitz parameter rs, can be entirely accounted for by quantum-mechanical effects, namely the kinetic, exchange, and correlation energies and the diffuseness of the electron density.

Photoabsorption and photofragmentation studies of Ar+n cluster ions

We have measured the photoabsorption spectra of mass selected Ar+n clusters, n=3–40, from 355–1064 nm. The smaller clusters, n<15, display a visible photoabsorption spectrum similar to Ar+3, i.e., a broad, intense band peaking near 520 nm. From n=15–20 this photoabsorption band shifts smoothly to a longer wavelength, peaking near 600 nm for Ar+20. This band does not change appreciably as n increases from 20 to 40. These results clearly demonstrate that the Ar+n clusters have photophysical properties quite different from those of Ar+2. We have also studied the photoabsorption and subsequent photofragmentation of Ar+n cluster ions, n=3–60, at selected visible wavelengths. The ionic photofragment distributions both indicate that photofragmentation proceeds through the loss of individual Ar atoms and place an upper bound of 90 meV on the cluster ion binding energy in the large cluster limit.

Photodissociation of mass-selected (CO2)n - clusters: Evaporation leading to magic numbers in fragment-ion dstributions.

Photodissociation of mass-selected ${{({\mathrm{CO}}_{2})}_{n}}^{\ensuremath{-}}$ clusters, $n<~40$ at 355 and 308 nm reveals that the same "magic numbers" are present in the fragmentation pattern as in the mass spectrum, demonstrating that these intensity anomalies are due to relative ionic stabilities. The photon energy dependence of the fragmentation pattern shows that photodissociation proceeds by an evaporative mechanism and yields an upper bound, 0.22 \ifmmode\pm\else\textpm\fi{} 0.01 eV, for the binding energy of a neutral C${\mathrm{O}}_{2}$ onto the ionic cluster in the large-cluster limit.

Matrix spectroscopy in the gas phase: IR spectroscopy of argon clusters containing SF 6 or CH 3F

Optothermal (bolometric) detection and a line-tunable CO 2 laser have been used, in conjunction with supersonic beams of dilute mixtures of SF 6 or CH 3F in Ar, to obtain the infrared spectra of Ar clusters containing these molecules. The spectra obtained at the limit of large clusters are remarkably similar to the infrared Ar matrix deposition spectra of the same molecules.

Monte‐Carlo Calculation of Density of States and Localization in Alloys Including Short‐Range Order

AbstractThe alloy density of states calculated with a Monte‐Carlo technique is compared to that calculated with a small cluster approximation. It is shown that the use of small clusters imbedded in an effective medium can give rise to spurious structure in the density of states while the two methods give the same results in the limit of large clusters. The conditions are determined for localization in such systems and some conjectures concerning the nature of localized states observed in real liquid alloys are made.