Computational results for the temperature-dependent conductivity of compressed arrays of size-selected Ag nanodots are discussed. Special attention is given to the role of phase transitions of the array as a function of external control variables: the applied voltage, the temperature, and the compression of the array. The computations are based on a scattering formalism that is presented in detail so that all the assumptions are explicitly spelled out. The results demonstrate the ability of low-lying excited electronic states of 2D lattices to probe by temperature-dependent conductivity measurements.

An experimental study of molecular fusion in fullerene-fullerene collisions is presented and the theoretical interpretation of the cross section is reconsidered in terms of phase space arguments and competition with direct collision induced dissociation. The form and absolute magnitude of the cross sections for C60+ + C-70 (or C-70(+) + C-60) and C-70(+) + C-70 can be understood, however, the much smaller cross section for C-60(+)+ C-60 remains a puzzle. The fragmentation behaviour of the hot fusion product is well described by a maximal entropy model indicating equipartition of the centre of mass collision energy followed by statistical fragmentation. (C) 2002 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.

The temperature dependence of the coherent DC conductivity of an Ag quantum dot (QD) monolayer has been computed allowing for size fluctuations of the QDs as well as for packing disorder. The computation uses a scattering formalism with an electron exchange coupling for adjacent QDs. The strength of this coupling can be tuned by compression of the array, and the same coupling is used as previously deter-mined from second harmonic generation spectroscopy of such monolayers. To agree with the experimental results, the computations center attention on the regime of not fully compressed arrays, when the exchange coupling does not fully mask the role of disorder. At very low disorder and/or at higher compressions. the computations show a phase transition to a fully delocalized conducting regime. At very low temperatures, the computed conductivity increases with temperature as exp(-2(E-0/kT)(1/2)). The characteristic energy Eo is found to be a measure of the effective coupling of next-nearest neighbors, suggesting that conduction occurs by variable range charge hopping or, in the language of electron transfer, by super-exchange, At higher temperatures, there is a crossover to an activated regime, exp(-(E-a/kT)), where the activation energy E. is shown to be a measure of the mean excess energy of the moving charges. The transition temperature to activated conduction scales with the extent of disorder. The increase of conductivity with temperature is interpreted as reflecting a gap in the density of conducting states for energies just above the ground electronic state of the array.

Molecular-dynamics simulations of a cluster impacting a hard surface show that, initially, the cluster is rapidly compressed and translationally heated. During this short but distinct stage, the cluster is a suitable medium for chemistry: the number of layers of the cluster is not changing; the constituents of the cluster can collide several times and both bimolecular and collisionally driven unimolecular reactions can occur. Hypersonic velocities of impact are needed for a considerable temperature rise. Following compression, the cluster fragments by expanding into a hemispheroidal plume. For supersonic impact. the cluster expands nearer to the surface forming an oblate, omelet-like, hemispheroid. (C) 2002 Elsevier Science B.V. All rights reserved.

Surface potential imaging (see Figure) reveals the transition to collective behavior in a two-dimensional quantum dot solid. As described in this communication, an electrical potential gradient is applied across the film, and various scanning probe and electron microscopy images are correlated to interrogate the role of disorder in the transition from local to collective behavior.

Computing on the (sub) nanoscale is discussed and illustrated by a specific example of charge transfer along a molecular frame. The general research program is to implement an entire finite state logic machine on a molecule. It is proposed to do so in stages. The first stage is to implement Boolean logic circuits on a single molecule. This has already been achieved up to the level of a full adder. Our current work seeks to implement even more elaborate circuits, to go beyond Boolean logic gates and to go beyond combinational logic circuits to the level of sequential machines. In the longer run it will be necessary to concatenate logical units so that a molecule-like assembly is needed. Here we show by a concrete experimental example that intramolecular concatenation is possible: The molecular backbone is used to move information between two ends of a short peptide. The experiment is a gas phase laser excitation of a molecule with an aromatic chromophore at one end. The absorption by the chromophore localizes the initial excitation. Different outcomes are possible depending on additional inputs. Specifically, charge can be made to migrate to the other end of the molecule. (C) 2002 Elsevier Science B.V. All rights reserved.

This perspective examines quantum dot (QD) superlattices as model systems for achieving a general understanding of the electronic structure of solids and devices built from nanoscale components. QD arrays are artificial two-dimensional solids, with novel optical and electric properties, which can be experimentally tuned. The control of the properties is primarily by means of the selection of the composition and size of the individual QDs and secondly, through their packing. The freedom of the architectural design is constrained by nature insisting on diversity. Even the best synthesis and separation methods do not yield dots of exactly the same size nor is the packing in the self-assembled array perfectly regular. A series of experiments, using both spectroscopic and electrical probes, has characterized the effects of disorder for arrays of metallic dots. We review these results and the corresponding theory. In particular, we discuss temperature-dependent transport experiments as the next step in the characterization of these arrays.

We present the real-space block renormalization group equations for fermion systems described by a Hubbard Hamiltonian on a triangular lattice with hexagonal blocks. The conditions that keep the equations from proliferation of the couplings are derived. Computational results are presented including the occurrence of a first-order metal-insulator transition at the critical value of U/t approximate to 12.5.

Implementing a logic machine on a single molecule was recently discussed with experimental roadmarks. Lasers were used to control the input and sometimes also the output of information with additional processing done via inter- and intramolecular dynamics. We examine the special requirements for an experiment that mimics a logic circuit. We use two-photon processes as physical examples of our considerations and discuss both combinational and sequential logic machines.

We show by computations that even low voltages can significantly modify the electronic states of a small compressed array of metallic quantum dots. This is because the voltage counteracts the effects of inherent disorder on the wave function. The low-lying excitations can be thermally probed. At lower voltages the array breaks into islands that are superexchange coupled. At higher voltages the response is ohmic, then it cuts out due to formation of a junction layer.

The principle of corresponding states is re-examined in the light of recent experimental and theoretical fluid equation of state data compilations. The results are used to critically test and extend the fundamental concept of corresponding states scaling for simple fluids (including rare gases, diatomics and methane). Classical corresponding states scaling based on critical point constants is found to produce weaker universal behavior than a new scaling procedure linked directly to the two intermolecular interaction potential parameters of a Lennard-Jones-6-12 fluid. The improved universal behavior revealed using this Lennard-Jones-corresponding-states scaling may either reflect inaccuracies in previous critical constant estimates, or perhaps point to more fundamental differences between the critical properties of different fluids. (C) 2002 American Institute of Physics.

Transport properties of arrays of metallic quantum dots are governed by the distance-dependent exchange coupling between the dots. It is shown that the effective value of the exchange coupling, as measured by the charging energy per dot, depends monotonically on the size of the array. The effect saturates for-hexagonal arrays of over 7(5) unit cells. The discussion uses a multistage block renormalization group approach applied to the Hubbard Hamiltonian. A first-order phase transition occurs upon compression of the lattice, and the size dependence is qualitatively different for the two phases.

The use of a classical limit for the electronic degrees of freedom avoids the need to keep the nuclei clamped while solving for the dynamics of the electrons. The Hamiltonian for the electrons will then depend on the nuclear coordinates as dynamical variables. The resulting (classical) electron-nuclear coupled equations of motion exhibit dynamical symmetry and are shown to depend only on the ratio, kappa (-4), of the electron to nuclear mass, We explore the coupled electron-nuclear dynamics as a function of kappa for the special case of a single electron moving between two centers. Ln the dynamical regime where the nuclei are heavy and the Born-Oppenheimer separation should work, the full dynamical procedure is in excellent agreement with the nuclear dynamics as computed using the Born-Oppenheimer separation. In the opposite regime where the period of the electronic motion is long, a case that can be physically realized for very high Rydberg states, one reaches an `inverse' behavior where the nuclei adiabatically adjust to the slow electronic motion. The failure of the Born-Oppenheimer separation, as judged by the electronic coupling not being governed solely by the instantaneous position of the nuclei, is more severe when the initial electronic state is not stationary.

It is sometimes stated that in order to be amenable to a simple statistical description. a system needs to have many coupled degrees of freedom. In this view, the statistical limit is to be understood from the dynamics. Here we discuss a complementary point of view where the role of `size' is to ensure that the probabilities of simple events, which are technically marginal probabilities, settle down to a canonical distribution, conditioned by additive constants of the motion. The requirement that the conditioning is on additive variables plays an essential technical role and it is not dear that this condition can be relaxed. In the view discussed here, the effective `size' is determined by the variance of the physical variables of interest. Implications for Monte Carlo sampling are also discussed, with examples. (C) 2001 Elsevier Science B.V. All rights reserved.

Connected logic gates can be operated on the levels of one molecule by making use of the special properties of high Rydberg states, Explicit experimental results for the NO molecule are provided as an example. A number of other options, including that of several gates concatenated so as to operate as a full adder, are discussed. Specific properties of high Rydberg states that are used are: their autoionization is delayed so that they can be distinguished from direct multiphoton ionization, during their long life such states also can decay by energy transfer to the molecular core in a way that can be controlled by the judicious application of very weak external electrical fields, and the Rydberg states can be detected by the application of an ionizing electrical field. The combination of two (or three) color photons with and without external weak fields allows the construction of quite elaborate logic circuit diagrams and shows that taking advantage of the different intramolecular dynamics of levels that differ by their excitation enables the compounding of logic operations on one molecular frame.

We propose a scheme for molecule-based information processing by combining well-studied spectroscopic techniques and recent results from chemical dynamics. Specifically it is discussed how optical transitions in single molecules can be used to rapidly perform classical (Boolean) logical operations. In the proposed way, a restricted number of states in a single molecule can act as a logical gate equivalent to at least two switches. it is argued that the four-level scheme can also be used to produce gain, because it allows an inversion, and not only a switching ability. The proposed scheme is quantum mechanical in that it takes advantage of the discrete nature of the energy revers but we here discuss the temporal evolution, with the use of the populations only. On a longer time range we suggest that the same scheme could be extended to perform quantum logic, and a tentative suggestion, based on an available experiment, is discussed. We believe that the pumping can provide a partial proof of principle, although this and similar experiments were not interpreted thus far in our terms.

Quantum dots are clusters of atoms (or molecules) that are small enough that their electronic states are discrete. They can be prepared with a variety of compositions and covering ligands but Bare not quite identical. In particular, the dots will have a variable size. The study of the properties of individual dots is an active subject in its own right. Here we examine the electronic structure of assemblies of dots, where the dots are near enough that they interact. For the purpose of an elementary discussion, metallic dots are regarded as ``atoms'' with one valence orbital. The key point is at they are ``designer'' atoms because their electronic properties be controlled through the synthetic method that is used to prepare the dots. Of direct concerns to us are the size of the dot and the nature of the ligands used to passivate the dots so that they do not coalesce. An important parameter is the energy cost, I, of adding an electron to a dot. The large size of the dots means that, unlike ordinary atoms, the Coulomb repulsion of the added electron is low. Other experimental control parameters are externally applied and include the ability to compress an assembly S of dots, and thereby change the distance between them, or to subject them to static or alternating electromagnetic fields. The response to spectral probes:for the electronic structure is discussed with special emphasis on: new features, such as the onset of conjugation or the insulator-to-metallic transition made accessible by the low charging energy of the dots. We propose a-phased diagram of electronic isomers that can be: accessed under realistic conditions.

Superexchange is a longer-range electron-transfer mediated by a nonresonant bridge between the donating and accepting states. We discuss a coupled set of donor/acceptor levels that are not resonant, with special reference to coupling of intermediate strengths. Examples of such systems are peptide cations or arrays of quantum dots. If the coupling is strong enough to overcome the gaps, charge can migrate. If the coupling is too weak, the charge remains localized. In the intermediate case, the charge is shown to be localized over a finite, connected, subset of sites. Degenerate perturbation theory provides a suitable zero-order basis for this intermediate regime. In a time dependent language, in the domain-localized regime, the charge migrates over a limited range of states. Also discussed is an effect of electron correlation, the so-called Coulomb blockade, on charge localization with computational examples. The experimental probing of the domain-localized regime is considered. Probes of the energy dependence of the local density of states such as scanning tunneling microscopy (STM) of arrays of quantum dots and photoelectron spectroscopy (PES) of chromophore bearing molecules are suggested.

The collision energy dependence of cross-section for reactions where the reactants attract is discussed. Examples include charge recombination A(+) + B- –> products, ion-molecule reactions and other curve crossing processes. The common characteristic of such processes is that on physical grounds there is a critical distance d where capture occurs. Special attention is given to the case where the critical separation is independent of energy and/or impact parameter. A modern example where this is the case is laser-induced association of atoms. The capture cross-section has the functional form sigma = pid(2) (1 - Vg(d)/E-T) where for the collisions discussed the potential is attractive, V-g(d) < 0. Such a cross-section is a decreasing function of the collision energy ET. The same functional form is also useful if the potential is repulsive, V-g(d) > 0. For this well-known case, the cross-section is an increasing function of the collision energy. (C) 2001 Elsevier Science B.V. All rights reserved.