Analytical and numerical results are presented for the intersection of electronic energies of the same space symmetry for electrons in the field of two Coulomb centers in D-dimensions. We discuss why such crossings are allowed and may be less ``exceptional'' than one could think because even for a diatomic molecule there is more than one parameter in the electronic Hamiltonian. For a one electron diatomic molecule at the large-D limit, the electronic energies are shown analytically to diverge quadratically from the point of their intersection. The one electron two Coulomb centers problem allows a separation of variables even when the charges on the two centers are not equal. The case of two electrons, where their Coulombic repulsion precludes an exact symmetry, is therefore treated in the large-D limit. It is then found that, in addition to the quadratic intersection, there is also a curve crossing where the energies diverge linearly. (C) 2001 American Institute of Physics.

We present symmetry-breaking and electronic-structure phase diagrams for two-center molecules with one and two electrons in the limit of a space of large dimensions. For one electron, the phase diagram in the internuclear distance-nuclear charge (R-Z) plane has two different stable phases. One corresponds to the electron equidistant from the two nuclei; the other where the electron is localized on one of the nuclei. The phase diagram for two electrons with two equally charged centers shows three different stable phases corresponding to different electronic-structure configurations. This phase diagram is characterized by a bicritical point. When the charges are unequal, the phase diagram shows only two stable phases, covalent and ionic. This phase diagram is characterized by a tricritical point, where the first-order transition line meets with the second-order transition line. The role of the inter-electron Coulombic repulsion in giving rise to different electronic structures and the distinction between a continuous deformation of one structure into another versus a discontinuous, so-called first-order, transition, where two isomers can coexist, are emphasized. The connection to the spectroscopic notion of intersecting potential energy curves is discussed.

Rydberg series of C-60 are reported for the first time. The Rydberg states are seen in photoelectron spectra using ultrashort pulsed-laser excitation, where the excited states formed are ionized with one further photon from the same laser pulse. The structure is observed for pulse durations as short as 100 fs with indications of residual structure for even shorter pulse excitation. The production mechanism is discussed and the Rydberg states are modeled by analytically solving the Schrodinger equation with a simple jelliumlike potential for C-60.

Logic circuits operating on different molecules or on different parts of the same molecule can be connected. As an example, a circuit known as a full adder is described. It is made up of two circuits, a half adder on a donor (rhodamine 6G) and another half adder on an acceptor (azulene). The signal, (an intermediate sum), is moved from donor to acceptor by electronic energy transfer. The concatenated logic arrangement is described, and potential applications using other bichromophoric molecules are outlined. Polychromophoric molecules will allow a fanout operation.

Finite state logic machines can be realized by pump-probe spectroscopic experiments on an isolated molecule. The most elaborate setup, a Turing machine, can be programmed to carry out a specific computation. We argue that a molecule can be similarly programmed, and provide examples using two photon spectroscopies. The states of the molecule serve as the possible states of the head of the Turing machine and the physics of the problem determines the possible instructions of the program. The tape is written in an alphabet that allows the listing of the different pump and probe signals that are applied in a given experiment. Different experiments using the same set of molecular levels correspond to different tapes that can be read and processed by the same head and program. The analogy to a Turing machine is not a mechanical one and is not completely molecular because the tape is not part of the molecular,machine. We therefore also discuss molecular finite state machines, such as sequential devices, for which the tape is not part of the machine. Nonmolecular tapes allow for quite long input sequences with a rich alphabet (at the level of 7 bits) and laser pulse:shaping experiments provide concrete examples. Single molecule spectroscopies show that a single molecule can be repeatedly cycled through a logical operation. (C) 2001 American Institute of Physics.

{{The distinct electronic states of assemblies of metallic quantum dots are discussed in a simple approximation where each dot is mimicked as an ``atom'' that carries one valence electron. Because of their large size, the charging energy of the dots

Fermions need to satisfy the Pauli exclusion principle: no two can be in the same state. This restriction is most compactly expressed in a second quantization formalism by the requirement that the creation and annihilation operators of the electrons satisfy anti-commutation relations. The usual classical limit of quantum mechanics corresponds to creation and annihilation operators that satisfy commutation relations, as for a harmonic oscillator. We discuss a simple classical limit for Fermions. This limit is shown to correspond to an anharmonic oscillator, with just one bound excited state. The vibrational quantum number of this anharmonic oscillator, which is therefore limited to the range 0 to 1, is the classical analog of the quantum mechanical occupancy. This interpretation is also true for Bosons, except that they correspond to a harmonic oscillator so that the occupancy is from 0 up. The formalism is intended to be useful for simulating the behavior of highly correlated Fermionic systems, so the extension to many electron states is also discussed.

The classical limit is shown to provide a description exactly equivalent to the quantum mechanical one in the approximation where each electron is assigned to an orbital. Strictly speaking it is therefore not a limit but an alternative way of solving the problem. There are some merits of this reformulation, most notably in that it brings the phase of the orbitals to the forefront, on equal footing as the occupancies. This allows one to discuss, e.g., electron localization, in a clearer manner. But computationally the classical description is not superior. There will be a definite advantage for more realistic electronic Hamiltonians, i.e., for implementing configuration interaction, and/or when the nuclear motion is coupled to the electronic dynamics. In this paper we limit attention to a derivation and discussion of the simple orbital approximation. (C) 2000 American Institute of Physics. [S0021-9606(00)30435-4].

Charge transport in molecular and extended systems is discussed with special reference to the mixing of covalent and ionic states and the evolution of this mixing with time. The formalism allows the electron to acquire an extra phase when it moves from one site to the next so that a hopping limit can be reached where the electron transfers with a random phase. The equations of motion are solved for both quantum mechanical and classical dynamics. An appendix discusses a classical representation of orbital occupancies in a manner consistent with the Pauli exclusion principle.

Thermionic emission is discussed as a long time (microseconds) decay mode of energy-rich large molecules, metallic and metcar clusters, and fullerenes. We review what is known and consider the many experiments, systems, and theoretical and computational studies that still need to be done. We conclude with a wish list for future work. Particular attention is given to the experimental signatures, such as the dependence on the mode of energy acquisition, and theoretical indications of a not-quite-statistical delayed ionization and to the competition of electron emission with other decay modes, such as fragmentation or radiative cooling. Coupling of the electronic and nuclear modes can be a bottleneck and quite long time-delayed ionization can be observed, as in the decay of high Rydberg states probed by ZEKE spectroscopy, before the onset of complete energy partitioning.

Quantum dots present the chemist with the opportunity to synthesize atomic-like building blocks with made-to-measure electronic properties. For the theorists this allows a study of the same Hamiltonian for a range of parameters. Hen we consider a lattice of quantum dots, where the dots can be prepared with a narrow distribution of properties but are never quite identical. This is unlike an ordered lattice of atoms or molecules. We report computations of the frequency-dependent dielectric response of a two-dimensional array of quantum dots, as a function of the distance between the dots. When the dots are not closely packed, the response is dominated by the Coulomb repulsion of electrons (of opposite spin) on a given dot. This gives rise to an insulator-metal transition as the expanded array is compressed. The interplay between the three effects, the ``disorder'' due to the size, shape, and environmental fluctuations of the dots, the coupling of adjacent dots, and the Coulomb repulsion are studied as functions of the lattice spacing. The computations are performed in the approximation where each dot carries one valence electron, but these electrons are fully correlated so as to fully account for the Coulomb blocking. This is possible by a diagonalization of the Hamiltonian in a many-electron basis. Comparison is made with experimental results for the dielectric response, as described in a companion to this paper.

The dynamics of the K + CH3I reaction is discussed with special reference to two factors that govern the electron transfer. One is that at higher collision velocity the behavior need not be adiabatic so that there can be a finite probability for the electron not to transfer, resulting in no reaction. The other is the marked increase of the electron affinity of CH3I with its bond extension. The electron transfer can therefore take place at much larger separation of the reactants if CH3I is stretched. The barrier to reaction is then much lower. These observations are used to discuss the stereodynamics of the reaction. Several open problems are identified.

Broken symmetry is characteristic of arrays of quantum dots and can be observed in the failure of selection rules of optical spectroscopy or in the dielectric properties. Here we discuss scanning tunneling spectroscopy, where electrons are detached or attached. In the lowest order of description (sometimes known as Koopmans theorem), the orbitals of a system are regarded as given and, one adds or removes electrons from these orbitals. if one has a half-full band of states whose energies have a reflection symmetry about the center, the density of states should be symmetric about the energy of the highest occupied state. Features that are special to arrays of nanodots and lead to the breaking of the expected symmetry are identified. Computations of the density of states of an array of Ag nanodots that are in accord with the available experimental observations are also provided. For a disordered array, the response of the STM probe can be qualitatively different at different lattice points and we interpret this in terms of a change in the nature of the ground electronic state of the array when it is more disordered.

A many-electron description of charge migration along a molecular backbone is discussed. Reference is made to site selective reactivity and the recent experiments of Weinkauf and Schlag on the dissociation of peptide ions following a localized ionization. The use of many-electron states allows a classification of the charge migration pathways through either covalent or ionic states. Electron correlation is introduced via Coulomb repulsion of electrons of opposite spins a-la Hubbard. Complete configuration interaction is implemented using the unitary group basis of Paldus. The primary factor determining charge migration is found to be the local ionization potential. It is shown that, at lower levels of excitation, the majority of possible initial states which describe localized ionization at one end of the chain lead to a preferential dissociation at the other end of the chain. (C) 1999 American Institute of Physics. [S0021-9606(99)30111-2].

Computational results for the surface impact of (CH3I)(n) clusters are presented, and the dynamics of formation of molecular products is examined. The mechanism is compared to the high energy bimolecular CH3I + CH3I collision and to other reactions in impact-heated clusters, in particular, the burning of air. The results are discussed in reference to the experimentally: observed formation of molecular iodine (as I-2(-)) in surface collisions of (CH3I)(n)(-) clusters.

For large molecules, electronically excited stales are denser than can be simply judged from the gap between the ground state and excited states. This is particularly true for large open shell systems, such as peptide cations. In such systems, short laser pulses can be used to prepare initial electronic states that are not stationary. These are non Born-Oppenheimer states, and therefore, the motion of the nuclei is not determined by a single potential. It is argued that such states could offer the possibility of control of reactivity. They can impede the usually facile vibrational energy redistribution, which is characteristic for a motion on a potential surface with a well. After a localized ionization, the dependence of site-selective fragmentation of small peptide ions on time is discussed with computational results based on a Pariser-Parr-Pople Like electronic Hamiltonian. We predict a strong nonstatistical and site selective reactivity on a short time scale and also a dependence on the nature of the initial excitation. Results are presented for the fragmentation of Leu-Leu-Leu-Trp(+) and Ala-Ala-Ala-Tyr(+) ions and are compared with nanosecond laser pulse experiments.

The effective energy threshold for the crossing into an electronically excited state and the post threshold rise of the yield of crossing are discussed. The time-dependent Schrodinger equation for multiple electronic states is solved using the full multiple spawning (FMS) methodology. The quantal results are compared with classical path methods. The potential energy function is of the LEP form including the electronically excited surface. For kinematic reasons, the yield is exponentially small until an effective threshold, at similar to 10 km s(-1), with a steep rise of the yield in the post threshold regime. (C) 1999 Elsevier Science B.V. All rights reserved.

Why do some quite complex events appear to be built up from seemingly independent elementary events? It is, of course, fortunate that this is so, for otherwise, it would be hard to analyze the world around us. But the technical question remains. It is here argued that a sufficient condition is that the possible complex events all have the same sum(s) for (one or more) additive variable(s). Constants of the motion are one example of such variables. In addition, it is shown that the independent distribution of the elementary events is one of maximal entropy. (C) 1999 John Wiley & Sons, Inc.