It is well understood that energy rich polyatomic molecules do not dissociate promptly because the number, P, of their energy states far exceeds the number, N, of the decay channels. In the simplest RRK theory, the fraction N/P is the probability of dissociation. We discuss the distribution of the decay rates of maximal entropy and conclude that it is governed by at most N linearly independent constraints, N < P, or, more typically, N << P. This mathematical requirement already severely restricts the number of constraints. Beyond it however, on physical grounds, one constraint, or at most a few, may be dominant. We discuss why just one constraint, or a few but less than N, can be sufficient to describe the product state distribution.

Dynamics of electronic motion when the nuclei are clamped is discussed and shown to be always described as a superposition of adiabatic electronic states. These states are stationary when the nuclei are clamped but their superposition leads to multiply periodic motion where the natural frequencies are the differences in the energies of the adiabatic electronic states. When one or more of the frequencies are low and the atoms are allowed to move, the electronic rearrangement is commensurate with the motion of the nuclei. This is the usual breakdown of the Born-Oppenheimer approximation. But when the electronic frequencies are higher there is an electronic motion before the nuclei move. The motion can be demonstrated through expectation values such as the multipole moments of the charge distribution. Such superposition states will be excited when the laser pulse width in energy exceeds the spacings of the states. For low-lying valence excited or low Rydberg states this requires a femtosecond or shorter laser pulse. Since the carrier frequency has to be comparable to the excitation energy, the required laser pulses must span only a few cycles.

A time-dependent multiconfiguration method with a large electronic basis set is used to compute the response of all the electrons of LiH to a few-cycle intense pump field followed by a probe pulse. The ultrashort pump pulse excites a coherent superposition of stationary electronic states and, by changing the pump parameters such as intensity, duration, polarization and phase of carrier frequency, one can steer the motion of the electrons. Particular attention is given to the control provided by the polarization and by the phase. For example, a change in polarization is used to select an electronic wave packet that is rotating in a plane perpendicular to the bond or rotation in a plane containing the bond. The electronic wave packet can be probed by a delayed second pulse. This delayed probe pulse is also included in the Hamiltonian with the result that the frequency dispersed probe spectrum can be computed and displayed as a two-dimensional plot.

The feasibility of controlled ultrafast pumping in the mid IR and the probe of the subsequent intramolecular dynamics is illustrated for vibrational excitation of the two metal carbonyls W(CO)(6) and Mn(CO)(5)Br in solution. Pumping and probing is performed by short, 130 fs, pulses centered at about 2000 cm(-1). Frequency resolved measurements of the time delayed probe pulse are performed. Measured two dimensional spectra are fitted by a kinetic scheme that models the vibrational dynamics. Fast relaxation is solvent induced with the solvent acting also as a heat bath. The (several) probe signals in the experiment can be thought of as the response of a finite state logic machine. This suggests that the molecular machine can act as an ultrafast (petaHertz) processor. The number of internal (memory) states of the machine is determined by the number of vibrational states in the kinetic scheme that can fit the observed relaxation. The number of outputs of the machine is the number of the several different available probe signals. It is shown that the machine is massively parallel because in each (sub ps) time step it produces an entire vector as an output and that each component of the output vector is, by itself, a transform over the input. Beyond that, the machine can produce a (finite number of) different output vectors in sequential time steps. (c) 2008 Elsevier BN. All rights reserved.

Charge and electronic energy transfer (ET and EET) are well-studied examples whereby different molecules can signal their state from one (the donor, D) to the other (the acceptor, A). The electronic energy transfer from the donor (Rh) to the acceptor (Az) is used to build an all-optical full adder on a newly synthesized bichromophoric molecule Rh-Az. The results are supported and interpreted by a full kinetic simulation. It is found that the optimal design for the implementation of the full adder relies in an essential way on the intramolecular transfer of information from the donor to the acceptor moiety. However, it is not the case that the donor and the acceptor each act as a half adder.

Pulsed electrical set and reset inputs are used to simulate the temporal action of a finite state machine in a three terminal configuration for a variety of arrangements. The gate electrode is necessary only if it is of interest to tune the tunneling rate and to compensate for background charges. When the output is the current, a source and drain electrodes are required. If the output is determined by measuring charge occupancy, then a single junction suffices. The electron transfer rates are computed from the free energy change for a single electron transfer to or from a quantum dot of size such that only charge quantization matters. For a small enough dot the device could operate at room temperature. An asymmetric configuration of the source and drain favors a longer term time preservation of the memory of the device. An alternative design that operates with the same energetics and kinetic parameters is to pulse the resistance rather than the voltage. (C) 2008 American Institute of Physics.

A pump-probe experiment that can examine a pure charge migration on a time scale short compared to the onset of nuclear motion is discussed. The mass spectrometric studies of Schlag et al. suggest that short peptide terminated by an aromatic amino acid are particularly suitable test compounds. The pump pulse needs to ionize the molecule on a time scale short compared to the period of the electronic motion, typically sub-fs. However, ionization occurs preferentially when the electrical field of the light is maximal so that the duration of the pulse envelope can be somewhat longer. Detection by photoelectron spectrometry of the peptide cation, to produce a dication, is shown to be able to probe the electronic rearrangement.

The electrical characteristics of Si nanowire gated by an array of very closely spaced nanowire gate electrodes are experimentally determined and theoretically modeled. Qualitative and quantitative changes in the transport characteristics of these devices, as a function of gate-array voltage, are described. Experiments are reported for two widths of Si nanowires, 40 and 17 nm, and for a varying number of gate electrodes, all spaced at a pitch of 33 tim. We find that these top nanowire gate electrodes can be utilized to locally deplete the carriers in the underlying Si nanowire and thus define an array of coupled quantum dots along the nanowire. Reproducible Coulomb blockade is observed, and clear diamond features are obtained when the conductance is plotted in the plane of the source-drain and gate voltages. The regularity of the diamond diagrams is imposed by the regularity of the SNAP top gate electrodes. Model computations of the electronic structure starting from a tight-biding Hamiltonian in the atomic basis suggest that the control made possible by the top gate voltage induces the emergence (and reversible submergence) of a coupled quantum dot structure in an otherwise homogenously doped Si nanowire.

Computing the entropy of a system from a single trajectory is discussed when the energy exchange with the environment includes both mechanical and thermal terms. The physical example chosen as an illustration is a cluster of atoms impacting a hard surface. Each atom of the cluster interacts with the smooth surface by a momentum transfer using the hard cube model [ E. K. Grimmelmann, J. C. Tully and M. J. Cardillo, J. Chem. Phys. 72, 1039 ( 1980)]. Because of the thermal motion of the surface atoms the atoms of the cluster rebound from the surface with a ( random) thermal component to their momentum. The change in the internal energy of the cluster has therefore both a mechanical, work, term and a heat transfer and the heat term contributes to the change in entropy of the cluster but the major contribution is the loss of potentially available work.

Excitation of a coherent electronic wave packet, a linear combination of several electronic stationary states, is discussed with a computational example, the A and B low lying excited states of LiH. Such linear combination results in the electron executing a rotation-like motion in the xz plane with a period of 4 fs. The excitation needs to be shorter than this purely electronic reorganization time and yet the mean energy of the photon should be relatively low so that the A and B states are coherently accessed. These two requirements limit the wave form of the few cycle pump pulse. (c) 2007 Elsevier B.V. All rights reserved.

The response of the electronic system of LiH to a few-cycle strong field is computed by a time-dependent multiconfiguration method using a large, adaptive, basis set. The intensity, pulse duration, polarization, and phase of carrier frequency can all be tuned to steer the motion of the electrons. It is shown possible to, e.g., direct the electrons to move along the Li-H bond or normal to it. By shifting the phase, the electrons can be driven toward the Li nucleus or away from it. When the pulse is polarized not along the bond the result is a rotation of the charge density.

Electrical conduction through a molecule tethered by thiol bridges between two gold clusters is examined from a time-dependent point of view. The shortest electronic time scale for charge migration is a few femtoseconds transit, which is too swift for coupling to the nuclei, that proceeds by super exchange. An order of magnitude slower transfer occurs sequentially through the lower-in-energy sigma bonds. The electronic structure computations are performed at a high level ab initio density functional theory level where the external electric fields are included as part of the Hamiltonian. The structure computed includes the thiol bridge as well as the gold trimer at either end of the molecule. The results shown in detail are for the saturated dithiohexane -S-(CH2)(6)-S- bridge between the two gold trimers.

A chemical system displaced not far from equilibrium is shown to offer a physical realization of a linear sequential digital logic machine. The requirement from the system is that its state is described by giving the current values of the concentration of different chemical species. The time evolution is therefore described by a classical master equation. The Landau-Teller process of vibrational relaxation of diatomic molecules in a buffer gas is used as a concrete example where each vibrational level is taken to be a distinct species. The probabilities (= fractional concentrations) of the species of the physicochemical system are transcribed as words composed of letters from a finite alphabet. The essential difference between the finite precision of the logic machine and the seemingly unbounded number of significant figures that could be used to specify a concentration is emphasized. The transcription between the two is made by using modular arithmetic that is, is the arithmetic of congruence. A digital machine corresponding to the vibrational relaxation process is constructed explicitly for the simple case of three vibrational levels. In this exploratory effort we use words of only one letter. Even this is sufficient to achieve an exponentially large number of memory states.

Physical considerations supported by numerical solution of the quantum dynamics including electron repulsion show that three weakly coupled quantum dots can robustly execute a complete set of logic gates for computing using three valued inputs and outputs. Input is coded as gating (up, unchanged, or down) of the terminal dots. A nanosecond time scale switching of the gate voltage requires careful numerical propagation of the dynamics. Readout is the charge (0, 1, or 2 electrons) on the central dot.

Stimulated Raman adiabatic passage (STIRAP) is a well-studied pump-probe control scheme for manipulating the population of quantum states of atoms or molecules. By encoding the digits to be operated on as ``on'' or ``off'' laser input signals we show how STIRAP can be used to implement a finite-state logic machine. The physical conditions required for an effective STIRAP operation are related to the physical conditions expected for a logic machine. In particular, a condition is derived on the mean number of photons that represent an on pulse. A finite-state machine computes Boolean expressions that depend both on the input and on the present state of the machine. With two input signals we show how to implement a full adder where the carry-in digit is stored in the state of the machine. Furthermore, we show that it is possible to store the carry-out digit as the next state and thereby return the machine to a state ready for the next full addition. Such a machine operates as a cyclical full adder. We further show how this full adder can equally well be operated as a full subtractor. To the best of our knowledge this is the first example of a nanosized system that implements a full subtraction.

The dissociation of peptide ions has been found to have ultrafast components that in many ways are uniquely different from typical unimolecular kinetics. As such, some peptide reactions provide new channels, which do not conform to statistical models of reaction kinetics. When the dissociation rates are in the 100 fs range, they are in a time scale where statistical methods do not yet apply, although molecules that have not yet dissociated will later in time undergo statistical redistribution of their excess energy, which, however, may not lead to noticeable reactivity within the experimental time frames for large peptides and hence are simply dissipative. This work is meant to reconcile the long time statistical results of Lifshitz et al. (2003) with the work of Schlag et al. (1995/6) that suggests an alternate parallel and much faster time scale for dissociation. It is argued that the two sets of results and interpretations augment one another and in fact open up a most interesting new field of peptide kinetics in addition to the unimolecular behavior, which becomes de facto arrested by the shear size of the molecule being unable to find a transition state on any reasonable time scale.

The mechanism for charge transport in dithio molecular wires tethered between two gold electrodes is investigated, using both a steady state and a time-dependent quantum mechanical approach. The interface with the electrodes is modeled by two gold clusters and the electronic structure of the entire Au-n-S-bridge-S-Au-n system is computed ab initio at the DFT level and semi-empirically, with the extended Huckel theory. Current vs. applied bias, I-V, curves are computed using a scattering Landauer-type formalism in a steady state picture. The applied source-drain and gate voltages are included at the ab initio level in the electronic Hamiltonian and found to influence strongly the I-V characteristics. The time evolution of a non stationary electronic wave packet initially localized on a gold atom at one end of the extended system shows that charge transfer proceeds sequentially, by a hopping mechanism, to the opposite end. Analysis of the effective one electron Hamiltonian matrix shows that the sulfur atom endows a resistive character to the Au-C-S junctions. The S atoms are however rather well coupled to both the gold and carbon atoms so that typically the super exchange limit for electron transfer is not reached unless the molecular bridge is saturated and the Fermi window function is narrow.

Ultrafast, subfemtosecond charge migration in small peptides is discussed on the basis of computational studies and compared with the selective bond dissociation after ionization as observed by Schlag and Weinkauf. The reported relaxation could be probed in real time if the removal of an electron could be achieved on the attosecond time scale. Then the mean field seen by an electron would be changing rapidly enough to initiate the migration. Tyrosine-terminated tetrapeptides have a particularly fast charge migration where in < 1 fs the charge arrives at the other end. A femtosecond pulse can be used to observe the somewhat slower relaxation induced by correlation between electrons of different spins. A slower relaxation also is indicated when removing a deeper-lying valence electron. When a chromophoric amino acid is at one end of the peptide, the charge can migrate all along the peptide backbone up to the N end, but site-selective ionization is probably easier to detect for tryptophan than for tyrosine.

The temporal evolution of the entropy of a mechanical system as described by a single trajectory is computed using the Clausius [Philos. Mag. 40, 122 (1868)] equality. This requires computing the maximal work that can be done by the system and comparing it to the actual work performed. A single trajectory suffices to determine the entropy when it is ``typical,'' meaning that average values of mechanical variables will not be different when computed using trajectories with different initial conditions. The results are illustrated for small rare gas clusters heated and compressed by an impact at a hard surface. (c) 2006 American Institute of Physics.

A cold atomic cluster can be very rapidly heated and compressed by a hypersonic impact at a hard surface. The impact can be simulated by computing a classical trajectory for the motion of the atoms. By suddenly confining the hot and dense cluster within a rigid container, it is possible to monitor the time evolution of the force acting on the faces of the container. It is found that the pressure computed this way very rapidly decays to a time-independent value. After a somewhat longer time, this value reproduces the value for the pressure computed as the sum of the kinetic and internal pressures. This agreement is expected for a system in equilibrium. These observations support the conclusion that there is a fast relaxation to thermal equilibrium in these essentially hard-sphere systems. The deviation from equilibrium is primarily due to the propagation of shock waves within the cluster. The equilibrium pressure can reach up to the megabar range.