The full multiple spawning (FMS) methodology for solving the time dependent Schrodinger equation for multiple electronic states is extended to reactive collisions on several electronic states. The computational complexity remains unchanged, less than double that of a quasiclassical trajectory computation. It is shown how the spawning approach can describe the bifurcation of the wave function into components exiting in different directions of space, as is the case when rearrangement of the atoms takes place. Low energy H+ + D-2 and H + H-2 + collisions, which result in both reactive and nonreactive charge transfer are used as an illustration. The FMS method is used to generate converged opacity functions and cross sections even at higher energies when dissociation is energetically allowed. This suggests that also on a single potential energy function the FMS method offers a viable route to full dimensional reactive quantal scattering computations. For the H-3(+) system, a diatomics in molecules (DIM) potential energy function is used in a diabatic basis where three electronic states are coupled. Comparison is made with the classical path approximation, the trajectory surface hopping method and stationary quantum mechanical scattering computations, which used the sudden approximation and the coupled states method. For the H+ + D-2 collision, our results are close to those already published. The computations for the H + H-2(+) collision, where the initial channel is an excited one, are distinctly different from the results of earlier, approximate, approaches.

A Huckel-type effective Hamiltonian is used to examine the conditions for site-selected reactivity. The example is the dissociation of a positive ion, as in mass spectrometry. Coupling to the dissociative channels is included by a rate operator. We examine the time evolution of the charge and bond order matrices and of the yield of fragments following a localized initial ionization. Dissociation is found to follow the (positive) charge. Variations in the local properties can markedly change the dissociation pattern. A more statistical limit is reached when the migration of charge is unimpeded. (C) 1998 Elsevier Science B.V.

Translational to electronic energy transfer with or without a concomitant chemical reaction is studied for the Evans-Polanyi model. We explore the possibility of light emission from an electronically excited stare following a high-energy collision. This can be viewed as an inverse process to a Woodward-Hoffmann photochemically allowed four-center reaction. The collision is described using this Evans-Polanyi method where the two diabatic electronic states correlate with the states of the reactants and products. The effective coupling of the diabatic starts is found to be localized and the non-adiabatic regime is transversed rapidly so that facile electronic excitation is possible. (C) 1998 Elsevier Science B.V.

The separation of radial electronic and nuclear motions is discussed with special reference to high Rydberg states of molecules. An inverse separation is obtained when the rapid nuclear motion instantaneously adjusts itself to the position of the Rydberg electron. The electron moves in the potential averaged over the position of the nuclei (and their valence electrons). This inverse separation is useful when omega n(3) > 1, where omega is the spacing of nuclear energy states (in au) and n is the principal quantum number of the Rydberg electron whose orbital period increases as n(3). The inverse Born-Oppenheimer separation can break down owing to the finite kinetic energy of the Rydberg electron. Like the Born-Oppenheimer separation, its inverse can also be formulated in an adiabatic or a diabatic basis. The diabatic inverse Born-Oppenheimer is practical both for interpretation of zero electron kinetic energy (ZEKE) spectra and for computations. Explicit results are given for a model system of an electron orbiting a vibrating dipole, identifying the relevant coupling constants. The discussion emphasizes the radial motion and the limits discussed here are not quite equivalent to the four (or, actually, five) Hund's coupling cases relevant to angular momentum coupling schemes. (C) 1998 John Wiley & Sons, Inc.

The probability of an error in a Monte Carlo integration is shown to be exponentially small in the number of points used, with the magnitude of the exponent being determined by a relevant entropy. Implications for importance sampling and for the significance of the maximum entropy formalism an discussed. Specifically it is shown that the optimal sampling distribution is one of maximal entropy. The Monte Cal-lo method or its variants play an essential role in classical trajectory computations. Practitioners are aware that generating few trajectories is already sufficient for typical quantities such as the mean energy of the products to settle down to the correct value. The present results provide further insight and suggest why a distribution of maximal entropy can provide such useful representation of the results. The discussion is based on the information theoretic bound for the error of transmission and can also be derived from the Chernoff bound in hypothesis testing. (C) 1998 Elsevier Science B.V.

{{Size and kinetic energy distributions of the products of size and energy selected ammonia clusters, (NH3)(n)NH4+

{{Measurements of the collisional energy transfer of size and energy-selected ammonia cluster ions (NH3)(n)H+

Classical trajectory computations for thermal reactants on a six-atom potential show a forward scattering component which is correlated with the HF product being formed with high vibrational excitation. These trajectories are peripheral collisions where the F atom approaches CH4 with a high impact parameter and reaction is through a nearly collinear F-H-C configuration with a stretched F-H bond. Other trajectories are well described by a hard-sphere model whose cutoff is below the range of peripheral collisions. Comparison is made with the F + H(2 )and other reactions where nearly thermoneutral channels correlate with forward scattering. (C) 1998 Elsevier Science B.V. All rights reserved.

Classical trajectory computations and a kinematic analysis of the collision of two CH3I molecules are presented. The yield of molecular and atomic iodine is examined as a function of reactant translational and vibrational energy. The potential energy function is of the LEP form, which has a high late barrier where all bonds are extended. Vibrational excitation of CH3I enhances the barrier crossing and molecular products are formed highly vibrationally excited. Kinematic considerations indicate the same trends. The results are discussed as a possible mechanism for the formation of molecular iodine via ultrafast heating achieved in wall collisions of CH3I clusters. (C) 1998 Elsevier Science B.V. All rights reserved.

Disorder is shown to induce qualitative changes in the electronic spectrum and hence in the response of assemblies of quantum dots. Lattices of quantum dots have one unique source of disorder: the dots themselves can be prepared with a narrow distribution of properties but they are never quite identical. This is unlike a lattice of atoms or molecules. In addition, lattices of quantum dots have a configurational disorder and can also be prepared with compositional disorder. The relaxation of selection rules and the splittings of degeneracies due to symmetry breaking induced by these fluctuations can be probed by optical means. Special attention is given to the enhancement and to the variation of the second harmonic response as a function of the spacing between the dots.

Coexistence of prompt and delayed decay modes of energized polyatomic molecules is discussed with reference to the special features of larger molecules which makes it amenable to experimental observation by a suitable choice of initial conditions. The molecular parameters identified by the RRKM theory of unimolecular (delayed) decay suffice to characterize the prompt process as well. The expected ``kinetic stability'' of large molecules is thus not necessarily the rule, and fast processes are possible, suggesting the possibility of experimental control.

The optical second-harmonic response of a finite hexagonal lattice is computed as a function of the inter particle separation. In agreement with experiments on Langmuir monolayers of silver quantum dots, the computed response exhibits a peak due to a transition from localized electronic states to a band-like structure. The localization is due to the fluctuations in the particle size and position. For a perfect lattice the variation of the nonlinear response with the inter particle separation is qualitatively different. The role of the symmetry breaking is demonstrated at the tight binding level of electronic structure computations. (C) 1998 Elsevier Science B.V. All rights reserved.

A classification of ZEKE spectra into two classes based on operational criteria is useful for discussion. The proposal is that some of the different and seemingly conflicting effects reported for different molecular (or the same molecule for different excitations), such as the role of an external field, are due to these two distinct classes of states which can be optically accessed. Class A is the direct, ``front door'' entry where the states excited are those which are detected by the delayed ionization. Class B is a very prevalent but indirect ``backdoor'' route where it is only the interaction of the Rydberg electron with the core, possibly aided by external perturbations, that allows a signal to be detected upon ionization. The operational criteria for distinguishing between or even exploiting the features of the two classes are discussed. Such attention might be useful as new techniques for class B spectra are developed.

Chemical reaction dynamics is making increasing contact with `real' chemistry: examination of more elaborate reaction mechanisms typical of organic chemistry, the study of chemical reactions where the medium plays an active role (as is often the case in solution and on surfaces) and the ability to mimic systems of biochemical complexity are all of current interest. Much of our early conceptual understanding was acquired by the study of isolated, simple chemical exchange reactions in which one bond is broken and another bond is formed, in concert. A central feature in these reactions is the high selectivity which can be achieved by the choice of initial conditions and the considerable specificity of the resulting products. These themes do carry over to the world of more complex systems. Applications discussed include four center reactions, activated chemical reactions in solution, in clusters and on surfaces and photochemical processes. Surprisal analysis, long used to characterize the selectivity and specificity in simple reactions, is equally applicable here and the dynamical origin for the approach is discussed. The primary conclusion is that at the dawn of the new millennium, chemical reaction dynamics is ready to make inroads into the world of reactions of realistic complexity.

High molecular Rydberg states, whose time evolution exhibits multiple time scales are discussed as an example of a system which can be examined in detail. Three bottlenecks to the sampling of phase space, associated with an incomplete mixing of the zeroth order quantum numbers, are identified. The physics of all three is that the number of open ionization channels is smaller than the number of quasi isoenergetic zero order discrete states and that an electron with a high orbital angular momentum, which is far from the core, cannot effectively couple to it. States trapped behind the bottlenecks have a high resilience to decay and such states are possible even high above the ionization threshold and in the presence of external perturbations. On the other hand, states that are directly coupled to the ionization channels decay promptly, with less sampling of the dense manifold of isoenergetic delayed states. We conclude that the decay of high molecular Rydberg states provides a useful analogue for unimolecular reactions from a dense set of states which typically results in a prompt and a delayed decay.

The conical intersection in the collision of a Na(3p(2)P) atom with H-2, occurs at large H-H distances, Time dependent quantal computations exhibit many sequential non-adiabatic couplings, each of which is localized in time, where the quenching probability per traversal is small. During the collision, the population of the ground state increases almost in a random walk fashion until the partners recede after many H-2, vibrational periods. Changing the masses suggests that other systems can also exhibit such a snarled quenching process which cannot be described as a single non-adiabatic event per collision.

A classically motivated quantal method, designed to allow for molecular dynamics occurring on more than one potential-energy surface, is extended in two directions. The extensions are shown to be accurate while retaining the classical flavour which is useful for both interpretation and computation. The first extension allows for the evaluation of the required inter-state coupling matrix elements for potential-energy surfaces even when these are given numerically rather than fitted to some analytical form. Moreover, the procedure is a local one, requiring only the values of the two potentials and their gradients. It is thus particularly suitable for applications where the electronic and nuclear problems are solved simultaneously. The second extension strengthens the connections to classical mechanics while avoiding ambiguities in the choice of the classical trajectories which will represent the dynamics. The accuracy and limitations of the proposed procedures are tested for several model problems.

The qualitative physical aspects and the quantitative description of time and frequency resolved absorption spectroscopy of high molecular Rydberg states are discussed. The frequency is that of the excitation laser and the time is the independently variable delay before detection. The discussion allows for the presence of a weak external electrical field. The essential new ingredient is the finite slice of Rydberg states that are detected (=are in the detection window) and the variation of this population with time due to the coupling of the Rydberg electron with the molecular core. Line shapes are provided showing the effect of the depth of the detection window and the advantages and limitations imposed by the finite width of the excitation laser. The sharpening of the spectrum as the delay time to detection is increased is also illustrated. The quantitative theory is expressed in terms of the expectation value of a detection operator; describing the range of states that can be ionized by the delayed field, taken over a wave function. This wave function is the state of the system at the time of detection. However, even just at the end of the excitation stage, due to the interseries coupling, this wave function is not identical to the state that is directly optically accessed. The time correlation function of this wave function, obtained as a Fourier transform. of the frequency resolved spectrum, is shown to provide further insight into the dynamics, the more so when the excitation laser has a narrow width in frequency. (C) 1997 American Institute of Physics.

The absorption spectrum of bound Rydberg states which can be detected by a delayed, pulsed field ionization is computed. The spectrum, measured for various delay times, provides information on the short and the longer time dynamics of high molecular Rydberg states. A quantitative dynamical theory, based on an effective Hamiltonian formalism is applied, illustrating the role of the Rydberg electron-core coupling and of an external electrical field in the delay-time dependent spectra. The sharpening of the spectra for longer delay times is reproduced by the dynamical computations. It is found that the overall intensity, as a function of the delay time before detection, is well described by a double exponential decay where the short lifetime is primarily a manifestation of the direct autoionization to the continuum, while the long lifetime is due to interseries coupling. Both lifetimes increase with the principal quantum number of the Rydberg states. The notion of trapped `'reservoir states'' is illustrated by the computational results, with special reference to a kinetic model analysis. The role of the initially optically accessed state(s) and of the depth of detection, in particular with regard to the intensity, is demonstrated. The effect of varying the strength of an external de field in the time interval prior to the detection is illustrated by the dynamical computations, with respect to both the decay kinetics and the intensity of the spectrum. (C) 1997 American Institute of Physics.