Ultrafast femtosecond Coulomb explosion of charged homogeneous (Xen) and heterogeneous doped (HIArn) small and medium sized clusters (n<60) is studied resting on the picture of a vertical high-order multiphoton ionization from the ground state nuclear configuration. The final average atomic velocity (simulated at constant charge) increases with increasing the cluster size, and at constant cluster size increases linearly with the ion charge, in accord with the predictions of an analytical model. The linear dependence of the reciprocal explosion time on the charge is also in accord with the analytical prediction. From the energetics of the Coulomb explosion (reflecting a probable initial atomic distribution of the cluster size for small clusters), a nonvertical multiphoton ionization during the Coulomb explosion cannot be inferred.

We address some of the unique and basic features of molecular clusters, which involve (i) surface, interior, and site-selective energetics and dynamics, and (ii) the size dependence of the energetic, spectroscopic, electromagnetic, and dynamic attributes of large finite systems. Cluster-size equations provide a unified (but not universal) description of the “transition” of different attributes of clusters to those of the macroscopic bulk material. We explored fundamental issues, e.g., the physical origins of cluster-size effects, which originate either from cluster packing or from excluded volume contributions, and discussed some applications for the quantification of the size dependence of site-specific ionization potentials, extravalence and intravalence electronic spectroscopy, collective vibrational excitations, and dynamic effects. The quantification of dynamic cluster-size effects for energy acquisition in high-energy cluster-wall collisions opens avenues for the exploration of cluster-impact thermal femtosecond chemistry.

Microshock wave propagation in ArN (N=55–555) clusters generated by high-energy cluster-Pt surface impact (cluster velocities v=1–10 km s−1) is explored by molecular dynamics simulations. The gross features of the dynamics of the intracluster microshock wave propagation at this impact velocity range are not sensitive to the details of the repulsive potential (i.e., the Lennard-Jones or the exp-6 form). The propagation of the microshock within the cluster was quantified by the time dependence of the first moment of the total energy. A linear dependence between the microshock (compression) velocity us and the cluster impact velocity v is observed and for sufficiently large clusters (N≥321) us≊v. For large clusters (N≳321), the cluster Hugoniot temperature–pressure relations are qualitatively similar to those for the compression of macroscopic fluid Ar.

Molecular dynamics simulations of the dissociation of I2 embedded in large Arn (n = 319, 553) clusters, which impact at high velocities (ν = 7–15 km s−1 1 ) on Pt surfaces, result in information on heterogeneous and homogeneous dissociation mechanisms. A broad distribution of dissociation lifetimes is exhibited, which can be attributed to prompt and retarded heterogeneous dissociation and to prompt, retarded and outbound homogeneous dissociation events. The propagation of a microshock wave within a large cluster can be interrogated by the homogeneous dissociation of a chemical probe, with the velocity of the propagation of the dissociation front being close to the cluster impact velocity.

Molecular dynamics simulations demonstrate facile dissociation of halogen molecules embedded in rare gas clusters upon impact at a surface at collision velocities up to 10 km/s. Two pathways are discerned: a heterogeneous dissociation of the molecule on the surface and a homogeneous mechanism where rare gas atoms which have rebounded from the surface cause the translational–vibrational coupling. The total yield of dissociation of the clustered molecule can reach up to 100%, whereas the yield of dissociation of the bare, vibrationally cold molecule saturates below 40%. A systematic study of the role of different conditions is made possible by not accounting for the atomic structure of the surface. The role of dissipation at the surface is found, however, to be quite important and is allowed for. Larger clusters, clusters of the heavier rare gases and a more rigid surface, all favor the homogeneous mechanism. Evidence for a shock front which, upon the initial impact, propagates into the cluster; the binary nature of the homogeneous dissociation process; and the absence of a dominant cage effect are discussed. A quantitative functional form of the velocity dependence of the yield of dissociation, which accounts for the size of the cluster, the rigidity of the surface and other attributes, is used to represent the data. The physics of the processes within the cluster is dominated by the novel dynamical features made possible when the duration of the atom–molecule collisions is short compared to the vibrational period. This ‘‘sudden’’ regime is sudden with respect to all modes of the nuclear motion and provides a hitherto unavailable tool for examination of reaction dynamics under extreme conditions.

In this paper, we explore cluster–surface impact induced dissociation of an I2 molecule initially embedded within an I2ArN (N=11–553) cluster, which collides with a Pt surface. Molecular dynamics simulations of high-energy I2ArN–Pt surface collisions (with initial center of mass velocities v=0.2–10 km s−1 and initial kinetic energies E0K=1 eV−1.2×104 eV) provide information on the yields and time scales for energy acquisition by the cluster and by the surface and energy deposition to the guest molecule via the formation of an intracluster microscopic shock wave, as well as on the I2 dissociation dynamics. The intracluster shock wave is characterized by a temporal peak in the cluster potential energy and in the saturation of the cluster temperature, with the sum of the yields for potential and kinetic energy deposition into the cluster being 0.5–0.6. The cluster residence time (τ=50–800 fs over our velocity and cluster size domain) coincides (within 20%) with the time scale for the cluster energy acquisition, decreasing linearly with v−1 and obeying a dynamic size equation τ∝(N+2.9)1/3. The characteristic time tp for energy deposition to the I2 molecule via a local mechanism involving pair interactions is also close to τ. The initial cluster kinetic energy dependence of the dissociation yields YD of I2 reveals a gradual increase of YD towards unity above a threshold at the energy Et. For smaller (N=11,53) clusters, Et/N is close to the dissociation energy of bare I2, while for larger clusters Et exhibits an exponential N dependence. Cluster impact dissociation of I2 in I2ArN results in higher YD values (≳0.4) than the high-energy collision of bare I2 with the Pt surface for which YD saturates at 0.35. The I2 dissociation times 〈τD〉, which were characterized by averaging over the first passage times for the attainment of the turning point of the I–I intramolecular Morse potential for reactive trajectories, fall in the range 170–800 fs, exhibiting a marked inverse kinetic energy dependence, revealing an increase with increasing cluster size and obeying the rough relation 〈τD〉≂2τ, i.e., being proportional to the cluster radius. Energy acquisition and dissociation times are comparable to or even shorter than the vibrational time [τ(I2)=156 fs] of the I2 molecule, opening up a new research area of thermal femtosecond chemistry.

Molecular dynamics simulations of high-energy collisions (initial kinetic energies E(k)0 = 10-10(6) eV) of Kr(n) (n = 8-512) clusters with a rigid Pt surface provide a microscopic description of the formation of an intracluster shock wave (temperatures up to 3 x 10(5) K and cluster internal potential energies up to approximately 10(4) eV) on a time scale of 10-500 fs, which is accompanied by novel ultrafast energy acquisition processes. High-energy ((10(-5)) x 10(3) eV) high-yield (0.5%-10%) interatomic Kr-Kr pair repulsive excitation is exhibited, being manifested in outer-shell electronic excitations and ionization, multiple ionization and Auger processes.

The time-resolved dynamics of diffusionless cube → ring isomerization of the (NaCℓ)4ionic cluster was interrogated by constant energy molecular dynamics simulations utilizing the first passage time method. The isomerization was induced by several excitation modes of the nuclear motion, i.e., nonselective, bond selective, ion selective and normal mode selective vibrational excitations. The dependence of the isomerization rates on the excess vibrational energy was successfully analysed in terms of the statistical RRK theory. Concurrently, we have calculated the intracluster vibrational energy redistribution times, their dependence on the excitation mode and on the excitation energy. At high excess vibrational energies traces of the onset of mode selectivity are manifested in the nonstatistical temporal distribution of the isomerization events.

The time resolved dynamics of diffusionless cube → ring isomerization of the Na4Cl4 cluster was interrogated by constant energy molecular dynamics simulations, utilizing the first passage time method. The nonreactive isomerization induced by nonselective vibrational excitation is well accounted for in terms of the statistical RRK theory, opening avenues for experimental exploration of time-resolved cluster isomerization dynamics.

A mean first passage time expression is developed for a complex system embedded in a heat bath following reduction into a 1D equivalent chain, using Lanczos tridiagonalization. The results are compared to 1D, 2D and 3D random walk results.

A new approach to discretization of a continuous band coupled to a discrete state is provided by the Lanczos tridiagonalization procedure, which uses linked moments of the continuum with respect to the discrete state. Numerical convergence of this scheme is shown for two models of the line-shape function.

The irreducible moment version of the recursive-residue-generation method is used to study the dynamical behavior of a multimode system, where one radiatively active mode is coupled to a laser field and in turn, intramolecularly, to a set of inactive background modes. Nonperiodic behavior of the survival probability ``observable'' is numerically detected under certain conditions (large enough background and a randomly scattered frequency spectrum). A quantitative condition is given for the prevalence of this seemingly ``chaotic'' dynamics.

Previous studies on the use of diagrammatic moment methods in the recursive residue generation method [I. Schek and R. E. Wyatt, J. Chem. Phys. 83, 3028, 4650 (1985)] are extended, with emphasis upon the role played by linked diagrams. Equivalence between the Green function for the source state (which initiates the recursion method) in the zero order and the corresponding tridiagonal (Lanczos) representation is shown. Chain parameters in the tridiagonal representation are constructed by comparing linked diagrams in the two representations and the dynamics of the source state is introduced in terms of the linked moments. The equivalence between Lanczos states and generalized doorway states is shown. Finally, a closed expression for the level shift of the source state (due to its interaction with the rest of the states) is given, using a diagrammatic approach in the tridiagonal representation.

In this paper we analyze the effects of the fluctuations of laser amplitude on the multiphoton excitation of a sparse multilevel molecular system. It is found that contrary to the excitation by a laser with phase fluctuations, the stochastic contribution of the amplitude fluctuations is non-diagonal and scrambles the off-diagonal elements of the general molecular density matrix, resulting in temporal oscillations of these terms. The chaotic field model for the laser amplitude cannot force the applicability of the kinetic master equation for a general multilevel system. It is found that, for the two-level system driven by a chaotic field model laser, The stochastic interlevel rate dumps the oscillatory behaviour of the molecular populations, validating the master equation by T1-type effects.

Irreducible moments - power moments of the Hamiltonian in which diagrammatic paths not contributing new information are deleted before the numerical evaluation - are used to construct a tridiagonal (chain) representation of the Hamiltonian. From the chain parameters, residues and eigenvalues are computed so that the time evolution of multi-state (up to about 12000 states have been used) systems can be predicted.

Three theoretical models were advanced for the dynamics of molecular multiphoton excitation: (i) The zero-order optically active mode connected by intramolecular random anharmonic couplings to a background manifold. (ii) Molecular eigenstates coupled by random radiative transition dipole moments. (iii) The kinetic master equation approach. It is demonstrated that in the Markoffian limit, as long as the intramolecular vibrational relaxation width is small relative to the Rabi frequency, these three approaches are equivalent. In the case of high-field excitation, coherent quantum effects are exhibited even in a randomly coupled system. Resurrection of the quantum oscillations and coherent pumping can be exhibited in intense field excitation on the time scale of intramolecular vibrational relaxation.

In this paper we investigate the effect of laser phase fluctuations on the ionization dynamics of a two-level system. The conditions for validity of the kinetic master equation for the description of a resonant two-photon ionization process of an isolated molecule were established on the basis of analytical results and numerical simulations.