The fractal properties of the total potential energy V as a function of time t are studied for a number of systems, including realistic models of proteins (pancreatic polypeptide, bovine pancreatic trypsine inhibitor, and myoglobin). The fractal dimension of-V(t), characterized by the exponent gamma, is almost independent of temperature, and increases with time, more slowly the larger the protein. Perhaps the most striking observation of this study is the apparent universality of the fractal dimension, which depends only weakly on the type of molecular system. We explain this behavior by assuming that fractality is caused by a self-generated dynamical noise, a consequence of intermode coupling due to anharmonicity. Global topological features of the potential energy landscape are found to have little effect on the observed fractal behavior. [S1063-651X(99)11402-8].

An improved approximation to the time-dependent Schrodinger equation is developed by correcting the time-dependent self-consistent field ansatz with a Jastrow prefactor defined via a set of variationally determined time-dependent parameters and a linearly independent set of prespecified spatial functions. The method is applicable in any number of dimensions, conserves norm and energy, is without parametric singularities, possesses an internal estimate of the accuracy, and has computational costs that scale algebraically with the number of degrees of freedom. The new formalism is applied to a two-dimensional double well potential to demonstrate the improved accuracy of the method. An extension of the method to electronically nonadiabatic problems is also presented. (C) 1999 American Institute of Physics. [S0021-9606(99)01616-5].

An algorithm for first-principles calculation of vibrational spectroscopy of polyatomic molecules is proposed, which combines electronic ab initio codes with the vibrational self-consistent field (VSCF) method, and with a perturbation-theoretic extension of VSCF. The integrated method directly uses points on the potential energy surface, computed from the electronic ab initio code, in the VSCF part. No fitting of an analytic potential function is involved. A key element in the approach is the approximation that only interactions between pairs of normal modes are important, while interactions of triples or more can be neglected. This assumption was found to hold well in applications. The new algorithm was applied to the fundamental vibrational excitations of H(2)O, Cl(-)(H(2)O), and (H(2)O)(2), using the Moller-Plesset method for the electronic structure. The vibrational frequencies found are in very good accord with experiments. Estimates suggest that this electronic ab initio/VSCF approach should be feasible, with reasonable computational resources, for all-mode calculations of vibrational energies and wave functions for systems of up to 10-15 atoms. The new method can be also very useful for testing the accuracy of electronic structure codes by comparing with experimental vibrational spectroscopy. (C) 1999 American Institute of Physics. [S0021-9606(99)01928-5].

A considerable effort has been recently directed toward developing separable (mean-field) approximations for quantum molecular dynamics, such as the time-dependent self-consistent field (TDSCF) or the classical separable potential (CSP) methods. Unlike numerically exact solutions of the time-dependent Schrodinger equation, the accuracy of separable quantum dynamical simulations crucially depends on the choice of the coordinate frame. Since the approximate methods replace exact interactions between individual degrees of freedom by mean-field couplings, the goal is to work with coordinates which separate modes as well as possible. Unfortunately, for a larger system no practical way to optimize coordinates for mean-field quantum dynamics exists. Here, we suggest a simple and practical method for estimating the error of separable simulations, which allows us to select from a given set the optimal coordinate frame, or to identify modes, the couplings between which have to be treated more accurately. In the spirit of the CSP method, the time-dependent error estimate is based on differences between the exact and mean-field Hamiltonians along a swarm of classical trajectories. This makes it possible to very simply determine optimal coordinates for CSP or TDSCF propagation before actually performing any quantum simulation. The present methodology is applied to realistic and experimentally relevant systems, namely to the ultrafast relaxation following electron photodetachment in I- Ar-n (n=2 and 12) and Cl-H2O clusters. It is shown that the accuracy of separable quantum methods is strongly system and coordinate dependent. Comparison with numerically exact results shows that the suggested error measure correlates well with the actual error of the approximate quantum propagation, the accuracy of which can be consequently improved significantly, practically without additional computational effort. Finally, the feasibility of the proposed method for simulations of large polyatomic systems is demonstrated. (C) 1999 American Institute of Physics. [S0021-9606(99)00820-X].

The photodissociation of HCl adsorbed on the surface of an Ar-12 cluster is studied by semiclassical molecular dynamics simulations, using a surface-hopping approach for the nonadiabatic transitions. The DIM method is used to construct the 12 potential energy surfaces that are involved, and the nonadiabatic couplings. The results are compared with previous studies on HCl embedded inside Ar clusters and on the triatomic Ar-HCl cluster. The main findings are the following: (1) There is a yield of about 1% for recombination onto the ground electronic state of HCl, roughly the same as for HCl embedded inside Ar-12. (2) Photodissociation lifetimes much longer than for Ar-HCl are found. (3) The kinetic energy distribution of the H atom shows large energy transfer to the cluster, greater than in the case of HCl in the embedded geometry in (Ar)(12)HCl. (4) An interesting mechanism leads to the formation of some fraction of very ``hot'' Cl atoms. (5) About 10% of the Cl is left trapped in (Ar)(m)Cl clusters. (6) The branching ratio P-1/2:P-3/2 for the Cl atoms that leave the cluster shows electronic cooling compared to the isolated HCl molecule case. The results throw light on the role of local geometry in photodissociation/recombination processes, and in particular on the mechanisms pertinent in the case of surface-adsorbed species. The nature of the results, showing strong cage effects at the surface geometries is to a large extent a consequence of the encapsulation of the H atom, obtained for the structure of the (Ar)(12) HCl cluster. (C) 1999 American Institute of Physics. [S0021-9606(99)70222-9].

Helium atoms are scattered from a beam of water clusters with mean size (n) over bar = 10 in an angular and velocity resolved collision experiment. The measured peaks are identified as elastic scattering, rotationally inelastic scattering of monomers, and vibrational excitation of the clusters. To interpret the latter processes quantum calculations are performed for He+(H2O)(11) collisions using the TDSCF approximation which includes the anharmonic force field of the water clusters and energy transfer between the modes. By comparison of the calculated and experimental results, the most probable excitations correspond to energy transfer for around 7 meV and, with smaller intensities, up to 20 meV. The excitations correspond to shearing modes of the outer rings and the middle ring of the highly nonrigid cluster against each other. (C) 1999 American Institute of Physics. [S0021-9606(99)01546-9].

An approximate quantum mechanical method is proposed for the calculation of inelastic scattering of an atom from a large anharmonic cluster or molecule. The method is based on: (a) computing the vibrational states of the cluster (or molecule) in the vibrational self-consistent field approximation; (b) treating the scattering of the atom to a first approximation as taking place from a vibrationally frozen cluster; (c) obtaining inelastic transitions by a distorted wave approximation, where the coupling is the vibrationally dependent part of the atom/cluster potential. Computationally convenient expressions are worked out. The method is applied to He scattering from Ar-13 and the results are compared to experimental data for size-dispersed clusters. Good qualitative agreement is found. The merits of the proposed method compared with alternative approaches are discussed. (C) 1998 American Institute of Physics. [S0021-9606(98)00215-3].

An approach based on the Time-Dependent Self-Consistent Field (TDSCF) is used to carry out quantum calculations of inelastic atom scattering from large, highly anharmonic clusters. The computation is carried out for low-energy collisions of Ar with (H2O)(11), and all the vibrational modes of the cluster are included. The method treats the collider atom classically, but the dynamics of the interacting anharmonic modes of (H2O)(11) is handled quantum mechanically. The results provide insight into the collision physics of large systems having soft anharmonic modes, and into the role of quantum effects in such cases. The main findings are the following: (a) Large differences are found between quantum and classical results with regard to energy transfer into specific cluster modes. (b) Classical calculations wrongly predict efficient excitation of many stiff modes, including processes that are quantum-mechanically forbidden. (c) Single quantum excitations are the most important transitions at the collision energy used. (d) Atom-atom pair distribution functions of (H2O)(11) after the collision show insignificant differences from the corresponding precollision distribution functions. The results show that quantum calculations of collision dynamics of low-temperature anharmonic clusters are feasible, and also necessary in view of the prediction of significant quantum effects. (C) 1998 American Institute of Physics.

The structural and dynamical properties of a saturated chemisorbed hydrogen monolayer on a model bcc(110) metal surface were studied by molecular dynamics simulations over a range of temperatures from 100 to 300 K. The potential function used, including both the hydrogen/metal interaction and the interactions between the hydrogens, was calibrated in part from experimental data. At low temperatures, the monolayer has an ordered, broken symmetry state with regard to the underlying metal surface. As temperature is increased, an order-disorder transition takes place. We report studies of static and dynamical structure factors; of pertinent order parameters and, where applicable, of phonon dispersion in order to gain insight into the phases. The disordered phase exhibits anisotropy with uniaxial short-range order. We comment on the relation of the results to recent experimental studies of H/W(110) and H/Mo(110), and suggest future experiments to explore the high temperature phase. (C) 1998 Published by Elsevier Science B.V. All rights reserved.

An approach based on He scattering is used to develop an atomic-level structural model for an epitaxially grown disordered submonolayer of Ag on Pt(111) at 38 K. Quantum scattering calculations are used to fit structural models to the measured angular intensity distribution of He atoms scattered from this system. The structure obtained corresponds to narrowly size-dispersed compact clusters with a modest translational disorder, and not to fractals, which might be expected due to the low surface temperature. The clusters are up to two layers in height, the lower one having only a few defects. The relations between specific features of the angular scattering distribution, and properties such as the cluster sizes and shapes, the inter-cluster distance distribution, etc, are discussed. The results demonstrate the usefulness of He scattering as a tool for unraveling new complex surface phases. (C) 1998 Elsevier Science B.V. All rights reserved.

{{A semiempirical model is developed, based on ab initio calculations, to provide an analytic representation of excited-state potential energy surfaces for (H2O)(n)

The vibrational predissociation rates of triatomic van der Waals complexes were investigated by a new, computationally simple method. The method is based on three approximations: (a) metastable vibrationally excited states of the complex are described by the vibrational self-consistent field (VSCF) approximation, (b) the coupling among the rotational states of the dissociating diatomic fragment is treated by the infinite order sudden (IOS) approximation, and (c) the vibrational transition that leads to dissociation is treated by the distorted wave Born approximation (DWBA). The predissociation rates, the product rotational state distributions, and the lifetimes of vibrationally excited states of He-ICl and He-I-2 are all computed and are in reasonable agreement with other theoretical and/or experimental results. The suggested VSCF-DWBA-IOS scheme is found to be a very simple but efficient theoretical tool to investigate the dissociation dynamics of van der Waals complexes.

The photodissociation of HCl embedded in argon clusters is studied by semiclassical molecular dynamics, based on a surface-hopping approach for the non-adiabatic transitions. The diatomics-in-molecules (DIM) method is used to construct the 12 electronic potential energy surfaces that are involved, and the non-adiabatic couplings. Caging effects, including recombination and electronic relaxation are investigated for Ar-12(HCl) and Ar-54(HCl), corresponding respectively to one and two complete solvation layers. The effects of the process on the cluster, e.g. fragmentation and structural deformation, are also studied. The main findings are: (1) non-adiabatic transitions play a major role in the dynamics for both clusters; (2) some recombination occurs in Ar-12(HCl), and it is much greater, about 7%, in Ar-54(HCl); (3) all 12 electronic states are visited, at least to some extent, in the process, but the distributions remain non-statistical throughout in both systems; (4) rates of spin-forbidden transitions are roughly of similar magnitudes to these of spin-allowed transitions between electronic states; (5) the energy gap law of radiationless relaxation theory does not work well for these systems. Symmetry and shape of the electronic states greatly affect the relaxation rates; (6) the clusters undergo melting and extensive evaporation in the processes.

A theoretical study is made on He scattering from three basic classes of disordered adlayers: (a) translationally random adsorbates, (b) disordered compact islands, and (c) fractal submonolayers. The implications of the results to experimental studies of He scattering from disordered surfaces are discussed, and a combined experimental-theoretical study is made for Ag submonolayers on Pt(111). Some of the main theoretical findings are: (1) The scattering intensities from the three disorder classes differ significantly, and can be used to distinguish between them. (2) Structural aspects of the calculated intensities from translationally random clusters were found to be strongly correlated with those of individual clusters. (3) For fractal islands, just as for all surfaces considered here, the off-specular intensity depends on the parameters of the He/Ag interaction, and does not follow a universal power law as previously proposed in the literature. In the experimental-theoretical study of Ag on Pt(111), we use experimental He scattering data from low-coverage (single adsorbate systems to determine an empirical He/Ag-Pt potential of good quality. Then, we carry out He scattering calculations for high coverage and compare with experiments for these systems. The conclusion is that the actual experimental phase corresponds to small compact Ag clusters of narrow size distribution, with partial translational disorder. (C) 1997 American Institute of Physics.

The photodissociation of HCl in solid Ar is studied by non-adiabatic Molecular Dynamics simulations, based on a surface-hopping treatment of transitions between different electronic slates. The relevant 12 potential energy surfaces and the non-adiabatic interactions between them were generated by a Diatomics-in-Molecules (DIM) approach, which incorporated also spin-orbit coupling. The focus of the study is on the non-adiabatic transitions, and on their role both in the cage-exit of the H atom, and in the recombination process. It is found that non-adiabatic transitions occur very frequently. In some of the trajectories, all the 12 electronic states are visited during the timescale studied. At least one non-adiabatic transition was found to occur even in the fastest cage-exit events. The other main results are: (1) The total yields for photofragment separation (by cage exit of the H atom) and for H+Cl recombination onto the ground state are roughly equal in the conditions used. (2) The cage exit events take place in the time-window between similar to 70 fs and similar to 550 fs after the excitation pulse, and are thus all ar least somewhat delayed. The recombination events span a much broader time-window, from almost immediately after excitation, and up to similar to 1100 fs and beyond. (3) The electronic energy relaxation events during the process depend significantly on symmetry and interactions of the states involved, and not only on the energy gaps between them. (4) Different electronic stales reached in the course of the process exhibit; different propensities with regard to the recombination versus cage exit outcome. (5) Spin-orbit interactions, and spin-forbidden transitions play an important role in the process, especially for recombination events. (C) 1997 American Institute of Physics.