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Notes: Time-dependent quantum-mechanical theories and simulations provide a clear and intuitive description of molecular processes. Due to ensuing simplification of the theory and the generally employed numerical algorithms, the vast majority of these treatments are based upon perturbation theory. Especially in light of the current level of experimental sophistication, with experiments being realized which are influenced by the spectral, temporal, and spatial shape of the laser pulse, it is important to move beyond treatments limited to weak fields or idealized δ-function wave forms. Various methods to examine the results of high-field simulations are presented. All of the techniques are shown to have the familiar linear response form in the weak-field limit. In a time-dependent framework the difference between the linear and nonlinear response expressions can be seen from expectation values over stationary versus nonstationary states. The high-field photodissociation of methyl iodide illustrates this approach. Methyl iodide represents a physical system well suited for examining the effects of such exciting laser-field characteristics as strength, linewidth, and frequency upon the photodissociation dynamics. Its dissociation occurs upon coupled repulsive excited electronic potential-energy surfaces which have recently been revised to fit the most current experimental data. The effect of the surface intersection has previously been typically studied by examining the branching and the internal state distributions of the products in the two channels as a function of excitation frequency only.The collinear photodissociation dynamics is examined using a numerically exact time-dependent quantum-mechanical method. The equations of motion for the amplitudes upon the ground and two coupled excited electronic surfaces, explicitly incorporating the laser field, are integrated by a scheme which employs a low-order polynomial approximation to the evolution operator. The effects of the three field characteristics upon the branching ratio and internal state distributions of the products and the spectroscopy of the process are delineated. The course of the photodissociation dynamics is shown to be affected by these characteristics. The results demonstrate the causal connections between the pulse shape and the resulting photoprocesses. Practical manifestations of strong fields (power broadening, sub-threshold absorption, higher harmonic generation, emission shaping of the ground state, temporal development) are stressed.

Notes: A study is made of the vibrational energy levels and the corresponding oscillation dynamics of the clusters Xe4He2, Xe3He2, and I24He. XeHe2 is a representative of the "three ball'' clusters, while I2He is a prototype of the "stick and ball'' systems. The treatment is based on the vibrational self-consistent field (SCF) method, which introduces an approximate separation of the modes involved. Success of the method depends on an adequate choice of the coordinates that are being mutually separated. We use physical arguments, based on mass ratios and potential function considerations, as well as comparative SCF calculations in different coordinate systems, to determine the appropriate modes for each system. Numerically exact results are also obtained by configuration interaction (CI) calculations using a basis of SCF states. The SCF and CI calculations include all modes and employ realistic potentials. Several states that are both rotationally and vibrationally excited are also calculated. The main conclusions are: (1) Hyperspherical coordinates are the best modes for XeHe2; ellipsoidal coordinates are best for I2He. In each case, the "good modes'' SCF gives energies in remarkable agreement with the exact (CI) ones. (2) XeHe2 resembles a quantum liquid drop: Even in the ground state, it is delocalized over and between the (two) classical equilibrium structures. (3) Structural distributions, rather than rigid geometry, are essential for the description of such floppy clusters. The single-mode SCF wave functions offer a highly accurate description of the structural distributions. (4) There is a sequence of bound, excited rotational states of I2He in which the He precesses around the I2 axis. The amplitude of the I2He bending vibrations are very large (θA〈20°), but none of the bound states involves a full rotational motion around the I2 stick (with angular momentum normal to the axis). The SCF method with the "good coordinates'' proposed here is expected to yield results of similar high accuracy for any cluster of the "three balls'' or "stick and ball'' types.

Notes: The dynamical formulation of electron transfer rate theory, including inner sphere and outer sphere reorganization terms, electronic structure polarization, and an ab initio treatment of the electrons on donor, acceptor, and bridge molecules, is presented and applied to electron transfer betwen benzene/anion radical and pyridine. The formulation involves the use of mean field (Ehrenfest) relations to obtain the time evolution of electron and vibration operators. This formulation yields an effective density matrix for the time evolution of the electronic system; the elements of this density matrix depend on averages over electronic and vibrational motions. For the electron transfer system actually studied, the rates are strongly dependent upon relative geometry of donor and acceptor, and maximize sharply at geometries such that electronic levels on donor and acceptor become degenerate—the so-called "coincidence event'' geometry.

Notes: The ground state properties of LixNa4−x (x=0–4) were investigated using extended basis Hartree–Fock calculations. The existence of substitution isomers was found for the mixed alkali clusters and planar singlet ground states were found for all clusters, including the isomers. The optical response of the clusters was modeled via configuration interaction—singles (CIS) in the hope of helping to interpret the experimental data. CIS results were found comparable to experiment at lower excitation energies, but inadequate at higher energies due to the neglect of doubles and higher excitations. Some exploration of the excited state surfaces of Li4 and of one isomer of Li2Na2 is also reported. Comparisons are made between CIS calculations, experiment, and multireference doubly excited configuration interaction calculations.

Notes: Dynamic percolation theory is adapted to obtain diffusion coefficients for particles with blocking interactions on incomplete lattices, within an effective medium approximation (EMA). The substrate lattices have static bond disorder. The motion of a tracer particle among identical background particles is regarded as particle motion in a fluctuating random environment superimposed on the statically disordered lattice; the fluctuations results from the motion of the background particles. Several schemes for incorporating the effect of the background particles are discussed, all relating their motion in different ways to the macroscopic diffusion. Comparisons with Monte Carlo simulations are performed for two-dimensional simple square and three-dimensional simple cubic lattices. In the range where single bond EMA is thought to be reliable, good agreement with the simulation is achieved.

Notes: We discuss a generalized dynamic mean-field method combining the advantages of explicit pair correlations and of configuration interaction. The approximate dynamical method, which we call time-dependent self-consistent-field configuration interaction (TDSCF2-CI), is constructed by including N(N−1)/2 TDSCF2 configurations. In each configuration a given pair of N coupled modes is directly (not in the mean-field approach) correlated; the N(N−1)/2 configurations include all such choices of pairs. As such, it has both the usual advantages of TDSCF and improvements due to some inclusion of correlations (exact results for any two-mode problem, improved descriptions of dynamical corrections, and greater accuracy). A three-mode model Hamiltonian is analyzed using five approximate treatments, i.e., the usual TDSCF, the three TDSCF2 forms, and the TDSCF2-CI one. The quantities for comparison with the exact results include the decay P(t) of the initial state, the time dependencies of the energies e(i) of individual modes, and the overlap S(t) of the corresponding approximate wave function with the exact one. We find, indeed, that explicit inclusion of pair correlations improves the description of the quantum dynamics of the system.

Notes: Ions move into biological cells through pores in proteins called ionic channels, driven by gradients of potential and concentration imposed across the channel, impeded by potential barriers and friction within the pore. It is tempting to apply to channels the chemical theory of barrier crossing, but important issues must first be solved: Concentration boundary conditions must be used and flux must be predicted for applied potentials of all sizes and for barriers of all shapes, in particular, for low barriers. We use a macroscopic analysis to describe the flux as a convolution integral of a mathematically defined adjoint function, a Green's function. It so happens that the adjoint function also describes the first-passage time of a single particle moving between boundary conditions independent of concentration. The (experimentally observable) flux is computed from analytical formulas, from simulations of discrete random walks, and from simulations of the Langevin or reduced Langevin equations, with indistinguishable results. If the potential barrier has a single, large, parabolic peak, away from either boundary, an approximate expression reminiscent of Kramers' formula can be used to determine the flux. The fluxes predicted can be compared with measurements of current through single channels under a wide range of experimental conditions.

Notes: Monte Carlo simulations were performed on lattice gas systems with Coulombic interactions. Emphasis was placed on two lattice gases. The first consists of both mobile anions and cations while the second is composed of mobile anions and a random distribution of fixed cations. Comparisons are made to a strictly repulsive lattice gas. The addition of attractive forces is shown to significantly retard particle motion relative to the repulsive system. In the mobile-anion, mobile-cation system, at temperatures high enough to suppress ion clustering, the effect of backward correlations on the particle diffusivity is found to be similar to that for the strictly repulsive system. In the mobile-anion, fixed-cation system, however, backward correlations are much stronger due to the presence of immobile Coulomb traps. Both systems deviate from Nernst–Einstein behavior. The mobile-anion, mobile-cation system exhibits diminished conductivity (Haven ratio (approximately-greater-than)1) due to the migration of neutral ion pairs, whereas the mobile-anion, fixed-cation system exhibits slightly enhanced conductivity (Haven ratio 〈1) due to the mutual repulsions between mobile charge carriers. The results of these simulations are discussed in terms of multiple timescale behavior, specifically including Funke's jump relaxation model, and observations on relaxation times are reported.