ALBERT

Notes: The coupling of a Rydberg electron to the vibrational motion is discussed in the intermediate regime in which the orbital period is long on the scale of the vibrational motion but is still considerably faster than the rotation of the core. Two dimensionless variables characterize the dynamics: the ratio of time scales and the action exchanged between the electron and the core, per one revolution. The classical dynamics are reduced to a map which provides a realistic approximation in the limit when the action exchanged is larger than (h-dash-bar). There are two distinguishable time regimes, that of prompt processes where the corresponding spectrum is so broad that individual Rydberg states cannot be resolved and a much slower process, where the electron revolves many times around the core before it ionizes. The overall spectrum is that of a Rydberg series, where the lines are broadened by (the delayed) vibrational autoionization superimposed on a broad background. The semiclassical dynamics is quantitatively more accurate in the typical situation when the action exchanged is comparable or smaller than (h-dash-bar). Explicit analytical expressions are obtained for the width for vibrational autoionization including for the case when resonances are possible. The presence of resonances is evident in Rydberg lines which are broader. For low Rydberg states the present approach recovers the Herzberg–Jungen approximation in the weak coupling limit. © 1996 American Institute of Physics.

Notes: The effect of an electrical field on the dynamics and decay kinetics of a high Rydberg electron coupled to a core is discussed with special reference to simulations using classical dynamics and to experiment. The emphasis is on the evolution of the system within the range of Rydberg states that can be detected by delayed pulsed ionization spectroscopy (which is n(approximately-greater-than)90 for both the experiment and the computations). The Hamiltonian used in the computations is that of a diatomic ionic core about which the electron revolves. The primary coupling is due to the anisotropic part of the potential which can induce energy and angular momentum exchange between the orbital motion of the electron and the rotation of the ion. The role of the field is to modulate this coupling due to the oscillation of the orbital angular momentum l of the electron. In the region of interest, this oscillation reduces the frequency with which the electron gets near to the core and thereby slows down the decay caused by the coupling to the core. In the kinetic decay curves this is seen as a stretching of the time axis. For lower Rydberg states, where the oscillation of l is slower, the precession of the orbit, due to the central but not Coulombic part of the potential of the core, prevents the oscillation of l and the decay is not slowed down. Examination of individual trajectories demonstrates that the stretching of the time axis due to the oscillatory motion of the electron angular momentum in the presence of the field is as expected on the basis of theoretical considerations.The relation of this time stretch to the concept of the dilution effect is discussed, with special reference to the coherence width of our laser and to other details of the excitation process. A limit on the principal quantum number below which the time stretch effect will be absent is demonstrated by the computations. The trajectories show both up and down processes in which the electron escapes from the detection window by either a gain or a loss of enough energy. Either process occurs in a diffusive like fashion of many smaller steps, except for a fraction of trajectories where prompt ionization occurs. The results for ensembles of trajectories are examined in terms of the decay kinetics. It is found that after a short induction period, which can be identified with the sampling time of the available phase space, the kinetics of the decay depend only on the initial energy of the electron and on the magnitude of the field, but not on the other details of the excitation process. The computed kinetics of the up and down channels are shown to represent competing decay modes. A possible intramolecular mechanism for long time stability based on the sojourn in intermediate Rydberg states is discussed. The available experimental evidence does not suffice to rule out nor to substantiate this mechanism, and additional tests are proposed. The theoretical expectations are discussed in relation to observed time resolved decay kinetics of high Rydberg states of BBC (bisbenzenechromium) and of DABCO (1,4-diazabicyclo[2.2.2]octane).The experimental setup allows for the imposition of a weak (0.1–1.5 V/cm) electrical field in the excitation region. The role of the amplitude of the time delayed field, used to detect the surviving Rydberg states by ionization, is also examined. The observed decay kinetics are as previously reported for cold aromatic molecules: Most of the decay is on the sub-μs time scale with a minor (∼10%) longer time component. The decay rate of the faster component increases with the magnitude of the field. Many features in such an experiment, including the absolute time scales, are similar to those found in the classical trajectory computations, suggesting that the Hamiltonian used correctly describes the physics of the faster decay kinetics of the high Rydberg states. © 1995 American Institute of Physics.

Notes: We present a detailed study of the electronic properties of CdSe nanocrystals in the absence and presence of a dielectric medium. The electronic structure of the nanocrystal is modeled within the framework of the empirical pseudopotential method. We use a real-space grid representation of the wave function, and obtain the eigenvalues and eigenstates of the one-electron Hamiltonian using a slightly modified version of the filter-diagonalization method. The band gap, density of states, charge density, multipole moments, and electronic polarizabilities are studied in detail for an isolated nanocrystal. We discuss the implications of the results for the long range electrostatic and dispersion interactions between two CdSe nanocrystals. To study the effects of the surroundings we develop a self-consistent reaction field method consistent with the empirical pseudopotential method. We use the eigenstates of the isolated nanocrystal and iterate the self-consistent equations until converged results are obtained. The results show that the electronic properties of polar CdSe nanocrystals are quite sensitive to the environment. © 1999 American Institute of Physics.

Notes: We have extended our study of the vibronic absorption spectrum in condensed matter [S. A. Egorov, E. Rabani, and B. J. Berne, J. Chem. Phys. 108, 1407 (1998)] to the case when the electronic dephasing rate is slow compared to the vibrational relaxation rate in both electronic states. We find that under such circumstances, unlike the case of fast electronic dephasing, treating all nuclear degrees of freedom classically provides better agreement with the exact quantum treatment than the mixed quantum-classical approximation. These results are consistent with the conclusions reached by Bader and Berne in their study of mixed quantum-classical treatments of vibrational relaxation processes. © 1998 American Institute of Physics.

Notes: We discuss whether or not local information on the potential energy surface embodied by the distribution of unstable instantaneous normal modes can be used to predict the hopping rates and barrier heights for Zwanzig's model of self-diffusion [R. Zwanzig, J. Chem. Phys. 79, 4507 (1983)] in simple liquids. Results from a set of simulations of Lennard-Jones particles done at multiple temperatures and densities are presented. These simulations show that the theories which predict diffusive barrier heights from the distribution of imaginary frequencies are questionable. This discrepancy is due to the presence of imaginary frequency instantaneous normal modes which persist into the solid phase. Model systems are used to show that imaginary frequency instantaneous normal modes (and even those at the top of the barrier along that mode) are not necessarily indicators of diffusive barrier crossing as used in Zwanzig's model. These false barriers are shown to be the cause of all of the imaginary frequency zero-force modes in the solid as well as many of the imaginary frequency modes in the high-density super-cooled liquid. We therefore dispute their utility as predictors of barrier heights or hopping rates in related liquid systems. We also show that attempts to separate the modes that are truly diffusive from those with false barriers using a frequency cutoff or local information on the potential energy surface are not successful at removing all of the non-barrier modes. © 1997 American Institute of Physics.

Notes: We extend the cage correlation function method for calculating the hopping rate in Zwanzig's model of self-diffusion in liquids [R. Zwanzig, J. Chem. Phys. 79, 4507 (1983)] to liquids composed of polyatomic molecules. We find that the hopping rates defined by the cage correlation function drop to zero below the melting transition and we obtain excellent agreement with the diffusion constants calculated via the Einstein relation in liquids, solids, and supercooled liquids of CS2. We also investigate the vibrational density of states of inherent structures in liquids which have rough potential energy surfaces, and conclude that the normal mode density of states at the local minima are not the correct vibrational frequencies for use in Zwanzig's model when it is applied to CS2. © 1999 American Institute of Physics.

Notes: We propose a new method to calculate ground state position dependent observables in quantum many-body systems. The method, which we call the path-integral diffusion Monte Carlo (PI-DMC) method, is essentially a combination of path-integral Monte Carlo (PIMC) and diffusion Monte Carlo (DMC) methods. The distribution resulting from a DMC simulation is further propagated in imaginary time by PIMC sampling. Tests of the new method for simple cases such as the harmonic oscillator, a double well, and a set of ten coupled harmonic oscillators show that the results for several observables converge rapidly to the exact result. © 1999 American Institute of Physics.

Notes: In our original critique [J. Chem. Phys. 107, 4618 (1997)] of the instantaneous normal mode (INM) theory for self-diffusion, we concentrated on atomic Lennard-Jones systems, in which we found a large number of "false-barrier" modes. These are modes which quench to the same local minimum from either side of the imaginary frequency region. We now extend our inquiry to a molecular system (CS2), and find very similar results to what we observed in the atomic system, i.e., a large number imaginary frequency instantaneous normal modes that persist into the crystalline solid. © 1998 American Institute of Physics.

Notes: We consider the problem of calculating the vibronic absorption spectrum of a diatomic molecule coupled to a condensed phase environment, where all nuclear degrees of freedom are taken in the quadratic approximation, and where the two electronic states couple differently to the solvent. This simple model is used to examine several commonly used semiclassical approximations. The method of Kubo–Toyozawa is adapted to enable exact calculation of the real-time dipole autocorrelation function for the quantum mechanical treatment. Alternatively, we derive an expression for this correlation function in terms of a path-integral influence functional, which is not limited to a finite number of bath modes and could be applied to treat anharmonic solutes in condensed matter. We then obtain an analytical solution for the classical treatment of nuclear dynamics, and develop a mixed quantum-classical approach, where the dynamics of the diatomic vibrational mode is treated quantum mechanically and the bath is treated classically. It is shown that the mixed quantum-classical treatment provides better agreement with the exact quantum treatment than the other approximations for a wide range of parameters. Exact analytical results similar to the pure dephasing theory of Skinner and Hsu are obtained for the asymptotic long time behavior of the dipole autocorrelation functions. © 1998 American Institute of Physics.