H. Keith McDowell

Theoretical studies of ion neutralization: A tight binding linear chain model

A tight binding semi‐infinite chain is used to model the neutralization of ions impinging on a solid surface. Starting from the equations of motion for the appropriate annihilation operators of site‐centered orbitals, two approaches to computing the neutralization probability are developed. The first approach is based on using the well‐known molecular orbitals of such a chain. We conclude that this method, in general, is dependent on one’s ability to obtain molecular orbitals for an extended solid system. The second approach developed is based on a Langevin‐type model in that we separate out a primary zone where the collision of the ion with the surface occurs and treat the remainder of the chain by using a memory kernel. We conclude that this method offers hope for treating realistic systems. Numerical computations are carried out using both approaches for specific choices of the parameters of the model. Exact agreement between the methods is obtained. In addition, the neutralization probability is found...

Charge transfer: An electronic bath approach

A charge transfer theory is developed for systems in which an atom, molecule, or ion interacts for a period of time with a substrate. The Hamiltonian of the system is taken to be one‐electron and the nuclear motion of the substrate is ignored. The theory is structured so as to mimic generalized Langevin theory; namely, the equations of motion for annihilation operators of spin orbitals localized at the interaction site are developed such that a primary zone is defined with the remainder of the substrate being included through a memory kernel and a driving term. An electronic bath approximation is presented which leads to equations of motion for the occupation numbers of spin orbitals in the primary zone. These equations have the property that primary‐zone occupation numbers damp to an equilibrium state at long time independent of their initial values. Specific application to a substrate modeled as a semi‐infinite, Huckel chain is presented and numerical results are obtained. The electronic bath approximat...

Second-quantized molecular time scale generalized Langevin equation theory: Coupled oscillator model

A second‐quantized, coupled oscillator model is presented which explicitly displays the structure of a second‐quantized MTGLE theory. The Adelman ansatz [J. Chem Phys. 75, 5837 (1981)] for a quantum MTGLE response function is shown to generate the correct response function for the model. This result paves the way for the development of a general second‐quantized MTGLE theory.

Second‐quantized molecular time scale generalized Langevin equation theory: Boson equivalent chain

A second‐quantized version of molecular time scale generalized Langevin equation theory is developed in an equivalent chain format for quantum boson systems. The approach allows for nonlinear Hamiltonians and strong coupling to the bath. A bath average is defined which permits reduced dynamics prescriptions to be developed. The bath average is shown to be consistent with the notion that perturbations of a primary zone should damp away at long time.

Second-quantized molecular time scale generalized Langevin equation theory and the quantum oscillator

The short‐time Gaussian approximation to the molecular time scale generalized Langevin equation (MTGLE) friction kernel is introduced and used to compute the time dependence of a fluctuation time correlation function. The fluctuations are shown to have two time scales, namely, the dissipation time scale and a quantum time scale given by exp[−2πkTt/ℏ]. Absorption and emission spectral functions for a quantum oscillator coupled to a bath are derived with no approximations made. The second‐quantized MTGLE approach is applied to the problem of a quantum oscillator coupled linearly to a bath of quantum oscillators. The method is shown to be consistent with previous work and to provide a systematic methodology to examine more general many‐body boson problems.

Theoretical studies of ion neutralization: Two-dimensional tight binding models☆

Abstract The neutralization of ions impinging on a substrate is modeled by treating the substrate as both a two-dimensional, tight-binding, semi-infinite sheet and a two-dimensional, tight-binding, infinite sheet. In both cases the equations of motion are set up in a generalized Langevin format. Results are presented for a model interaction and compared with previous computations using a semi-infinite chain model and an infinite chain model.

Exact Time Correlation Function for a Nonlinearly Coupled Vibrational System

AbstractThe time correlation function

Electronic bath theory: Multi-orbital primary zone

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