Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 18 of 18 for “"Born-Oppenheimer Approximation"”.
-
The Born-Oppenheimer approximation in scattering theory
… and electrons with masses of order 1. The Born-Oppenheimer approximation consists of the adiabatic approximation to the motion of electrons and the semiclassical approximation to the time evolution of nuclei. The quantum propagator associated with this Schrödinger Equation is exp(-itH(â …
-
Time-Dependent Perturbation and the Born-Oppenheimer Approximation
… using a time-dependent perturbation of the Born-Oppenheimer approximation to the Schrodinger equation. Using previous results that develop asymptotic series solutions in the Born-Oppenheimer parameter ε, we derive a formal Dyson series expansion in the perturbation parameter μ, which is …
-
Excited State Chemical Dynamics: Beyond the Born-Oppenheimer Approximation
… are found to naturally arise from successive approximations to the quantum mechanical treatment of all molecular degrees of freedom, and presented along with details of their implementations in electronic structure programs utilizing atom-centered basis sets. Specic scientic studies and …
-
Electron-lattice interaction and the generalized Born-Oppenheimer approximation
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 1962.
-
The Born-Oppenheimer Approximation for Triatomic Molecules with Large Angular Momentum in Two Dimensions
We study the Born-Oppenheimer approximation for a symmetric linear triatomic molecule in two space dimensions. We compute energy levels up to errors of order ε⁵, uniformly for three bounded vibrational quantum numbers n₁, n₂, and n₃; and nuclear angular momentum quantum numbers â ≤ …
-
Vibrational Energies of the Hydrogen Bonds of H₃O₂⁻ and H₅O₂⁺
… an improvement to the standard time-independent Born-Oppenheimer approximation. These two molecules are symmetric around a central hydrogen which participates in hydrogen bonding. Unlike the standard Born-Oppenheimer approximation, this approximation appropriately scales the hydrogen nuclei …
-
Development of multicomponent coupled-cluster theory and its application to nanoclusters and molecular systems
… and computational methods are based upon the Born-Oppenheimer approximation. This approximation greatly simplifies the search for a wave function that describes all electrons and nuclei in a chemical system. This is accomplished by assuming that the motion of nuclei and electrons are vastly …
-
Theoretical study of hydrogen in [alpha]-YH[subscript x] and on Si(111) surface
… to study hydrogen in an hcp metal, Y, under a Born-Oppenheimer approximation between Y and H. The equilibrium interstitial location, heat of formation, the change in the lattice constants and the bulk moduli, and the vibration frequencies of hydrogen are in excellent agreement with the …
-
A High Order Correction of the Energy of a One Dimensional Model of an H2+ Molecule
… motion about the internuclear axis. Performing a Born-Oppenheimer approximation of such a system will break the relevant energy degeneracy at eighth order. This degeneracy breaking is known as L-doubling.
-
On Adiabatic Quantum Molecular Dynamics
In this thesis, we consider the time-dependent Born-Oppenheimer approximation (BOA) of a non-relativistic quantum molecule involving a possibly large number of nuclei and electrons described by the Schrödinger equation. The full molecular equation is difficult to solve and compute approximations …
-
Quantum Monte Carlo studies of dense hydrogen and two-dimensional Bose liquids
… as quantum particles, thereby avoiding the Born-Oppenheimer approximation. Fermi-Dirac exchange statistics are treated within the fixed-node approximation, with the nodes specified by the free Fermi gas. In the region of molecular dissociation, we observe properties consistent with and …
-
Electron-ion correlation and finite-size effects in quantum Monte Carlo simulations
… can mostly be explained by the diagonal Born-Oppenheimer correction. We applied this method to solid hydrogen at megabar pressures and tackled additional problems involving geometry optimization and finite-size effects. The phase diagram produced by our electron-ion DMC simulations differ …
-
Dissociation dynamics of diatomic molecules in intense fields
… a function of the pump-probe delay τ. Within the Born-Oppenheimer approximation, we calculate ab-initio adiabatic potential-energy curves and their electric dipole couplings, using the quantum chemistry code GAMESS. In Chapter 6, the dissociation dynamics of the noble gas dimer ions …
-
Electron-proton nonadiabaticity: characterization and development of non-Born-Oppenheimer electronic structure methods
… variety of chemical reactions. Moreover, non-Born-Oppenheimer effects are important in reactions such as proton-coupled electron transfer (PCET), which are integral to various electrocatalytic applications and bioenzymatic processes. The breakdown of the Born-Oppenheimer approximation between …
-
Born-Oppenheimer Expansion for Diatomic Molecules with Large Angular Momentum
Semiclassical and Born-Oppenheimer approximations are used to provide uniform error bounds for the energies of diatomic molecules for bounded vibrational quantum number n and large angular momentum quantum number l. Specifically, results are given when (l + 1) < κ𝛜⁻³/². Explicit formulas for the …
-
Nonlinear Optical Response of Simple Molecules and Two-Photon Semiconductor Lasers
… a bulk semiconductor gain medium. Within the Born-Oppenheimer approximation, nonlinear refraction in molecular liquids and gases can arise from both bound-electronic and nuclear origins. Knowledge of the magnitudes, temporal dynamics, polarization and spectral dependences of each of these …
-
Born-Oppenheimer Corrections Near a Renner-Teller Crossing
We perform a rigorous mathematical analysis of the bending modes of a linear triatomic molecule that exhibits the Renner-Teller effect. Assuming the potentials are smooth, we prove that the wave functions and energy levels have asymptotic expansions in powers of ε, where ε4 is the ratio of an …
-
Simulating and controlling non-adiabatic effects in ultrafast photochemistry
… states and therefore the breakdown of the Born-Oppenheimer approximation means that many photochemical processes are dominated by non-adiabatic effects, such as conical intersections. The study of such reactions is therefore vital to our understanding of many fundamental processes and the …