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Showing 1 to 20 of 79 for “"oppenheimer"”.
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Oppenheimer-Snyder Collapse in the BSSN Formalism
… simplifications of complicated scenarios. Oppenheimer-Snyder collapse, an exact solution for the gravitational collapse of a uniform, pressure-less ball of dust into a black hole, provides valuable insight into the collapse of realistic mass distributions such as stars. Early numerical …
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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 ¬)/â …
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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 …
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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 …
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Excited State Chemical Dynamics: Beyond the Born-Oppenheimer Approximation
Herein, numerical approaches for describing the time evolution of molecular systems in nonequilibrium, and excited electronic states using the tools of non-adiabatic molecular dynamics will be built up from the full molecular Hamiltonian and associated quantum mechanical equation of motion. This …
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Electron-lattice interaction and the generalized Born-Oppenheimer approximation
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 1962.
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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 …
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Electron-proton nonadiabaticity: characterization and development of non-Born-Oppenheimer electronic structure methods
… 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 …
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Development of non-born-Oppenheimer methods for ground and excited state molecular properties
… has great potential in applications to non-Born-Oppenheimer processes such as proton-coupled electron transfer (PCET). Additionally, NEO can also capture nuclear quantum effects such as zero-point energy and proton delocalization in a direct and efficient manner. This dissertation describes the …
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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 ≤ …
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Diatomic molecules as perturbed Morse oscillators and the effect of the breakdown of the Born-Oppenheimer approximation.
Values of the PMO parameters (including the velocity-dependent parameter) are obtained for the ground state of the three isotopic molecules H(, 2), HD and D(, 2) using two approaches. In the first approach, iteration computations are used to evaluate the different parameters from the experimentally …
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Transport theory through single molecules : Jahn-Teller effect: breakdown of Born-Oppenheimer picture and adiabatic time-dependent driving out of equilibrium
In this thesis, we theoretically investigate the interplay of the vibrational, charge and spin degrees of freedom characteristic of complex dimer molecules. The influence of the pseudo Jahn-Teller effect, well known in molecular chemistry, is investigated in the new situation where an electric …
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Development of multicomponent coupled-cluster theory and its application to nanoclusters and molecular systems
… 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 …
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Vibrational Energies of the Hydrogen Bonds of H₃O₂⁻ and H₅O₂⁺
… 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 …
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On Adiabatic Quantum Molecular Dynamics
… 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 for …
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A Mathematical Study of Hawking Radiation on Collapsing, Spherically Symmetric Spacetimes
… spacetime models, known as Reissner–Nordström Oppenheimer–Snyder (RNOS) models. We will discuss the derivation of the Oppenheimer– Snyder model [39], before moving on to the more general charged case. We will then summarise the interesting and useful properties of these models. The second …
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Theoretical study of hydrogen in [alpha]-YH[subscript x] and on Si(111) surface
… 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 experiment. …
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A High Order Correction of the Energy of a One Dimensional Model of an H2+ Molecule
… 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.
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Theoretical studies of compressed xenon oxides, tin selenide thermoelectrics, and defects in graphene
… involves a large scale exploration of the Born-Oppenheimer energy surface, and secondly the use of a vibrational self-consistent field (VSCF) approach to investigate the effects of nuclear motion and anharmonicity in crystal systems, which involves a local exploration of the Born-Oppenheimer …
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Close-Coupling Calculations for NaAr, NaNe, and NaHe
… and Wang for NaAr. The effects of different Born-Oppenheimer potentials on D1/D2 line intensity is considered by also treating NaNe and NaHe. The individual parity contributions to the line intensities are significantly different from each other.</p>
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