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Showing 1 to 20 of 37 for “"Born-Oppenheimer"”.
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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 …
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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
… 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 …
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Development of non-born-Oppenheimer methods for ground and excited state molecular properties
… quantum mechanical level. NEO does not make the Born-Oppenheimber approximation between electrons and select protons, and therefore has great potential in applications to non-Born-Oppenheimer processes such as proton-coupled electron transfer (PCET). Additionally, NEO can also capture nuclear …
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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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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 …
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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 …
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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 …
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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.
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Theoretical studies of compressed xenon oxides, tin selenide thermoelectrics, and defects in graphene
… which 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 …
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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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Soluciones exacta y adiabática para el modelo de Hubbard-Peierls en un cúmulo finito
… como la solución en la aproximación de Born-Oppenheimer. La principal conclusión del presente trabajo es que, al considerar las vibraciones de la red dentro de un marco cuántico, la distorsión de Peierls pierde el carácter estático, existiendo un tiempo de túnel finito T entre los dos …
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Énergie fondamentale de la molécule muonique ionisée
… du procédé utilisé, i.e. l'approximation de Born-Oppenheimer, pour trouver le niveau d'énergie de l'état fondamental de ce système formé de trois corps. Ce travail montre aussi que la paramétrisation peut s'avérer un moyen-efficace et rapide pour obtenir une précision accrue. La puissance de …
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Coupled electron and nuclear dynamics in model systems
… for a facile switching between and adiabatic (Born-Oppenheimer type) and a strongly coupled dynamics. The first part of the work determined the “static” properties of the model system: The calculation of electronic eigenfunctions, adiabatic potential curves, kinetic coupling elements and …
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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 …
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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 …
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