Electronic Structures of Diatomic Molecules
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Born–Oppenheimer Approximation: An approximation in molecular quantum mechanics that assumes nuclei are fixed while electrons move, simplifying the molecular Hamiltonian operator 1. Molecular Hamiltonian: The operator representing the total energy of a molecule, including kinetic energy of nuclei and electrons, and potential energy from repulsions and attractions between nuclei and electrons 1. Schrödinger Equation: A fundamental equation in quantum mechanics used to find the wave functions and energies of a molecule 1. Electronic Schrödinger Equation: The Schrödinger equation for electronic motion, obtained by omitting nuclear kinetic energy terms 1. Purely Electronic Hamiltonian: The Hamiltonian operator for electronic motion, excluding nuclear kinetic energy terms 1. Internuclear Repulsion: The potential energy term representing the repulsion between nuclei in a molecule 1. Equilibrium Internuclear Distance: The internuclear separation at which the potential energy of a molecule is minimized 1. Equilibrium Dissociation Energy: The energy difference between the potential energy at infinite internuclear separation and at the equilibrium internuclear distance 1. Zero-Point Energy: The lowest possible energy that a quantum mechanical system may have, even at absolute zero temperature 1. Harmonic Oscillator Approximation: An approximation that treats the vibration of a diatomic molecule as a harmonic oscillator, useful for calculating vibrational energy levels 1. Vibrational Anharmonicity: The deviation of a molecule's vibrational energy levels from those predicted by the harmonic oscillator approximation 1. Centrifugal Distortion: The distortion of a molecule due to rotational motion, affecting its vibrational energy levels 1. Morse Function: A potential energy function used to approximate the potential energy of a diatomic molecule, accounting for anharmonicity 1. Atomic Units: A system of units used in quantum chemistry where fundamental constants like the electron mass, charge, and Planck's constant are set to 1 1. Hartree: The atomic unit of energy, equivalent to the energy of the ground state of the hydrogen atom 1. Bohr Radius: The atomic unit of length, representing the average distance between the proton and electron in a hydrogen atom 1. Hydrogen Molecule Ion (H₂⁺): The simplest diatomic molecule, consisting of two protons and one electron, used as a model for studying molecular electronic structure 1. Confocal Elliptic Coordinates: A coordinate system used to solve the Schrödinger equation for the hydrogen molecule ion 1. LCAO-MO (Linear Combination of Atomic Orbitals - Molecular Orbital): A method for constructing molecular orbitals by combining atomic orbitals 1. Bonding and Antibonding Orbitals: Molecular orbitals formed from the combination of atomic orbitals, where bonding orbitals lower the energy and antibonding orbitals raise the energy of the molecule 1.