Many Electrons Atoms
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Hartree–Fock Self-Consistent-Field Method: A computational approach used to find approximate wave functions for many-electron atoms. It involves iteratively solving the Schrödinger equation by assuming each electron moves in the field created by the nucleus and a hypothetical charge cloud formed by other electrons 1. Hamiltonian Operator: An operator representing the total energy of a system, including kinetic and potential energy. For an n-electron atom, it includes terms for electron-nucleus attractions, electron-electron repulsions, and kinetic energy of electrons 1. Central-Field Approximation: An approximation where the effective potential acting on an electron in an atom is assumed to depend only on the distance from the nucleus, simplifying calculations by averaging over angular coordinates 1. Slater Determinant: A mathematical expression used to describe the wave function of a multi-electron system, ensuring the antisymmetry required by the Pauli exclusion principle. It is a determinant of spin-orbitals 1. Spin-Orbit Interaction: A relativistic effect where the electron's spin interacts with its orbital motion, leading to energy level splitting. It is proportional to the dot product of the electron's spin and orbital angular momentum 1. Coulomb Integral: An integral representing the electrostatic interaction energy between two electrons in different orbitals. It is part of the Hartree–Fock energy calculation 1. Exchange Integral: An integral representing the exchange interaction energy between two electrons with the same spin in different orbitals. It arises due to the antisymmetry of the wave function 1. Configuration Interaction (CI): A method to improve the accuracy of wave functions by considering contributions from multiple electron configurations. It involves expressing the wave function as a linear combination of configuration state functions 1. Electron Correlation: The interaction between electrons that is not accounted for in the Hartree–Fock method. It includes instantaneous interactions that cause electrons to avoid each other, leading to a more accurate description of the system 1. Term Symbol: A notation used to describe the quantum state of an atom, including its total electronic spin and orbital angular momentum. It is written as 2S+1LJ, where S is the spin multiplicity, L is the orbital angular momentum, and J is the total angular momentum 1.