How does symmetry affect the electron density of an atom?
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The electron density of an atom is affected by symmetry. The density of an atom in a state of well-defined angular momentum has a specific finite spherical harmonic content, without and with interactions . Approximate single-particle schemes, such as the Hartree, Hartree-Fock, and Local Density Approximations, generally violate this feature . However, the correct symmetry of the density can be assured by a constrained-search formulation without significantly altering the calculated energies . Noncrystallographic symmetry (NCS) also affects the electron density. NCS occurs when symmetry operations are true only within a confined envelope. Averaging electron density within the range of NCS operators accurately indicates the limits of the NCS envelope . Therefore, symmetry plays a crucial role in determining the electron density of an atom, both in terms of angular momentum and in the context of NCS.
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| The symmetry of the electron density of an atom is violated in approximate single-particle schemes such as Hartree, Hartree-Fock, and Local Density Approximations. | |
| Symmetry affects the electron density of an atom by determining the symmetry-adapted parts of the fitting equation systems in auxiliary density functional theory. | |
Open access•Posted Content | The symmetry of the potential energy in the vicinity of its minimum causes the electronic density of the triplet states in a three-electron parabolic quantum dot to possess approximate symmetry. |
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