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Natural Orbitals

John Linderman

Natural orbitals are eigenfunctions of the 1st order reduced density matrix (1-RDM), forming a complete, orthonormal set of orbitals. They are obtained by diagonalizing the 1-RDM, and they can be related to electronic occupancy. The electronic occupancy of any orbital can be defined as the expectation value of the 1-RDM.

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Normal Vibration Modes

Liv Mumma

A vibration is when the movements of atoms in a molecule move in a coordinated, oscillating, fashion in and out of equilibrium. These motions make up the superposition of the overall motion of the molecule. Another way of thinking about this is in terms of point groups, which are sets of symmetry operations that when applied to a species result in the original configuration. The normal mode of vibration forms a basis for some irreducible representation of the point group of the molecule.

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