The Eckart conditions, named after Carl Eckart, sometimes referred to as Sayvetz conditions, simplify the nuclear motion (rovibrational) Schrödinger equation that arises in the second step of the Born-Oppenheimer approximation. The Eckart conditions allow to a large extent the separation of the external (rotation and translation) motions from the internal (vibration) motions. Although the rotational and vibrational motions of the nuclei in a molecule cannot be fully separated, the Eckart conditions minimize the coupling between these two.
Read more about Eckart Conditions: Definition of Eckart Conditions, Separation of External and Internal Coordinates, Overall Translation and Rotation, Vibrational Energy, Relation To The Harmonic Approximation
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