Eckart conditions

The Eckart conditions, named after Carl Eckart, simplify the nuclear motion (rovibrational) Hamiltonian that arises in the second step of the Born–Oppenheimer approximation. They make it possible to approximately separate rotation from vibration. Although the rotational and vibrational motions of the nuclei in a molecule cannot be fully separated, the Eckart conditions minimize the coupling. The Eckart conditions are explained by Louck and Galbraith.

In Section 10.2 of the textbook by Bunker and Jensen, a numerical example of the application of the Eckart conditions is given. This example shows how the orientation of the axes, as obtained by application of the Eckart conditions, is minimally rotated when the molecule is vibrationally distorted.

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