Eckart conditions

The Eckart conditions, named after Carl Eckart,[1] 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 close to a reference (usually equilibrium) configuration. The Eckart conditions are explained by Louck and Galbraith[2] and in Section 10.2 of the textbook by Bunker and Jensen,[3] where a numerical example is given.

  1. ^ Eckart, C. (1935). "Some studies concerning rotating axes and polyatomic molecules" (PDF). Physical Review. 47 (7): 552–558. Bibcode:1935PhRv...47..552E. doi:10.1103/PhysRev.47.552.
  2. ^ Louck, James D.; Galbraith, Harold W. (1976). "Eckart vectors, Eckart frames, and polyatomic molecules". Rev. Mod. Phys. 48 (1): 69. Bibcode:1976RvMP...48...69L. doi:10.1103/RevModPhys.48.69.
  3. ^ Molecular Symmetry and Spectroscopy, 2nd ed. Philip R. Bunker and Per Jensen, NRC Research Press, Ottawa (1998) [1]ISBN 9780660196282