Knowledge Bank

Approximate energy expression of a Rydberg electron of given orbital angular momentum L is derived showing its $mL$ dependence. The derivation takes into account of multipole potential field up to hexadecapole and includes mixing of different L’s by odd (dipole and octopole) potentials for systems without inversion symmetry. The proportion of different L’s will be estimated from (translational) $expansion1$ of atomic orbitals in the LCAO-MO’s. Symmetry constraints and correlation between Rydberg molecular orbitals and dissociated fragments will be discussed. $\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}$ see, for example, Y. N. Chiu, J. Math. Phys. 5, 283 (1964) and references therein.