A simple, direct method is detailed for evaluating the lowest energy term arising from any electronic configuration. Only a single solution is obtained and no other allowed terms can be derived. The method entails assignment of magnetic quantum numbers to electrons in uncompleted shells, according to a uniform scheme and summation of these quantum numbers algebraically to afford a number, the absolute value of which is definitive for <i>L</i>. With the aid of a simple diagrammatic scheme both the resultant <i>L</i> and <i>S</i> vectors defining the ground state can be seen at a glance. The method is valid for ionic ground states and is illustrated with a number of examples for atomic and ionic configurations. All terms calculated are in agreement with the established values, and the conclusion seems permissible that the method can be applied with confidence toward prediction of ionic ground states as yet undetermined experimentally.
MAYER B. GOREN, "A Simple Method for Evaluation of Atomic and Ionic Ground States," J. Opt. Soc. Am. 40, 74-74 (1950)