N-REPRESENTABILITY PROBLEM - CONDITIONS ON GEMINALS

The N-representability problem is approached by considering geminal product expansions of symmetric and antisymmetric functions. The N-completeness problem, i.e., the problem of determining when a set of geminals is a suitable basis for expanding symmetric or antisymmetric N-particle functions, is considered. New necessary conditions are given for both N-completeness and N-representability. In some cases, one can also obtain sufficient conditions; examples of such cases are discussed. The circumstances under which a density matrix can be derived from two or more different functions are also treated. Finally, extensions to higher order are also mentioned. © 1969 The American Physical Society.