The density equation proposed by Nakatsuji assumes a matrix form when a basis set is introduced. The matrix equation is shown to have highly degenerate solutions for almost any value of the energy, and thus to provide little useful information in the absence of $N$-representability constraints. The imposition of such constraints is also considered, and approximate constraints are predicted to be of little value.

• Received 25 September 1978

DOI:https://doi.org/10.1103/PhysRevA.19.1893