signs of matrix elements. This approximation treats the form and phase, $0$ or $\pi$, of each NSO as independent variables. The choice of signs for each index is not specified in [[**\[signprod\]**]{}]{}. Most computation schemes start their convergence towards the minimum energy with random initial NSOs, and similarly the choice of signs in [[**\[signprod\]**]{}]{} should be random, half positive and half negative. The number $L$ of initial NSOs should be greater than $M$ to allow for the possibility of unequal numbers of positive and negative signs associated with the $M$ active NSOs.

OP-NOFT-0
=========

The SD’s in [[**\[expansion\]**]{}]{} can be classified by their seniority, the number $A$ of singly-occupied one-particle states they contain. For $N$ even and for a global spin singlet ($S=0$) state, the $N$-particle Hilbert space divides into sectors of increasing even seniority starting with $A=0$, where all SD’s contain only doubly occupied states. That only even seniority occurs is a consequence of the orthogonality constraint. For molecular systems CI expansions converge rapidly with seniority, and $A=0$ calculations (DOCI calculations) describe dissociation rather well, as demonstrated in [@Bytautas2011].

We now formulate OP-NOFT explicitly in the $A=0$ sector both to illustrate further how an OP-NOFT functional is constructed and 