Appropriate constraints for variational optimization of electronic density matrices and electron densities

Euler equations characteristic of the electronic reduced density matrix have previously been obtained by minimizing an energy functional subject to trace constraints 〈PK 〉 =N , in whichN is the number of particles. It is shown that these constraints are inadequate to exclude variations that violateN -representability conditions. However, a first-order reduced density matrix that does satisfyN -representability conditions is formulated as a functional of the orbital densities through use of angular momentum recoupling. Modified variational constraints are proposed.