Two projector triple products in quantum crystallography.

Consider a projector matrix P, representing the first order reduced density matrix ρ1DETr,r′=2trPψrψ†r′ in a basis of orthonormal atom‐centric basis functions. A mathematical question arises, and that is, how to break P into its natural component kernel projector matrices, while preserving N‐representability of ρ1DETr,r′. The answer relies upon 2‐projector triple products, P′jPP′j. The triple product solutions, applicable within the quantum crystallography of large molecules, are determined by a new form of the Clinton equations, which—in their original form—have long been used to ensure N‐representability of density matrices consistent with X‐ray diffraction scattering factors. As such, the goal of this paper is to outline a possible pathway for the application of quantum crystallography to crystals of large molecular systems. [ABSTRACT FROM AUTHOR]