Two projector triple products in quantum crystallography

Consider a projector matrix P, representing the first order reduced density matrix.1oDETTHORNor, r0THORN 1/4 2trP.orTHORN.+or0THORN 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. 1oDETTHORN r,ro 0THORN. The answer relies upon 2-projector triple products, P0 jPP0 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.

Automated summary

This paper discusses the decomposition of the projector matrix P and introduces the use of 2-projector triple products to achieve this. These methods are applicable in quantum crystallography of large molecules, ensuring N-representability through Clinton equations.