Quantum crystallography: A perspective

• Published in: Journal of computational chemistry Vol. 39; no. 17; pp. 1021 - 1028
• Main Authors: Massa, Lou, Matta, Chérif F.
• Format: Journal Article
• Language: English
• Published: United States Wiley Subscription Services, Inc 30-06-2018
• Subjects: Antisymmetry; Biological properties; Clinton equations; Crystallography; Crystals; Density; density matrix; Electron density; Formalism; idempotent density matrix; kernel energy method; Mechanical properties; Molecular chains; N‐representability; projector density matrix; quantum crystallography; Quantum mechanics; quantum theory of atoms in molecules; Scattering; X-ray diffraction; N-representability; density matrix; idempotent density matrix; quantum theory of atoms in molecules; Clinton equations; kernel energy method; quantum crystallography; X-ray diffraction; electron density; projector density matrix
• ISSN: 0192-8651; 1096-987X
• DOI: 10.1002/jcc.25102

Extraction of the complete quantum mechanics from X‐ray scattering data is the ultimate goal of quantum crystallography. This article delivers a perspective for that possibility. It is desirable to have a method for the conversion of X‐ray diffraction data into an electron density that reflects the antisymmetry of an N‐electron wave function. A formalism for this was developed early on for the determination of a constrained idempotent one‐body density matrix. The formalism ensures pure‐state N‐representability in the single determinant sense. Applications to crystals show that quantum mechanical density matrices of large molecules can be extracted from X‐ray scattering data by implementing a fragmentation method termed the kernel energy method (KEM). It is shown how KEM can be used within the context of quantum crystallography to derive quantum mechanical properties of biological molecules (with low data‐to‐parameters ratio). © 2017 Wiley Periodicals, Inc.
Extraction of the full quantum mechanics from the X‐ray scattering experiment.