The total energy from X-ray electron density?

Area of Science:

• Quantum crystallography
• Computational chemistry
• Solid-state physics

Background:

• Ensures idempotency, hermiticity, and normalization of the one-body density matrix during X-ray diffraction.
• N-representability is crucial for the variational theorem, mapping density matrices to N-body antisymmetric wavefunctions.
• Antisymmetry aligns with the experimental indistinguishability of fermions.

Purpose of the Study:

• Develop a procedure for fast and accurate quantum crystallography on large systems.
• Guarantee N-representable results for quantum crystallography calculations.
• Integrate quantum conditions with X-ray diffraction problem-solving.

Main Methods:

• Utilizes the kernel energy method (KEM) to assemble the one-body density matrix from fragment sub-matrices for large molecules.
• KEM approximates interactions up to two-body, ignoring higher orders, validated by past numerical testing.
• Provides an explicit form of the N-representable two-body density matrix derived from the one-body counterpart for total energy calculations.

Main Results:

• A procedure for fast and accurate N-representable quantum crystallography on large systems is developed.
• The method simultaneously solves the X-ray diffraction problem and ensures quantum conditions.
• Enables extraction of conceptual density functional theory and quantum theory of atoms in molecules properties from experimental structure factors.

Conclusions:

• The developed quantum crystallography approach is efficient and accurate for large systems.
• Guarantees N-representability and satisfaction of key quantum conditions.
• Facilitates advanced chemical property analysis from experimental diffraction data.