Topological partition of the crystal elastic constants
Alberto Otero‐de‐la‐Roza, Vı́ctor Luaña · Acta Crystallographica Section A Foundations of Crystallography · 2011
We report for the first time the total constrained refinement of a quantum mechanical wavefunction to X-ray diffraction data.This means that the geometrical and atomic displacement parameters (ADP's) used to define the structure factors from the wavefunction are completely refined to the X-ray data by a least-squares procedure, using aspherical atomic form factors derived from the quantum mechanical charge density by Hirshfeld atom partitioning [1].The electronic variables -the orbital coefficients -are refined subject to the restraint/constraint that they minimise the total quantum mechanical energy because there are more parameters than data.Both geometrical refinement and electronic constraints are applied simultaneously, for the first time, using a "block-diagonal" iterative procedure.In addition, refinement/constraint to the structure factor magnitudes is used for the first time.Furthermore, the procedure is extended to remove the previous restriction to Z'=1 and single-molecule structures.Each unique molecular wavefunction in the unit cell is self-consistently embedded in the multipole field of its neighbours.The technique is reported using DFT-type wavefunctions in a gaussian basis set expansion.We report results (geometric parameters and other derived properties) for the dipeptide Gly-L-Ala.Geometrical parameters are compared to those from a neutron diffraction analysis.We also report results for a tripeptide L-Alanyl-L-Tyrosyl-L-Alanine cocrystallizing with dimethylformamide.