Current Methods and Optimization Algorithms for the Refinement of X-Ray Crystal Structures

Abstract

Optimization algorithms and other techniques used for the crystallographic refinement of both small molecule and macromolecular X-ray crystal structures are reviewed in this work. Emphasis is made on the advantages and disadvantages of every method in its application to the refinement process of different problems, as well as on their actual implementation in current program packages. A description of the most basic (first-level) algorithms based on physical grounds, such as maximum-likelihood, least-squares, molecular dynamics, maximum-entropy, Fourier and graphical methods, and holographic methods, is followed by a second-level approach, including Newton methods, simulated annealing, and gradient methods, among others, and finally by a third-level study which includes matrix decompositions and iterative methods for the solution of the resulting linear systems ofequations. In addition, by descending to the most basicmathematical and physical level, connections with other disciplines that use almost the same tools are easily made, showing not only the interdisciplinarity of crystallography but also the flow of information between different sciences.

Triruthenium and Triosmium Carbonyl Cluster Complexes Containing Bridging Ligands Derived from 2-Amino-7,8-benzoquinoline

“…Hydrogen atom positions were geometrically calculated and refined riding on their parent atoms, except the hydrides of 2 ·CH 2 Cl 2 , which were located and refined with free coordinates and thermal parameters, and the NH hydrogen atoms of 2 ·CH 2 Cl 2 , which were located and refined with free coordinates and fixed thermal parameters. The disorder of a chlorine atom of the solvent molecule of 2 ·CH 2 Cl 2 was treated with a mixture of constraints and restraints as described elsewhere . Plots were made with the EUCLID program package .…”

Ag2O versus Cu2O in the Catalytic Isomerization of Coordinated Diaminocarbenes to Formamidines: A Theoretical Study

“…The rather disordered floppy ligands could be finally modeled by means of convenient constrained/restrained algorithms. Further details about the refinement protocols used may be found elsewhere [18,19]. DFT theoretical calculations supporting the finding that the exclusive behavior of Ag2O in the catalytic isomerization of diaminocarbenes to formamidines is essentially based on an ideal combination of the basic character of the oxide ion and the Lewis acid character of the Ag + ion.…”

Di‐ and Trinuclear Ruthenium and Osmium Bis(2‐pyridyl) Ketone Oximate Derivatives

“…The disordered solvent molecule of 1·C 6 H 14 was treated with a mixture of constraints and restraints as described elsewhere. [24] The solvent molecule of 5·CH 2 Cl 2 was found disordered over two positions, with partial occupancies of 0.5. The molecular plots were made with the EUCLID program package.…”