The pair-functional method for direct solution of molecular structures. II. Small-molecule tests.

Area of Science:

• Crystallography
• Computational Chemistry
• Structural Biology

Background:

• Direct methods are crucial for solving the phase problem in X-ray crystallography.
• Traditional direct methods can struggle with increasing structural complexity and data limitations.
• The Patterson function offers insights but has limitations at high resolution.

Purpose of the Study:

• To implement and test a novel pair-functional direct method for atomic structure determination.
• To develop and compare iterative algorithms for refining atomic models using pair potentials.
• To assess the method's performance on both model systems and realistic molecular structures.

Main Methods:

• Development of a pair-functional direct method incorporating imaging properties similar to the Patterson function.
• Implementation of two iterative refinement algorithms: a peak-picking method and a pair-and-square method.
• Computational experiments using point-atom grid models and realistic molecular test structures.

Main Results:

• The pair-functional method achieved exact ab initio solutions for up to 600 atoms in perfect data scenarios.
• Reduced structure searches successfully solved models with as few as 25% of the atoms.
• Seeded searches, utilizing known fragments, solved structures containing up to 30,000 atoms.
• Realistic molecular tests demonstrated successful structure solution for 50-200 atom structures under various conditions.

Conclusions:

• The pair-functional direct method demonstrates significant potential for solving complex atomic structures.
• Iterative refinement algorithms effectively refine pair potentials and intensity correlations.
• The method shows promise for ab initio structure solution and refinement in crystallography.