Crystal Structure Search using Constrained Optimization

Outlines

• Problem Statement
• Optimization Algorithm for Crystal Structure Search
• Gradient Descent with vs. without Momentum
• Optimization with vs. without Constraint
• Initial Structure Factor vs. the Experimental One
• Last Structure Factor vs. the Experimental One
• Pictures

Problem Statement

• Prediction of the atomic crystal structure plays an important role in chemistry, planetary science, and material science.

• This work aims to develop a new algorithm for the crystal structure search problem.

• The proposed algorithm redefines the crystal structure search problem as a constrained optimization problem, which is based on two premises:

  • Energy minimization: Stable crystal structure is the one that has minimum energy.
  • Prior constraint: The static structure factor of the predicted crystal structure should match the experimental one, which is obtained from crystallography.

Optimization Algorithm

Optimization with vs. without Momentum