Crystal Structure Search using Constrained Optimization

Hung P. Do, BSc

Trieste, Italy, August 2009


  • 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