1 Crystal structure prediction

Under thermodynamic equilibrium conditions, most materials form crystalline states, which can possess long range order and symmetry. Understanding the structure of materials is fundamental to being able to understand their properties. However, the prediction of crystal structure used to be a long-term challenge in physical science. Back in 1988, Maddox summarized this problem with the following words ¹: “One of the continuing scandals in the physical sciences is that it remains in general impossible to predict the structure of even the simplest crystalline solids from a knowledge of their chemical composition. Solid such as crystalline water (ice) are still thought to lie beyond mortals’ ken." Over the next few years, programs started appearing that attempted to do just this and, in 1994, Gavezzotti ² addressed the fundamental questions – “Are crystal structures predictable?" The answer was again safely concluded as “No".

What do we mean by “crystal structure prediction (CSP) problem"? For each chemical composition, there are an infinite number of possible atomic arrangements that can, in principle, exist, which correspond to all possible local minima of the free energy. Among these, at any given thermodynamic conditions (pressure, temperature, chemical potential) there are a finite number of special structures, extreme in some sense - the lowest energy (i.e. the most stable structures), the highest/lowest value of some other property (hardness, density, band gap, superconducting, ..). In the simplest and most important case, by CSP, we mean finding, at given pressure (and temperature) conditions, the stable crystal structure knowing only the chemical formula ³.

It was widely believed that crystal structures are still fundamentally unpredictable until it stepped into 21th century ⁴. Many types of advanced techniques have been proposed to address this problem. Their power has been evidenced by many recent discoveries in the field of CSP ^{4; 5; 6; 7; 8; 9; 10; 11}. Among them, the USPEX method based on evolutionary algorithm is the leading one, and been viewed as a revolution in crystallography ⁴. It has lead to many exciting discoveries, such as the partially ionic phase of boron ¹², transparent insulating phase of sodium ¹³, etc.