We have developed an efficient and reliable methodology for crystal structure prediction, merging ab initio total-energy calculations and a specifically devised evolutionary algorithm. This method allows one to predict the most stable crystal structure and a number of low-energy metastable structures for a given compound at any conditions without requiring any experimental input. Extremely high (nearly 100%) success rate has been observed in a few tens of tests done so far, including ionic, covalent, metallic, and molecular structures with up to 40 atoms in the unit cell. We have been able to resolve some important problems in high-pressure crystallography and report a number of new high-pressure crystal structures (stable phases: -oxygen, new phase of sulphur, new metastable phases of carbon, sulphur and nitrogen, stable and metastable phases of ). Physical reasons for the success of this methodology are discussed.
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Although an exhaustive search for all metastable structures is hardly possible.
Usually called “genetic crossover” or “two-parent variation operator.”
Like the method of Deaven and Ho (Ref. 12), our evolutionary algorithm involves the local optimization of each generated structure and a real-space representation of the atomic positions. Note that the method of Ref. 12 was developed specifically for molecules and has never been adapted or applied to the prediction of structures of crystals.
The hard constraints are the minimum acceptable interatomic distance, the minimum value of a lattice parameter, and the minimum and maximum cell angles. The minimum interatomic distance is usually set to values about , to exclude unphysical starting structures and problems with large pseudopotential core overlaps. The minimum length of a lattice parameter is usually set to less than the diameter of the largest atom under pressure, and the cell angles are allowed to take values between and (according to a well-known crystallographic theorem, cells with all other angles can always be transformed to cells with angles between 60° and 120° and having shorter cell vectors). These options can also be used to restrict the search space if any information about the cell shape is available (e.g., that the cell is cubic, hexagonal, etc.).
List of initial applications (as of December 2005) includes: hydrogen at 200 and (2, 3, 4, 6, 8, 12, and /cell), carbon (at fixed cell parameters of diamond and with variable cell at 0, 100, 300, 500, 1000, and and with /cell), silicon (10, 14, and with /cell), xenon (at 200 and , /cell), nitrogen at (with 6, 8, 12, and /cell) and at (with /cell), oxygen (at experimental cell parameters of the and phases, and with variable cell at 25, 130, and using 4, 6, 8, 12, /cell), iron at (/cell), sulphur at (with 3, 4, 6, 8, 9, and /cell) chlorine at (/cell), fluorine (50 and , /cell), at (/cell), at /cell), at (3, 6, 9, 12, 18, and /cell), (at experimental cell parameters of anatase, /cell), at /cell), at /cell), at /cell), urea at experimental cell parameters /cell), with /cell (at experimental cell parameters of postperovskite, and with variable cell at 80 and ) and 40 at/cell (at experimental cell parameters of postperovskite) at (5, 10, and /cell), (at 50, 80, and with 5, 10, and /cell; also at experimental cell parameters of postaragonite, /cell).
Because in shock compression temperature increases very quickly with pressure.
The simulation went through many structures that contained other molecules, e.g., , , , , and among other molecules and radicals. All the generated structures were molecular, but the most favorable structures contained only the urea molecules. Different packings of urea molecules were identified, the most stable one corresponds to the tetragonal structure of urea (Fig. 11) experimentally known to be stable at ambient conditions.
