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Crystal structure prediction using ab initio evolutionary techniques: Principles and applications
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Image of FIG. 1.
FIG. 1.

Prediction of the crystal structure of at (/cell). Enthalpy (per 20 atoms) of the best structure as a function of generation. Insets show the perovskite and postperovskite structures (blue polyhedra— octahedra; gray spheres—Mg atoms). Between 6th and 12th generations the best structure is perovskite, but at the 13th generation the postperovskite structure is found (at this structure is lower in enthalpy than perovskite). This simulation used no experimental information and illustrates that our method can find both the stable and low-energy metastable structures in a single simulation.

Image of FIG. 2.
FIG. 2.

Structures of carbon identified by USPEX. (a) Graphite (, stable state), (b) diamond (stable state up to , metastable above ), (c) bc8 structure (stable above ; structural parameters at : space group , , ), (d) lonsdaleite (metastable at ) and (e) “” structure [metastable at , with structural parameters: space group , , , , ; , , , ].

Image of FIG. 3.
FIG. 3.

Metastable “wall” structures of carbon found by USPEX at . (a) structure containing both - and -hybridized carbon atoms ( higher in energy than graphite) and (b) structure containing only -carbon atoms ( higher in energy than graphite).

Image of FIG. 4.
FIG. 4.

Some of the energetically competitive high-pressure structures of sulphur found by USPEX. (a) phase with ring molecules, (b) S-III phase with spiral tetragonal chains, (c) structure with distorted spiral tetragonal chains in twisted orientations, (d) S-II phase with trigonal spiral chains in three orientations, (e) Se-I structure with trigonal spiral chains in one orientation (space group ), and (f) structure with distorted spiral tetragonal chains running in two perpendicular directions.

Image of FIG. 5.
FIG. 5.

Structural elements of high-pressure phases of sulphur shown in Fig. 4. (a) Spiral trigonal chain, (b) spiral tetragonal chain, and (c) ring molecule.

Image of FIG. 6.
FIG. 6.

Enthalpies (relative to the phase) of the phases of sulphur. According to these calculations, at the structure is stable between 7 and .

Image of FIG. 7.
FIG. 7.

Structures of nitrogen identified by USPEX at : (a) cubic gauche and (b) metastable polymeric form related to cubic gauche. Cubic gauche structure at : space group , , . Related metastable structure at : space group , , , , , , .

Image of FIG. 8.
FIG. 8.

Structures of oxygen identified by USPEX at : (a) stable chain structure and (b) metastable structure with groups (higher in enthalpy by ). Stable structure at : space group , , , , . Metastable structure: space group , , , , , , , , , , .

Image of FIG. 9.
FIG. 9.

Structure of anatase found by USPEX.

Image of FIG. 10.
FIG. 10.

Stable high-pressure phases of found by USPEX (see Ref. 71 for details). (a) Structure of postaragonite (space group ): red spheres—Ca; blue—C; and green—O atoms. (b) Calculated and experimental powder diffraction for samples quenched to : top—experiment; and bottom—calculation (red peaks—postaragonite; green–NaCl; and blue–Pt). (c) Orthorhombic structure stable above .

Image of FIG. 11.
FIG. 11.

Metastable phases of found by USPEX in the range of (Ref. 71) (a) Triclinic , (b) trigonal , and (c) monoclinic . Between 50 and these metastable structures have enthalpies only above postaragonite.

Image of FIG. 12.
FIG. 12.

Structures of ice at found by USPEX. (a) Ice Ih and (b) ice Ic.

Image of FIG. 13.
FIG. 13.

Structure of urea, , found by USPEX at .


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Crystal structure prediction using ab initio evolutionary techniques: Principles and applications