4.4 Structure generation and variation operators

$\triangleright$ variable symmetries

Meaning: Possible symmetry groups for random symmetric structure generator crystals (spacegroups), layer plane groups for 2D-crystals, plane groups for surfaces, or point groups for clusters. A certain number of structures will be produced using randomly selected groups from this list, using randomly generated lattice parameters and atomic coordinates. During this process special Wyckoff sites can be produced from general positions (Fig. 7).

Default:

For 3D crystals: 2-230 For 2D crystals: 2-80 For clusters: E C2 D2 C4 C3 C6 T S2 Ch1 Cv2 S4 S6 Ch3 Th Ch2 Dh2 Ch4 D3 Ch6 O D4 Cv3 D6 Td Cv4 Dd3 Cv6 Oh Dd2 Dh3 Dh4 Dh6 Oh C5 S5 S10 Cv5 Ch5 D5 Dd5 Dh5 I Ih

Format:

% symmetries 195-198 200 215-230 % EndSymmetries

$\includegraphics[scale=0.3]{pic/Wyckoff_positions.png}$

Figure 7: Example of random symmetric structure generation and merging atoms onto special Wyckoff positions (for detail, see Ref. ¹³).

$\triangleright$ variable splitInto

Meaning: Defines the number of identical subcells or pseudosubcells in the unit cell. If you do not want to use splitting, just use the value 1, or delete the block. Use splitting only for systems with $>$ 25–30 atoms/cell.

Default: 1

Format:

% splitInto (number of subcells into which the unit cell is split) 1 2 4 % EndSplitInto

Subcells introduce extra translational (pseudo)symmetry. In addition to this, each subcell can be built using a special space groups algorithm developed by A.R. Oganov and H.T. Stokes and implemented by H.T. Stokes (see Reference ¹³).

$\triangleright$ variable fracGene

Meaning: Percentage of structures obtained by heredity; 0.5 means 50%, etc.

Default: 0.5

Format:

0.5 : fracGene

$\triangleright$ variable fracRand

Meaning: Fraction of the generation produced by random symmetric structure generator.

Default: 0.2

Format:

0.20 : fracRand

$\triangleright$ variable fracTopRand

Meaning: Percentage of structures obtained by topological random generator.

Default: 0.2

Format:

0.20 : fracTopRand

$\triangleright$ variable fracPerm

Meaning: Percentage of structures obtained by permutation; 0.1 means 10%, etc.

Default: 0.1 if there is more than one type of atom/molecule; 0 otherwise.

Format:

0.1 : fracPerm

$\triangleright$ variable fracAtomsMut

Meaning: Specifies the percentage of structures obtained by softmutation or coormutation.

Default: 0.1

Format:

0.1 : fracAtomsMut

$\triangleright$ variable fracRotMut

Meaning: Percentage of structures obtained by mutating orientations of randomly selected molecules; 0.1 means 10%, etc. Use it only for molecular crystal structure prediction (calculationType = 310, 311)

Default: 0.1 for molecular crystals; 0 otherwise.

Format:

0.1 : fracRotMut

$\triangleright$ variable fracLatMut

Meaning: Percentage of structures obtained from lattice mutations; 0.1 means 10%, etc.

Default: 0 for fixed-cell prediction; 0.1 otherwise. We tend to se always fracLatMut = 0

Format:

0.1 : fracLatMut

NOTE: If the sum of all the fractions (fracGene + fracRand + fracPerm + …) is not equal to 1, all fractions will be normalized.

$\triangleright$ variable fracSpinMut

Meaning: Percentage of structures obtained by spin mutation; 0.1 means 10%, etc. Used only for magnetic structure optimization.

Default: 0.1

Format:

0.2 : fracSpin

Notes:

(1) Spin mutaion operator always changes the magnetic structure. For example, FM-L states will never generate FM-L states after mutation, but can transform to NM, FM-H and so on. For AFM states, spin mutation can generate another AFM, but with different spin-up and spin-down arrangement.

(2) The ratio of mutation to new states is determined by magRatio.

$\triangleright$ variable howManySwaps

Meaning: For permutation, the number of pairwise swaps will be randomly drawn from a uniform distribution between 1 and howManySwaps.

Default: 0.5(maximum number of possible swaps). If atoms and , and atoms and are swappable, then the total number of possible swaps is , and the default for howManySwaps is . In most cases, it is a good idea to rely on this default.

Format:

5 : howManySwaps

$\triangleright$ variable specificSwaps

Meaning: Specifies which atom types you allow to swap in permutation.

Default: blank line, which means no specific swaps and all atoms are permutable.

Format:

% specificSwaps 1 2 % EndSpecific

NOTE: In this case, atoms of type 1 can be swapped with atoms of type 2. If you want to try all possible swaps, just leave a blank line inside this keyblock, or delete the block.

$\triangleright$ variable AutoFrac

Meaning: Enables automatic evolution of percentages of variation operators, which speeds up the calculation by up to $\sim$ 2 times. This is done by encouraging operators which produce more diverse and lower-energy structures. To switch to user-defined percentages, set AutoFrac=0.

Default: 0

Format:

1 : AutoFrac