5.7 Evolutionary metadynamics code

This is a very powerful method for finding the global minimum, as well as many low-energy metastable structures that are potentially kinetically accessible from the starting structure. The starting structure has to be high-quality and is given in the file POSCAR_1.

Evolutionary metadynamics is only enabled with the VASP and GULP codes at the moment.

To switch on the evolutionary metadynamics mode, you have to:

Specify
META : calculationMethod
300 : calculationType
Create file POSCAR_1 in the VASP5 format in your folder (evolutionary metadynamics requires a good starting structure, relaxed at the pressure of interest).
Specify the population size (in this case, this is the number of softmutations at each metastep):
30 : populationSize
Specify the pressure:
$\triangleright$ variable ExternalPressure
Meaning: The pressure at which you want to perform the calculation, in GPa.
Default: no default
Format:
10 : ExternalPressure (GPa)
Specify the following metadynamics-only options:

$\triangleright$ variable GaussianWidth

Meaning: The width of each of the Gaussians added to the energy surface to accelerate phase transitions. A good rule of thumb is to choose a value close to 0.10–0.15 $L$ , where $L$ is the minimum length of the unit cell, in Angstroms.

Default: ()

Format:

0.80 : GaussianWidth

$\triangleright$ variable GaussianHeight

Meaning: The height of each of the Gaussians added to the energy surface to accelerate phase transitions. A good rule of thumb (Martoňák et al., 2005) is to choose a value close to $L(\delta h)^2 G$ , where $L$ is the average length of the unit cell in Angstroms, $\delta h$ is the Gaussian width in Angstroms (see below), and $G$ is the shear modulus in kbars.

Default: (kbar)

Format:

2000 : GaussianHeight

$\triangleright$ variable FullRelax

Meaning: Metadynamics as such only relaxes structures within a fixed cell. For analysis, you need to perform complete structure relaxation (i.e. relaxing also the cell).

FullRelax=0 — no full relaxation will be performed (very fast option, but inconvenient for analysis of the results).
FullRelax=1 — only the best structure of the generation will be fully relaxed (also fast, sometimes sufficient).
FullRelax=2 — all inequivalent structures are fully relaxed (still fast, only $\sim$ 2 times slower than FullRelax=1, but provides a lot more insight. Strongly recommended for most cases).

Default: 2

Format:

2 : FullRelax

For full relaxation, when performing evolutionary metadynamics the format of the block abinitioCode is slightly different, for example:

    abinitioCode
    3 3 3 3 (3 3)
    ENDabinit

In the example above, there are four stages of relaxation within a fixed cell, and two stages of full relaxation (in parentheses). Remember that in the last fixed-cell stage of relaxation, pressure tensor must be accurate — this is what drives metadynamics.

NOTE: the use of parentheses in evolutionary metadynamics (calculationMethod = META) input is different from its use in evolutionary optimizations (calculationMethod = USPEX) described earlier in section 4.8. There, calculations in parentheses were done for the fully symmetrized structure and only properties taken into account (energies ignored). Here, there is no symmetrization and no property calculations - calculations in parentheses indicate full structure relaxation (including relaxation of the unit cell).

$\triangleright$ variable maxVectorLength

Meaning: Together with minVectorLength, this sets boundary values for basic cell lengths in evolutionary metadynamics (note that this is a different meaning for minVectorLength from normal calculations, and maxVectorLength is only used in evolutionary metadynamics). When any of the basic cell lengths becomes smaller than minVectorLength or larger than maxVectorLength, we add a steep correction “force” in metadynamics, which drives cell evolution towards “good” values. The correction forces are exactly zero when all basic cell lengths are in the “good” range.

Default: No default

Format:

12.0 : minVectorLength

$\includegraphics[scale=0.6]{pic/evolutionary_metadynamics.png}$

Figure 13: Enthalpy evolution of Al $_2$ SiO $_5$ starting with andalusite at 10 GPa (black line: enthalpies for best structures with constant h; magenta line: enthalpies for best structures after full relaxation). Sequence of structures obtained in this run: generation 1 (andalusite) $\rightarrow$ generation 9 (sillimanite) $\rightarrow$ generation 14 $\rightarrow$ generation 66 $\rightarrow$ generation 68 $\rightarrow$ generation 69 $\rightarrow$ generation 70 (kyanite).

Note: if you specify maxAt variable, a generalized evolutionary metadynamics calculation (exploiting different supercells) will be performed. When you run metadynamics, additional files will be found in the results1 folder, most importantly:

force.dat — analysis of forces on the cell, internal (f_c) and from the Gaussians (f_g);
presten — pressure tensor;
lattice.dat — cell shape change during the simulation;
enthalpies and enthalpies_relaxed — enthalpies of structures at each metastep at fixed cell and after full relaxation, respectively;
gatheredPOSCARS and gatheredPOSCARS_relaxed — structures at fixed cell and after full relaxation, respectively.

Fig. 13 shows an example of use of evolutionary metadynamics: starting from one Al $_2$ SiO $_5$ polymorph (andalusite), we obtained the other two known polymorphs (kyanite and sillimanite) and non-trivial phase transformation mechanisms.