6.3 Transition path sampling (TPS) method

Transition path sampling (TPS) is a method for simulating rare events: a good example of a rare event is a transition of a system from one stable state to another; these occur due to rare fluctuations, which cannot be observed within typical timescales of molecular dynamics simulations. Examples include protein folding, chemical reactions and nucleation. TPS is a powerful method to study these phenomena. In short, TPS is a technique performing Monte-Carlo sampling over transition trajectories (each of which is a molecular dynamics trajectory).

Input options for TPS

The TPS method is only enabled with the LAMMPS and CP2K (will be available soon) codes at the moment.

To switch on the TPS mode, you have to:

Specify
TPS : calculationMethod
Create a MD restart file lammps.restart for LAMMPS code or cp2k.restart for CP2K code in the Seeds/ folder.
Create an order parameter calculation script or use USPEX’s fingerprints as default. (See more details below).
Specify the following TPS options:

$\triangleright$ variable numIterations

Meaning: Maximum number of TPS steps.

Default: 1000

Format:

500 : numIterations

$\triangleright$ variable speciesSymbol

Meaning: Describes identities of all chemical species (atomic or molecular).

Default: No default

Format:

% speciesSymbol CH4 Si O % EndSpeciesSymbol

NOTE: In TPS, we use speciesSymbol to replace the atomType to support molecular species, together with numSpecies. For example, we can use

% numSpecies 1 648 1296 % EndNumSpecies % speciesSymbol CH4 Si O % EndSpeciesSymbol

to study diffusion of a methane (CH $_4$ ) molecule in a silica zeolite (SiO $_{2}$ ). In this case, methane molecule will be considered as a whole particle in writing MD input files in LAMMPS.

$\triangleright$ variable mass

Meaning: Masses for each type of species.

Default: Default value corresponding to the species

Format:

% mass 16.000 % EndMass

$\triangleright$ variable amplitudeShoot

Meaning: Distribution amplitude of the momentum for A $\rightarrow$ B and B $\rightarrow$ A directions in shooting operation.

Default: 0.1 0.1

Format:

% amplitudeShoot 0.12 0.12 % EndAmplitudeShoot

$\triangleright$ variable magnitudeShoot

Meaning: Factor for increasing or decreasing the amplitude of magnitude distribution when succeeded or failed to have a new MD trajectory, respectively.

Default: 1.05 1.05

Format:

% magnitudeShoot 1.0 1.05 % EndMagnitudeShoot

NOTE: Unless the user has system-specific experience, we strongly suggest to use this option to automatically adjust the distribution amplitude of the momentum.

$\triangleright$ variable shiftRatio

Meaning: Ratio of applying a shifter operation after having a successful shooter operation.

Default: 0.1

Format:

0.5 : shiftRatio

$\triangleright$ variable orderParaType

Meaning: Method of order parameter calculation to distinguish different phases:

“0” — user-defined method to calculate the order parameter, a script should be provided in cmdOrderParameter;
“1” — fingerprint method (Oganov & Valle, 2009).

Default: No default

Format:

0 : orderParaType

$\triangleright$ variable opCriteria

Meaning: Two values here specify the tolerable degree of similarity to the starting and ending states, respectively. If one or both ends of the trajectory lead to different end structures, such a trajectory will be rejected in the TPS method.

Default: No default

Format:

% opCriteria 0.995 0.995 % EndOpCriteria

NOTE: If you use the fingerprint method, the larger system you have, the more strict criteria you should have. For example, we should set opCriteria=[ 0.995, 0.995 ] with 1,000 atoms; and opCriteria=[ 0.998, 0.998 ] in system more than 30,000 atoms when studying the fcc $\rightarrow$ hcp phase transition.

$\triangleright$ variable cmdOrderParameter

Meaning: User-defined command to calculate the order parameter. It is not needed if you use the fingerprint method.

Default: No default

Format:

% cmdOrderParameter ./extractOp.sh % EndCmdOrderParameter

$\triangleright$ variable cmdEnthalpyTemperature

Meaning: User-defined command to extract the enthalpy and temperature from MD results.

Default: No default

Format:

% cmdEnthalpyTemperature ./extractHT.sh % EndCmdEnthalpyTemperature

$\triangleright$ variable orderParameterFile

Meaning: File name to store the order parameter history in a single MD calculation for TPS to read.

Default: fp.dat

Format:

op.dat : orderParameterFile

$\triangleright$ variable enthalpyTemperatureFile

Meaning: File name to store the enthalpy & temperature history in a single MD calculation for TPS to read or user-defined script to analyze.

Default: HT.dat

Format:

HT0.dat : enthalpyTemperatureFile

$\triangleright$ variable trajectoryFile

Meaning: File name to store the MD trajectory. This name should be consistent with the MD trajectory output file name from the calculation.

Default: traj.dat

Format:

trajectory.xyz : trajectoryFile

$\triangleright$ variable MDrestartFile

Meaning: File name to store the MD restart file from the calculation for TPS to read. This name should be consistent with the MD restart file name from the calculation.

Default: traj.restart

Format:

lammps0.restart : MDrestartFile