Structure Perturbation¶

PESMaker currently implements a dpdata.System.perturb-style structure perturbation method. The goal is to generate configurations near a known structure by perturbing both the simulation cell and atomic coordinates.

Cell perturbation¶

Let the original cell matrix be:

\[ C = \begin{pmatrix} a_x & a_y & a_z \\ b_x & b_y & b_z \\ c_x & c_y & c_z \end{pmatrix} \]

where each row is a lattice vector in Cartesian coordinates.

PESMaker samples six random values:

\[ e_i \sim U(-f, f), \quad i = 1, \ldots, 6 \]

where \(f\) is cell_pert_fraction. The perturbation matrix is:

\[ P = \begin{pmatrix} 1 + e_1 & 0.5e_6 & 0.5e_5 \\ 0.5e_6 & 1 + e_2 & 0.5e_4 \\ 0.5e_5 & 0.5e_4 & 1 + e_3 \end{pmatrix} \]

The perturbed cell is:

\[ C' = C P \]

The diagonal terms stretch or compress the cell. The off-diagonal terms apply shear-like perturbations.

Coordinate transformation¶

Before adding independent atomic noise, PESMaker transforms the Cartesian atomic positions consistently with the cell perturbation:

\[ R' = R P \]

This keeps atoms deformed with the cell instead of changing only the lattice vectors.

Atomic displacement¶

For atom_pert_style: normal, each atom receives a Cartesian displacement:

\[ \Delta r = \frac{d}{\sqrt{3}} \begin{pmatrix} \eta_x \\ \eta_y \\ \eta_z \end{pmatrix}, \quad \eta_x,\eta_y,\eta_z \sim \mathcal{N}(0, 1) \]

where \(d\) is atom_pert_distance in Angstrom.

This means the three Cartesian components are sampled independently from a normal distribution with standard deviation \(d / \sqrt{3}\). For example, atom_pert_distance: 0.1 gives each Cartesian component a standard deviation of approximately \(0.0577\) Angstrom.

Implemented options¶

PESMaker currently supports three atomic perturbation styles:

normal: Gaussian Cartesian displacement.
uniform: random direction with radius sampled uniformly inside a sphere.
const: random direction with fixed displacement length.

Random perturbations are opt-in. If generation.perturb is omitted, or pert_num is 0, PESMaker writes only the expanded pristine structures.

A practical explicit perturbation setting is:

perturb:
  include_pristine: true
  pert_num: 49
  cell_pert_fraction: 0.03
  atom_pert_distance: 0.1
  atom_pert_style: normal

These values generate moderately distorted structures around the starting geometry and are useful for preparing initial DFT single-point candidates. The expanded pristine structure is always written as pristine_<supercell>.<format>, for example pristine_3x3x3.vasp. include_pristine: true also writes one pristine file for every generated defect variant when random perturbations are enabled. Defect-variant pristine files append the variant name, for example pristine_3x3x3_single_vacancy_Te_000001.vasp or pristine_3x3x1_line_defect_Te_const_a_000002.vasp. Without random perturbations, every generated variant is written once as a pristine structure.