The potential problem caused by kppa based method used in automatic_density function.

[hongyi-zhao]

Below is the source code of pymatgen automatic_density function:

pymatgen/src/pymatgen/io/vasp/inputs.py

Lines 1293 to 1335 in 4a2c3df

	def automatic_density(cls, structure: Structure, kppa: float, force_gamma: bool = False) -> Self:
	"""Get an automatic Kpoint object based on a structure and a kpoint
	density. Uses Gamma centered meshes for hexagonal cells and face-centered cells,
	Monkhorst-Pack grids otherwise.
	Algorithm:
	Uses a simple approach scaling the number of divisions along each
	reciprocal lattice vector proportional to its length.
	Args:
	structure (Structure): Input structure
	kppa (float): Grid density
	force_gamma (bool): Force a gamma centered mesh (default is to
	use gamma only for hexagonal cells or odd meshes)
	Returns:
	Kpoints
	"""
	comment = f"pymatgen with grid density = {kppa:.0f} / number of atoms"
	if math.fabs((math.floor(kppa ** (1 / 3) + 0.5)) ** 3 - kppa) < 1:
	kppa += kppa * 0.01
	lattice = structure.lattice
	lengths: Vector3D = lattice.abc
	ngrid = kppa / len(structure)
	mult: float = (ngrid * lengths[0] * lengths[1] * lengths[2]) ** (1 / 3)
	num_div: Tuple3Ints = cast(Tuple3Ints, [math.floor(max(mult / length, 1)) for length in lengths])
	is_hexagonal: bool = lattice.is_hexagonal()
	is_face_centered: bool = structure.get_space_group_info()[0][0] == "F"
	has_odd: bool = any(idx % 2 == 1 for idx in num_div)
	if has_odd or is_hexagonal or is_face_centered or force_gamma:
	style = cls.supported_modes.Gamma
	else:
	style = cls.supported_modes.Monkhorst
	return cls(
	comment,
	0,
	style,
	[num_div],
	(0, 0, 0),
	)

However, according to the discussion here, this method has the following potential risks:

In pymatgen, they try to correct this by dividing the cube root of the volume by the length of a vector. This should be constant for simple scaling of the cell. The expected coarser k-point mesh for larger systems comes from a division by the number of atoms instead. However, this is no way around the quantization problem. It eliminates the volume one but you could still change c/a for a cell at constant volume and run into the jump of 1 for the grid. By dividing by the number of atoms, they introduced a new problem that two structures in the same cell may have a different k-point mesh if one of them has a defect.

Regards,
Zhao