How to Calculate Grid Density for Given kspacing in Pymatgen?

[hongyi-zhao]

Hi Pymatgen Team,

I'm currently working on setting up my VASP calculations and trying to understand how to derive the k-point grid size based on the KSPACING parameter. Could you guide me on how to calculate or estimate the grid density from a given KSPACING value using Pymatgen?

Any advice or pointers to relevant documentation would be greatly appreciated.

Thanks,
Zhao

[janosh]

not sure i understand the question but perhaps the VASP KSPACING docs can help https://www.vasp.at/wiki/index.php/KSPACING

using KSPACING means VASP places the points equidistant in reciprocal space, i.e. the units are inverse Angstrom. e.g. kspacing = 0.25 corresponds to reciprocal_density=64, meaning 64 kpoints/A^3

[hongyi-zhao]

Say, I set the following in INCAR:

KSPACING = 0.02 in \AA ^-1

Then, I want to know the corresponding n1 * n2 * n3 mesh when using a KPOINTS file.

[janosh]

that depends on the shape of the cell in reciprocal space. not sure if pymatgen has functionality to auto-convert between these formats for a given Structure. if not, PRs would be welcome!

KSPACING = 0.02 seems very tight. i doubt you need that much

[hongyi-zhao]

that depends on the shape of the cell in reciprocal space. not sure if pymatgen has functionality to auto-convert between these formats for a given Structure. if not, PRs would be welcome!

Based on the specification described in INCAR tag KSPACING and source code file mkpoints.F, we need to focus on the logic that computes NKPX, NKPY, and NKPZ using the lattice norms (BNORM) and the spacing (KSPACING). The optional multiplier (MULTIPL) is also considered if provided. Here's the implementation in Python:

import math

def calculate_grid_dimensions(bnorm, spacing, multipl=None):
    """
    Calculate the Monkhorst-Pack grid dimensions based on lattice norms and spacing.

    :param bnorm: Lattice norms (list or tuple of three floats).
    :param spacing: KPOINTS spacing (float).
    :param multipl: Optional multiplier (list or tuple of three integers).
    :return: Tuple of grid dimensions (NKPX, NKPY, NKPZ).
    """
    # Calculate initial grid dimensions based on spacing
    nkpx = max(1, math.ceil(bnorm[0] * math.pi * 2 / spacing))
    nkpy = max(1, math.ceil(bnorm[1] * math.pi * 2 / spacing))
    nkpz = max(1, math.ceil(bnorm[2] * math.pi * 2 / spacing))

    # Apply multiplier if provided
    if multipl:
        nkpx *= multipl[0]
        nkpy *= multipl[1]
        nkpz *= multipl[2]

    return nkpx, nkpy, nkpz

# Example usage
bnorm = [1.0, 2.0, 3.0]  # Example lattice norms
spacing = 0.5  # Example KPOINTS spacing
multipl = [2, 2, 2]  # Example multiplier

nkpx, nkpy, nkpz = calculate_grid_dimensions(bnorm, spacing, multipl)
print("Grid dimensions:", nkpx, nkpy, nkpz)

This Python function calculate_grid_dimensions mirrors the Fortran logic for determining the Monkhorst-Pack grid dimensions (NKPX, NKPY, NKPZ) based on the lattice norms (BNORM), the Monkhorst-Pack spacing (KSPACING), and an optional multiplier (MULTIPL).

KSPACING = 0.02 seems very tight. i doubt you need that much

What are the optimal KSPACING values, based on your experiences?

See here for the related discussion.

[janosh]

MP uses 0.22 for metals and 0.44 for insulators with smooth interpolation in between based on band gap

[hongyi-zhao]

#3709 (reply in thread)
KSPACING = 0.02 seems very tight. i doubt you need that much

After a second thought, the units we're talking about here may be different, but I'm talking roughly based on the units in vaspkit, aka, 2*PI/Angstrom, as described here:

But in vasp, the unit for KSPACING is \AA ^ -1. So, in my case, what I'm trying to say is 0.02 * 2 * PI should be used to set KSPACING.