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GIPAW Tensor Diagonalization Tool

diag_tensor_gipaw_scf.py reads g-tensors and hyperfine A-tensors directly from a Quantum ESPRESSO gipaw.x output file, diagonalizes them, and prints the principal values and principal axes in a form suitable for visualization in VESTA.

The script supports two ways to define the simulation-cell axes:

  1. Read the lattice vectors automatically from a Quantum ESPRESSO pw.x input file (scf.in).
  2. Enter the lattice vectors manually on the command line.

Requirements

  • Python 3
  • NumPy

Install NumPy if needed:

pip install numpy

Basic usage

python diag_tensor_gipaw_scf.py gipaw.out

The script automatically detects whether the gipaw.x output contains:

  • a g-tensor, or
  • hyperfine A-tensors.

For VESTA conversion, however, the lattice vectors must be known. The recommended method is to provide the corresponding pw.x input file.

1. Recommended mode: read lattice vectors from scf.in

g-tensor

python diag_tensor_gipaw_scf.py g-tensor.out --qe-input scf.in

The script:

  1. reads the last Delta_g total tensor printed by gipaw.x,
  2. symmetrizes the tensor,
  3. diagonalizes it,
  4. prints the principal values and normalized principal axes,
  5. converts the principal axes to lattice-vector coordinates (u,v,w),
  6. prints VESTA-ready vectors.

The last Delta_g total block is used because gipaw.x may print more than one version of the total g-tensor.

Hyperfine A-tensor

python diag_tensor_gipaw_scf.py hyperfine.out --qe-input scf.in

By default, the script processes atoms 1 through 7.

This is useful, for example, for a defect calculation in which:

  • atom 1 is the defect atom (e.g. Sn),
  • atoms 2-7 are its six nearest-neighbor carbon atoms.

The full hyperfine tensor is constructed as

$$A_{\mathrm{total}} = A_{\mathrm{dipolar}}^{\mathrm{sym}} + A_{\mathrm{FC}} I $$

where:

  • A_dipolar(sym) is taken from the last
total dipolar (symmetrized)

block,

  • A_FC is taken from the total column of the
Fermi contact

table.

The resulting total A-tensor is diagonalized separately for each selected atom.

Selecting specific atoms

By default, atoms 1-7 are processed.

Therefore these two commands are equivalent:

python diag_tensor_gipaw_scf.py hyperfine.out --qe-input scf.in

python diag_tensor_gipaw_scf.py hyperfine.out --qe-input scf.in --atoms 1-7

To process a different set of atoms, specify another range, for example:

--atoms 1-12

Individual atoms can also be selected:

python diag_tensor_gipaw_scf.py hyperfine.out \
    --qe-input scf.in \
    --atoms 1,2,5

Supported CELL_PARAMETERS formats

The script can read:

CELL_PARAMETERS angstrom

CELL_PARAMETERS bohr

CELL_PARAMETERS alat

For alat, the script determines the lattice constant from either:

A = ...

or

celldm(1) = ...

The lattice vectors are internally converted to Angstrom.

Example:

CELL_PARAMETERS angstrom
10.701  0.000  0.000
0.000  10.701  0.000
0.000  0.000  10.701

2. Manual mode: enter lattice vectors explicitly

If the original scf.in file is not available, the lattice vectors can be supplied manually.

General syntax:

python diag_tensor_gipaw_scf.py gipaw.out \
    --a ax ay az \
    --b bx by bz \
    --c cx cy cz

For example, for a cubic cell with lattice constant 10.701 Å:

python diag_tensor_gipaw_scf.py g-tensor.out \
    --a 10.701 0 0 \
    --b 0 10.701 0 \
    --c 0 0 10.701

For hyperfine:

python diag_tensor_gipaw_scf.py hyperfine.out \
    --a 10.701 0 0 \
    --b 0 10.701 0 \
    --c 0 0 10.701 \
    --atoms 1-7

The manual vectors should correspond to the same simulation cell used in the original pw.x calculation.

Crystallographic axis definitions

By default, the script uses

z = c
y = b

which corresponds to

--iz 0 0 1
--iy 0 1 0

The vectors are defined as integer combinations of the lattice vectors:

$$ z = i_a a + i_b b + i_c c $$

$$ y = j_a a + j_b b + j_c c $$

For example:

--iz 1 1 1

defines the crystallographic z-axis along

$$ a+b+c $$

which corresponds to the [111] direction for a cubic cell.

Example:

python diag_tensor_gipaw_scf.py g-tensor.out \
    --qe-input scf.in \
    --iz 1 1 1 \
    --iy 0 1 -1

The x-axis is then constructed automatically from the chosen y and z directions.

Forcing the tensor type

Normally the script automatically detects the calculation type.

If necessary, it can be forced manually.

For a g-tensor:

python diag_tensor_gipaw_scf.py gipaw.out \
    --type g \
    --qe-input scf.in

For hyperfine:

python diag_tensor_gipaw_scf.py gipaw.out \
    --type A \
    --qe-input scf.in

Output

For each tensor, the script prints:

  • the tensor used for diagonalization,
  • principal values,
  • normalized principal axes in Cartesian coordinates,
  • theta and phi angles,
  • lattice-coordinate directions (u,v,w),
  • positive and negative VESTA vectors,
  • orthogonality checks for the eigenvectors.

For hyperfine calculations, the same information is printed separately for every selected atom.

Typical workflow

g-tensor

pw.x < scf.in > scf.out
gipaw.x < gipaw_g.in > g-tensor.out

python diag_tensor_gipaw_scf.py g-tensor.out \
    --qe-input scf.in

Hyperfine

pw.x < scf.in > scf.out
gipaw.x < gipaw_hf.in > hyperfine.out

python diag_tensor_gipaw_scf.py hyperfine.out \
    --qe-input scf.in \
    --atoms 1-7

Notes

  • The script uses numpy.linalg.eigh, which is designed for real symmetric matrices.
  • Tensors are symmetrized before diagonalization.
  • For the g-tensor, the last Delta_g total block is used.
  • For hyperfine calculations, the full tensor includes both the symmetrized dipolar contribution and the total Fermi-contact contribution.
  • If --qe-input is supplied, lattice vectors are read from that file.
  • If --qe-input is not supplied, lattice vectors can be given manually using --a, --b, and --c.
  • The default hyperfine atom selection is 1-7.

Help

Display all command-line options:

python diag_tensor_gipaw_scf.py --help

diag_tensor_gipaw_vesta_cartesian.py

Simplified Python script for analyzing EPR g-tensors and hyperfine tensors from Quantum ESPRESSO GIPAW calculations.

  • Uses a single Cartesian coordinate system consistent with QE and reads lattice vectors from QE input files.
  • Diagonalizes symmetric tensors to obtain principal values and eigenvectors.
  • Constructs HFI tensors from Fermi-contact and spin-dipolar contributions.
  • Generates VESTA files with bidirectional principal-axis vectors (±) attached to atoms. For that you need to prepare .vesta file with necessary view, then the script will modify it by adding double arrows.

How to use:

Prepare .vesta file with necessary view and then

python diag_tensor_gipaw_vesta_cartesian.py g-tensor.out \
    --qe-input scf.in \
    --vesta-template d.spin.vesta \
    --vesta-output g_tensor.vesta \
    --vesta-length-mode normalized

VESTA Vector Length Modes:

  • normalized — Vector lengths are proportional to the absolute eigenvalues, normalized to the largest eigenvalue of each tensor. Useful for visualizing tensor anisotropy.
  • direction — All vectors have equal lengths, regardless of eigenvalues. Useful for comparing principal-axis orientations, particularly under different strain conditions.

Example:

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