multitorch

Differentiable multiplet simulations for X-ray spectroscopy in PyTorch.

multitorch computes L-edge X-ray absorption (XAS), emission (XES), and resonant inelastic X-ray scattering (RIXS) spectra for 3d transition metal complexes using crystal-field and charge-transfer multiplet theory. The entire pipeline — from Wigner coupling coefficients through Hamiltonian diagonalization to broadened spectra — runs in pure PyTorch with float64 precision and full torch.autograd support.

Features

• Differentiable end-to-end — gradients flow from physical parameters (Slater reduction, spin-orbit coupling, crystal field, charge transfer) through eigenvalues and transition matrices to the final spectrum
• No Fortran runtime — all physics computed natively in Python/PyTorch; pre-computed angular coefficients are bundled as package data
• XAS, XES, RIXS — L-edge absorption, emission, and 2D resonant inelastic scattering maps via the Kramers-Heisenberg kernel
• Validated — 477 tests; numerical agreement with the established Cowan/ttmult Fortran suite across 9 Ti-Ni fixtures (cosine similarity

  = 0.97)

• GPU-ready — tensors move to any PyTorch device

Installation

git clone https://github.com/follmerlab/multitorch.git
cd multitorch
pip install -e .

Requirements: Python >= 3.10, PyTorch >= 2.2, NumPy, SciPy.

Optional extras:

pip install -e ".[plot]"# adds matplotlib
pip install -e ".[notebook]"# adds matplotlib + jupyter
pip install -e ".[dev]"# adds pytest, pytest-cov, sympy

Or with conda:

conda env create -f requirements/environment.yml
conda activate multi
pip install -e .

Quick start

importtorchfrommultitorchimportcalcXAS# Ni2+ L-edge XAS in D4h symmetryx, y=calcXAS(
element="Ni", valence="ii", sym="d4h", edge="l",
cf={"tendq": 1.0, "ds": 0.0, "dt": 0.01},
slater=0.8, soc=1.0, T=300,
)
# Plotimportmatplotlib.pyplotaspltplt.plot(x.numpy(), y.detach().numpy())
plt.xlabel("Energy (eV)")
plt.ylabel("Intensity")
plt.show()

Autograd example

slater=torch.tensor(0.8, dtype=torch.float64, requires_grad=True)
x, y=calcXAS(
element="Ni", valence="ii", sym="d4h", edge="l",
cf={}, slater=slater, soc=1.0,
)
# Gradient of the spectrum w.r.t. Slater reductionloss=y.sum()
loss.backward()
print(slater.grad) # d(spectrum)/d(slater)

RIXS

frommultitorchimportcalcRIXSrixs_map=calcRIXS(
"multitorch/data/fixtures/nid8ct/nid8ct.ban_out", # absorption"multitorch/data/fixtures/nid8ct/nid8ct.ban_out", # emission
)

API reference

Function	Description
calcXAS(element, valence, sym, edge, cf, ...)	Compute XAS from physical parameters (differentiable)
calcXAS(..., ban_output_path=...)	Compute XAS from a pre-computed .ban_out file
calcRIXS(ban_abs_path, ban_ems_path, ...)	2D RIXS map via Kramers-Heisenberg
calcXES(...)	X-ray emission spectrum
calcDOC(...)	Ground-state configuration weights
getXAS(ban_output_path, ...)	Convenience wrapper for file-based XAS
preload_fixture(fixture_dir)	Cache parsed fixture for fast parameter sweeps
calcXAS_cached(fixture, ...)	XAS from a cached fixture (no file I/O per call)

All functions are importable from multitorch directly:

frommultitorchimportcalcXAS, calcRIXS, calcDOC, getXAS

Notebooks

Four tutorial notebooks in notebooks/:

Notebook	Description
01_quickstart	One-call spectrum with broadening parameter sweep
02_pipeline_walkthrough	Layer-by-layer: Wigner symbols -> Hamiltonian -> sticks -> spectrum
03_parameter_exploration	Ti-Ni L-edge series, 10Dq/Slater sweeps with autograd
04_rixs_quickstart	2D RIXS maps, line cuts, autograd through the kernel

pip install -e ".[notebook]"
jupyter lab notebooks/

Architecture

Physical parameters (slater, soc, cf, delta)
|
v
Atomic scaling (multitorch.atomic)
|
v
Angular coefficients (multitorch.angular) -- Wigner 3j/6j, CFP, RME
|
v
Hamiltonian assembly + diagonalization (multitorch.hamiltonian)
|
v
Boltzmann stick spectrum (multitorch.spectrum.sticks)
|
v
Pseudo-Voigt broadening (multitorch.spectrum.broaden)
|
v
(x, y) spectrum tensors -- autograd-compatible

Testing

pytest tests/ -q

477 tests covering Wigner primitives, file parsers, angular RME construction, Hamiltonian eigenvalues, spectral broadening, autograd gradients, and end-to-end parity with Fortran reference outputs.

Background

multitorch implements the multiplet theory described in:

• F.M.F. de Groot, "Multiplet effects in X-ray spectroscopy," Coordination Chemistry Reviews 249 (2005) 31-63
• R.D. Cowan, The Theory of Atomic Structure and Spectra (University of California Press, 1981)

The computational approach follows the Cowan/Butler/ttmult framework, replacing the Fortran numerical core with differentiable PyTorch tensors while preserving numerical agreement.

License

MIT -- see LICENSE.