kaldo 2.1.0

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Overview

κALDo (kALDo) is an open-source Python package for computing vibrational, elastic, and thermal transport properties of crystalline, disordered, and amorphous materials from first principles and machine-learned interatomic potentials.

Built on the anharmonic lattice dynamics (ALD) framework, κALDo provides GPU- and CPU-accelerated implementations of:

• Boltzmann Transport Equation (BTE) for crystals
• Quasi-Harmonic Green-Kubo (QHGK) method for disordered and amorphous systems

The QHGK formalism uniquely extends thermal transport predictions beyond crystals to materials lacking long-range order, including glasses, alloys, and complex nanostructures.

Key Features

Transport Methods

Method	Use Case	Solvers
BTE	Crystalline materials	RTA, Self-consistent iteration, Full matrix inversion, Eigendecomposition
QHGK	Amorphous/disordered materials	Diffuson, locon, propagon decomposition

Force Constant Sources

κALDo interfaces with diverse computational tools:

• Ab initio codes: Quantum ESPRESSO, VASP (DFPT)
• MD packages: LAMMPS (with USER-PHONON)
• Machine-learned potentials: NEP, MACE, MatterSim, Orb, DeepMD (via ASE)
• External phonon codes: ShengBTE, phono3py, HiPhive
• TDEP: Temperature-dependent effective potentials from MD trajectories

Physical Corrections

• Isotopic scattering via Tamura perturbation theory
• Non-analytical corrections (NAC) for polar materials (LO-TO splitting)
• Finite-size effects and boundary scattering
• Anharmonicity quantification (σ_A score)

Performance & Scalability

• GPU acceleration via TensorFlow (5-10× speedup for N > 50 atoms)
• Sparse tensor operations for memory efficiency
• Multiple storage backends: formatted text, NumPy, HDF5, memory-only
• Scales to 10,000+ atom systems for QHGK calculations

Quickstart

Run κALDo interactively on Google Colab:

Tutorial	Description
	Thermal transport in crystalline silicon (BTE)
	Thermal transport in amorphous silicon (QHGK)

Installation

pip install kaldo

Docker deployment:

docker pull gbarbalinardo/kaldo:latest

Basic Usage

Example calculating thermal conductivity of SiC using the MatterSim machine-learned potential:

# Import kALDo classes and ASE
from kaldo.forceconstants import ForceConstants
from kaldo.phonons import Phonons
from kaldo.conductivity import Conductivity
import kaldo.controllers.plotter as plotter
from ase.build import bulk
from ase.optimize import BFGS
from ase.constraints import StrainFilter
from mattersim.forcefield import MatterSimCalculator

# Stage 1: Structure optimization
atoms = bulk('SiC', 'zincblende', a=4.35)
calc = MatterSimCalculator(device='cuda')
atoms.calc = calc

# Optimize lattice parameters and atomic positions
sf = StrainFilter(atoms)
opt = BFGS(sf)
opt.run(fmax=0.001)

# Stage 2: Compute force constants using finite differences
fc = ForceConstants(
    atoms=atoms,
    supercell=[10, 10, 10],
    third_supercell=[5, 5, 5],
    folder='fd_SiC_MatterSim'
)
fc.second.calculate(calc, delta_shift=0.03)
fc.third.calculate(calc, delta_shift=0.03)

# Stage 3: Calculate phonon properties
phonons = Phonons(
    forceconstants=fc,
    kpts=[15, 15, 15],
    temperature=300,
    is_classic=False,
    folder='ALD_SiC_MatterSim'
)

# Plot phonon dispersion
plotter.plot_dispersion(phonons, n_k_points=300)

# Stage 4: Calculate thermal conductivity
cond = Conductivity(phonons=phonons, method='inverse')

# Access results
kappa = cond.conductivity.sum(axis=0)
print(f"Thermal conductivity: {kappa.trace()/3:.1f} W/m/K")

Supported File Formats

Source	Format String	2nd-Order Files	3rd-Order Files
NumPy	numpy	second.npy	third.npz or third.npy
ESKM	eskm	Dyn.form	THIRD
LAMMPS	lammps	Dyn.form	THIRD
VASP + ShengBTE	vasp-sheng	FORCE_CONSTANTS_2ND or FORCE_CONSTANTS	FORCE_CONSTANTS_3RD
QE + ShengBTE [1]	qe-sheng	espresso.ifc2	FORCE_CONSTANTS_3RD
VASP + d3q [2]	vasp-d3q	FORCE_CONSTANTS_2ND or FORCE_CONSTANTS	FORCE_CONSTANTS_3RD_D3Q
QE + d3q	qe-d3q	espresso.ifc2	FORCE_CONSTANTS_3RD_D3Q
HiPhive	hiphive	model2.fcs	model3.fcs
TDEP	tdep	infile.forceconstant	infile.forceconstant_thirdorder

[1]: κALDo supports loading force constants with mixed formats. Here, it means that the second-order force constant comes from Quantum Espresso and the third-order force comes from thirdorder.py in ShengBTE. See examples on how to use thirdorder.py with Quantum Espresso. [2]: The second-order force constant comes from VASP and the third-order force constant comes from D3Q (Thermal2). See examples on how to use D3Q to calculate third order force constant for κALDo.

Theory Background

For detailed theoretical background on anharmonic lattice dynamics, the Boltzmann Transport Equation, and the Quasi-Harmonic Green-Kubo method, see the documentation.

Examples

Detailed examples for various materials and workflows are available in a stand-alone repository.

Citations

If you use κALDo, please cite:

Reference	When to Cite
[1]	Any work using κALDo (2.0)
[2]	Original κALDo implementation (v1)
[3]	QHGK method for disordered materials
[4]	Participation ratio analysis
[5]	Finite-size thermal conductivity with BTE
[6]	TDEP + path-integral MD workflows
[7]	Isotopic scattering and hydrodynamic extrapolation

References

[1] G. Barbalinardo, Z. Chen, D.A. Folkner, B. Li, N.W. Lundgren, N. Troup, A. Fiorentino, D. Donadio, κALDo 2.0: Scalable thermal transport from first principles and machine learning potentials, Comput. Phys. Commun. 327, 110282 (2026).

[2] G. Barbalinardo, Z. Chen, N.W. Lundgren, D. Donadio, Efficient anharmonic lattice dynamics calculations of thermal transport in crystalline and disordered solids, J. Appl. Phys. 128, 135104 (2020).

[3] L. Isaeva, G. Barbalinardo, D. Donadio, S. Baroni, Modeling heat transport in crystals and glasses from a unified lattice-dynamical approach, Nat. Commun. 10, 3853 (2019).

[4] N.W. Lundgren, G. Barbalinardo, D. Donadio, Mode Localization and Suppressed Heat Transport in Amorphous Alloys, Phys. Rev. B 103, 024204 (2021).

[5] G. Barbalinardo, Z. Chen, H. Dong, Z. Fan, D. Donadio, Ultrahigh convergent thermal conductivity of carbon nanotubes from comprehensive atomistic modeling, Phys. Rev. Lett. 127, 025902 (2021).

[6] D.A. Folkner, Z. Chen, G. Barbalinardo, F. Knoop, D. Donadio, Elastic moduli and thermal conductivity of quantum materials at finite temperature, J. Appl. Phys. 136, 221101 (2024).

[7] A. Fiorentino, P. Pegolo, S. Baroni, D. Donadio, Effects of colored disorder on the heat conductivity of SiGe alloys from first principles, Phys. Rev. B 111, 134205 (2025).

Publications Using κALDo

See the publications page.

Documentation

Full API documentation: nanotheorygroup.github.io/kaldo

Contributing

We welcome contributions! Please visit our discussions page for questions, feature requests, and workflow sharing.

Copyright

Copyright (c) 2022-2025, The kALDo Developers

Acknowledgements

We gratefully acknowledge support by the Investment Software Fellowships (grant No. ACI-1547580-479590) of the NSF Molecular Sciences Software Institute (grant No. ACI-1547580) at Virginia Tech.