kALDo 2.0: Scalable Thermal Transport from First Principles and Machine Learning Potentials

TL;DR

The theoretical framework, implementation details, software architecture, and validation examples demonstrating kALDo2.0's capabilities for studying complex materials, including halide perovskites with strong anharmonicity and polar oxides requiring long-range electrostatic corrections are described.

Abstract

We introduce kALDo2.0, an open-source Python package for computing vibrational, elastic, and thermal transport properties of solids from first principles and machine-learned interatomic potentials. Building on the anharmonic lattice dynamics (ALD) framework, kALDo2.0 provides efficient CPU and GPU-accelerated implementations of the Boltzmann transport equation (BTE) for crystals and the quasi-harmonic Green-Kubo (QHGK) method. QHGK extends thermal transport predictions beyond crystals to disordered materials, including glasses, alloys, and complex nanostructures. kALDo2.0 introduces native integration with modern machine-learned potentials (MLPs), enabling thermal transport workflows that combine the accuracy of first-principles methods with the scalability of classical force fields. It also features comprehensive support for temperature-dependent effective potentials workflows, flexible storage backends for large-scale calculations, and advanced quantification of anharmonicity. The software seamlessly interfaces with electronic structure codes (Quantum ESPRESSO, VASP), molecular dynamics packages (LAMMPS), and MLPs (ACE, NEP, MACE, MatterSim, Orb), enabling thermal transport studies from 0 K to finite temperatures. kALDo2.0 implements multiple BTE solution strategies and essential physical corrections, including isotopic scattering and non-analytical terms for polar materials. A modular Python architecture with lazy evaluation and multiple storage formats (ASCII, NumPy, HDF5) enables simulations of systems containing up to tens of thousands of atoms. This paper describes the theoretical framework, implementation details, software architecture, and validation examples demonstrating kALDo2.0's capabilities for studying complex materials, including halide perovskites with strong anharmonicity and polar oxides requiring long-range electrostatic corrections.

Figures (11)

• Figure 1: $\kappa$ALDo 2.0 input/output ecosystem. The software interfaces with diverse force constant sources, including ab initio codes (Quantum ESPRESSO, VASP), molecular dynamics packages (LAMMPS), TDEP, machine-learned potentials via ASE (NEP, MACE/MatterSim, Orb), and external phonon codes (ShengBTE, phono3py, HiPhive). The workflow progresses from force constant import/generation to phonon property calculation to thermal conductivity evaluation via BTE or QHGK methods.
• Figure 2: $\kappa$ALDo 2.0 object-oriented class structure. ForceConstants manages second- and third-order IFCs with methods for importing from external codes (from_folder()) or direct calculation via ASE (from_ase()). Phonons computes vibrational properties including frequencies, velocities, scattering rates, heat capacities, and populations. Conductivity solves for thermal transport via BTE (RTA, self-consistent, inverse, eigendecomposition) or QHGK methods, with outputs including thermal conductivity tensors, mean free paths, and diffusivities. All classes inherit from Storable, implementing lazy evaluation and flexible storage backends.
• Figure 3: Runtime profiling was performed for QHGK calculations of the lattice thermal conductivity of bulk Si across a range of system sizes, using a fixed $3\times3\times3$ q-grid. Benchmarks were run on a single NVIDIA L40S GPU and on 16 CPU cores of an Intel Xeon Platinum 8562Y processor. Interatomic force constants for the profiling were obtained using the Tersoff potential.tersoff1988new
• Figure 4: Phonon dispersion relation (left) and density of states (right) for cubic phase CsPbBr3 at 360 and 500K.
• Figure 5: Cumulative thermal conductivity with respect to phonon mode frequency (left) and phonon mean free path (right). Dashed lines are used to indicate coherent contribution from QHGK, dotted lines are used to indicate the BTE contribution, and solid lines indicate total thermal conductivity calculated by adding the coherent (diffuson) contribution, estimated as the difference between the full QHGK and RTA, to the exact BTE solution ($\kappa_{inv}$).