Add phonon-phonon interaction and related properties calculation to matcalc

[rul048]

Under the harmonic approximation, phonons are modeled as non-interacting quasiparticles within a perfectly quadratic potential energy landscape. While this simplifies calculations, it inherently neglects anharmonic effects such as volume effect, phonon-phonon interactions and finite phonon lifetimes, leading to limitations when predicting some temperature-dependent thermodynamic and transport properties, eg. thermal expansion and thermal conductivity (thermal expansion is considered zero and thermal conductivity is considered infinite, which is ridiculous), which are critical for understanding material behavior at finite temperatures.

The quasi-harmonic approximation (QHA) partially incorporates anharmonic effects by considering the volume dependence of phonon frequencies. Specifically, QHA assumes that the harmonic properties of the material remain applicable at different volumes, but the change in volume leads to alterations in the phonon spectrum, thereby reflecting thermodynamic properties such as thermal expansion. However, QHA still assumes no explicit interactions between phonons and cannot handle properties like thermal conductivity.

To better describe the anharmonicity of materials, especially properties related to phonon scattering and thermal transport, it is possible to compute higher-order force constants directly, which is an explicit approach for handling anharmonicity in materials. Calculating third-order force constants enables the capture of three-phonon interactions, allowing for the evaluation of phonon lifetimes, thermal conductivity, and other anharmonic properties. However, first-principles calculations of third-order force constants are computationally intensive due to the vast number of atomic displacement combinations required. This computational demand has historically limited the practical investigation of anharmonic effects in materials.

With the advent of machine learning interatomic potentials (MLIPs), it is now feasible to perform these complex calculations with significantly reduced computational resources while maintaining near ab initio accuracy. In particular, universal MLIPs offer efficient and accurate forces evaluations across diverse atomic and elemental configurations, making them candidates for extensive anharmonic calculations.

This pull request introduces a calculator for phonon-phonon interactions and related properties, utilizing MLIPs to efficiently compute third-order force constants. The developed code aims to provide an open-source implementation that leverages (u)MLIPs for anharmonic phonon calculations, enabling users to explore temperature-dependent thermal properties with greater efficiency and accuracy.

Summary

Major changes:

• feature 1: ...
• fix 1: ...

Todos

If this is work in progress, what else needs to be done?

• feature 2: ...
• fix 2:

Checklist

• Google format doc strings added. Check with ruff.
• Type annotations included. Check with mypy.
• Tests added for new features/fixes.
• If applicable, new classes/functions/modules have duecredit @due.dcite decorators to reference relevant papers by DOI (example)

Tip: Install pre-commit hooks to auto-check types and linting before every commit:

pip install -U pre-commit
pre-commit install

[shyuep]

Again, write proper PR messages. The message above is very sloppy. A one-liner is not sufficient.

[rul048]

For sure, just want to submit the pr promptly. I'll update it soon with a comprehensive description.