Phonon Dispersion, Anharmonicity and Nuclear Effects in Crystalline Solids.

The behaviour of materials at a fundamental level is dictated by lattice vibrations, known as phonons, which govern properties ranging from heat conduction to optical response and phase transitions. Accurately modelling these vibrations, however, presents a significant computational challenge, particularly when dealing with materials containing light atoms or subjected to extreme conditions. Researchers at the Centre Européen de Calcul Atomique et Moléculaire (CECAM) and PASTEUR, alongside collaborators at École Polytechnique Fédérale de Lausanne, PSL University, Sorbonne Université, and CNRS, now present a refined computational technique to address this issue. In their article, ‘Anharmonic phonons via quantum thermal bath simulations’, T. Baird, R. Vuilleumier, S. Bonella, et al, detail a method combining a recently developed correlator approach with the quantum thermal bath (QTB) method, a technique used to incorporate nuclear quantum effects without incurring prohibitive computational costs. This represents the first comprehensive application of QTB to the calculation of phonon dispersion relations, offering a potentially efficient and accurate means of simulating material behaviour under demanding conditions.

Researchers present a computational scheme for determining phonon dispersion relations in crystalline solids, addressing limitations inherent in modelling materials exhibiting substantial anharmonicity and nuclear quantum effects (NQEs). Phonons, quantised lattice vibrations, are fundamental to understanding a material’s thermal and mechanical properties, and accurately determining their dispersion—the relationship between frequency and wavevector—is crucial for materials science. Anharmonicity, deviations from simple harmonic oscillation, complicates these calculations, as does the influence of NQEs, which arise from the wave-like nature of atomic nuclei and become significant at low temperatures or for light elements.

The new method combines the correlators approach for extracting anharmonic phonon frequencies with the quantum thermal bath (QTB) method, a technique for efficiently incorporating NQEs into molecular dynamics simulations. Molecular dynamics simulates the time evolution of a system by solving Newton’s equations of motion for each atom. In contrast, path integral molecular dynamics, used in conjunction with QTB, accounts for quantum effects by representing each atom as a ‘ring polymer’ with multiple copies connected by imaginary time links. This represents the first comprehensive application of QTB to the calculation of phonon dispersion relations, offering a potentially significant improvement in both accuracy and computational efficiency.

Validation occurs through simulations, beginning with simpler one-dimensional systems before progressing to solid neon, a physically relevant material where both anharmonicity and NQEs are prominent. Results demonstrate the scheme’s ability to accurately capture phonon behaviour, providing a robust framework for investigating vibrational properties. The researchers carefully analyse the strengths and limitations of their method, offering a balanced assessment of its performance and potential applications.

The combination of the correlators approach and QTB circumvents computational bottlenecks traditionally encountered when modelling phonon properties, particularly in systems containing light ions or at low temperatures and high pressures. Conventional methods often struggle with the computational cost of accurately representing quantum effects and anharmonicity simultaneously. This new approach allows for a more tractable calculation of phonon dispersion relations while maintaining a high degree of accuracy, opening new avenues for materials exploration and design.

This research builds upon prior work in computational materials science. Suzuki’s 1976 development of the generalised Suzuki-Trotter decomposition, a method for approximating the time evolution operator in quantum mechanics, provides a foundation for efficient path integral simulations. Pérez and Tuckerman’s 2011 research focused on improving the convergence of path integral molecular dynamics, enhancing the accuracy of quantum simulations. Furthermore, Rodney and Barrat’s 2011 work on implementing quantum thermal baths for molecular dynamics simulations directly informs the development of the QTB method, providing a solid foundation for the current research. These publications demonstrate the ongoing efforts to refine and improve the accuracy and efficiency of computational methods for materials science.