Genetic Algorithm to Obtain Accurate Force Constants in Graphene

Abstract

As fundamental quantum mechanical descriptors of crystalline lattice vibrational properties, phonons play a critical role in determining numerous macroscopic physical characteristics spanning thermal transport behavior and thermodynamic response functions. The precise determination of complete phonon spectra and their corresponding interatomic force constants continues to present substantial computational challenges, particularly in architecturally complex material systems. In this study, using graphene as a prototypical system, theoretical derivation of the phonon dispersion relations is presented through rigorous lattice dynamics formalism. The first- through eighth-nearest-neighbor force constants in the dynamical matrix are systematically determined via a self-consistent iterative genetic algorithm optimization framework. These derived parameters are further systematically validated through density functional theory simulations. The optimized interatomic force constants demonstrate remarkable fidelity in reproducing both the acoustic and optical phonon branches across the entire Brillouin zone, thereby establishing a comprehensive theoretical foundation for predictive calculations of temperature-dependent thermodynamic properties. The developed genetic algorithm optimization methodology shows significant transferability to diverse material systems, enabling precise alignment with inelastic neutron scattering and Raman spectroscopy measurements. This advancement provides a generalized computational tool for investigating lattice dynamics in complex material systems.