Table 1 The theoretical framework for simulation techniques used in computational investigations of HEMs

Chemical Composition

Virtual crystal approximation (VCA)¹⁸⁷, coherent potential approximation (CPA)¹⁸⁸, special quasi-random structure (SQS)¹⁸⁹, small set of ordered structures (SSOS)¹⁹⁰, similar local atomic environment (SLAE)¹⁹¹

Cluster expansions, computational alchemy

Formation energies, elastic constants, defect concentrations

Equations of state (Murnaghan, Birch, etc.)¹⁹², convex Hulls¹⁹³, Self-consistent chemical potentials¹⁹⁴

Total energies, forces, and stresses for all different phases, defects, and periodic-boundary corrections for charged defects.

Chemistry And Reactivity, Surface Science

Potential-energy surfaces¹⁹⁵, transition-state theory¹⁹⁶, kinetic Monte Carlo (KMC)¹⁹⁷, Marcus’s theory¹⁹⁸, Franck–Condon Principle¹⁹⁹

Total energies and forces, van der Waals functionals, nudged-elastic-band method, constrained DFT, non-adiabatic dynamics (surface hopping)

Phonon dispersions and thermomechanical properties, thermal and electrical transport, superconductivity.

Linear-Response theory²⁰⁰, Quasi-Harmonic Approximation²⁰¹, Grüneisen Parameters²⁰², Boltzmann transport equation²⁰³, equilibrium/non-Equilibrium green’s functions²⁰⁴, Allen–Dyne’s formula²⁰⁵, Migdal–Eliashberg equations²⁰⁶

Density Functional Perturbation Theory And 2n + 1 Theorem for Electron-Phonon, Phonon-Phonon Interactions, Born Effective Charges, Dielectric Tensor.

Finite-temperature properties and Helmholtz or Gibbs free energies, transport coefficients.

Molecular dynamics (MD)⁹⁸, ab initio molecular dynamics (AIMD)²⁰⁷, thermodynamic integration²⁰⁸, meta dynamics, path-integral MD²⁰⁹, Green–Kubo relations²¹⁰, density functional perturbation theory (DFPT)²¹¹.

Born–Oppenheimer and Car–Parrinello MD, thermostat and barostat.