A unified approach for calculating free energies of liquid and defective crystals based on thermodynamic integration

Free energy calculation is fundamentally important in the research of physics, chemistry, and materials. Thermodynamic integration is the most common way to estimate free energies. In the research, we proposed a unified approach using atomic simulations to calculate the free energies of liquid and defective crystals. The new approach is based on thermodynamic integration using two alchemical pathways. Softcore potentials are developed for three-body interatomic potentials to realize the alchemical pathways. Employing the new approach, the free energy of the liquid can be calculated without requiring another reference system. The free energy of the defective crystal can be calculated directly at high temperatures. It avoids the singularity at the integration endpoint caused by the defect diffusion, which is a serious problem in the widely used Einstein crystal method. In addition, the new approach can capture the whole free energy of the defective crystal including the contribution of anharmonic and configurational entropy, which are particularly important at high temperatures. The new method is simple yet effective and can be extended to different materials and more complex liquid and defective crystal systems.