Efficient calculation of α- And β-nitrogen free energies and coexistence conditions via overlap sampling with targeted perturbation

A recently introduced solid-phase free-energy calculation method that is based upon overlap sampling with targeted free-energy perturbation is further developed and extended to systems with orientational degrees of freedom. Specifically we calculate the absolute free energy of the linear-molecular nitrogen model of Etter, examining both the low-temperature low-pressure α-N₂ structure and the orientationally disordered β-N ₂ phase. In each perturbation (for the α-N₂ phase) to determine the free-energy difference between systems at adjacent temperatures, harmonic coordinate scaling is applied to both the translational and rotational degrees of freedom in the nitrogen molecule to increase the phase-space overlap of the two perturbing systems and consequently, improve the free-energy difference results. For the plastic β-N₂ phase, a novel method that requires several perturbation paths is introduced to calculate its absolute free energy. Through these methods, the absolute free energies for both the α-N₂ and β-N₂ phase can be accurately and precisely determined. We find again that the anharmonic contribution to the free energy has weak dependence on system size. The transition properties for the α-N₂ and β-N₂ phase are also investigated. The α-β phase transition for the model at atmospheric pressure (0.1 MPa) is found to occur at 40.35 ± 0.01 K with volumetric and entropy changes of 0.44 ± 0.01 cm³mol and 1.99 ± 0.01 calmol.K respectively.