A generalized solid-state nudged elastic band (G-SSNEB) method is presented for determining reaction pathways of solid–solid transformations involving both atomic and unit-cell degrees of freedom. We combine atomic and cell degrees of freedom into a unified description of the crystal structure so that calculated reaction paths are insensitive to the choice of periodic cell. For the rock-salt to wurtzite transition in CdSe, we demonstrate that the method is robust for mechanisms dominated either by atomic motion or by unit-cell deformation; notably, the lowest-energy transition mechanism found by our G-SSNEB changes with cell size from a concerted transformation of the cell coordinates in small cells to a nucleation event in large cells. The method is efficient and can be applied to systems in which the force and stress tensor are calculated using density functional theory.

The dimer method is a minimum mode following algorithm for finding saddle points on a potential energy surface of atomic systems. Here, the dimer method is extended to include the cell degrees of freedom for periodic solid-state systems. Using this method, reaction pathways of solid-solid phase transitions can be determined without having to specify the final state structure or reaction mechanism. Example calculations include concerted phase transitions between CdSe polymorphs and a nucleation and growth mechanism for the A15 to BCC transition in Mo.

The Prussian Blue analog, Na_xFeMn(CN)₆, is a potential new cathode material for Na-ion batteries. During Na intercalation, the dehydrated material exhibits a monoclinic to rhombohedral phase transition, while the hydrated material remains in the monoclinic phase. With density functional theory calculations, the phase transition is explained in terms of a competition between Coulomb attraction, Pauli repulsion, and d–π covalent bonding. The interstitial Na cations have a strong Coulomb attraction to the N anions in the host material, which tend to bend the Mn–N bonds and reduce the volume of the structure. The presence of lattice H₂O enhances the Pauli repulsion so that the volume reduction is suppressed. The calculated volume change, as it depends upon the presence of lattice H₂O, is consistent with experimental measurements. Additionally, a new LiFeMn(CN)₆ phase is predicted where MnN₆ octahedra decompose into LiN₄ and MnN₄ edge-sharing tetrahedra.