  The temperature-induced orthorhombic to cubic phase transition in Li2C2 is a
prototypical example of a solid to solid phase transformation between an
ordered phase, which is well described within the phonon theory, and a
dynamically disordered phase with rotating molecules, for which the standard
phonon theory is not applicable. The transformation in Li2C2 happens from a
phase with directionally ordered C2 dimers to a structure, where they are
dynamically disorderd. We provide a description of this transition by employing
ab initio molecular dynamics (AIMD) based stress-strain thermodynamic
integration on a deformation path that connects the ordered and dynamically
disordered phases. The free energy difference between the two phases is
obtained. The entropy that stabilizes the dynamically disordered cubic phase is
captured by the behavior of the stress on the deformation path. We also show
that a combination of the stress-strain thermodynamic integration and machine
learning force field methodologies appears as a promising path in studies of
dynamically disordered materials.
