For the calculation of ∆A id→I E M , we found it was crucial to introduce intermediate states; we also switched to using the MBAR estimator. The original EMM calculation of the absolute free energy of a solid estimated ∆A id→I E M using exponential averaging (EXP) with just two states: the Einstein molecule (EM) and the interacting Einstein molecule (IEM) . As EXP is known to have convergence issues and biases , we switched to the superior MBAR free energy estimator . Additionally, when we did so, we found that overlap of states (as measured by the overlap matrix ) was insufficient so we created a series of intermediate states connecting both ends of the transformation.