Vibrational entropy of crystalline solids from covariance of atomic displacements

Understanding finite-temperature mechanical and dynamical properties of a material is essential for investigating its stability and phase behavior. The well-known harmonic approximation successfully predicts vibrational modes of harmonic systems yet fails when describing strongly anharmonic systems due to imaginary modes. Here we propose a method that overcomes mechanical instability of strongly anharmonic systems and is capable of predicting accurate vibrational entropy at finite temperature. In our method, we construct a covariance matrix by collecting pair correlations from molecular dynamic simulations and derive a relation between the covariance matrix and the vibrational entropy based on information entropy theory. We further obtain an effective force constant matrix in our approach, where harmonic approximation can be applied. Our approach is examined in both harmonic sytems (BCC Na and FCC Al) and anharmonic systems (BCC Ti).