where the subscript denotes the order and, as A 2 is usually not a square matrix, A -1 2 is the Moore-Penrose pseudoinverse. As Φ TD 2 and A(T ) are interdependent, Eqs. 7-8 are iterated until the free energy converges to a desired threshold determined by temperature. This only involves diagonalization of the dynamical matrix constructed from Φ TD 2 , between two iterations, to obtain ω and ê.