where the subscript "h" indicates the original harmonic term. In strict terms, Eq. 12 is only applicable as is when ω λq,h , the original harmonic frequencies at 0 K, are all real. To use it still in the presence of imaginary ω λq,h , one could set those imaginary frequencies to 0 and sum over the frequency shift on the real axis. The self-consistent phonon theory, a many-body perturbation theory, provides the explicit correction due to 4th-order interaction (the so-called "loop" correction) ,