where, μ× Â ≡ [μ, Â] and ρ(g) is the equilibrium ground state of the system. 1 Here, the system is perturbed at times t 0 , t 1 , and t 2 and the system response is detected at t 3 . In Eq.14, R (3) can be separated into 8 different Liouville pathways, each can be categorized as either rephasing or non-rephasing signals. Four of these Liouville pathways correspond to