where ωA = -ω B -ωC , the permutation operator P ABC symmetrizes with respect to permutations of the operators A, B, and C together with the accompanied frequencies, and Ĉ±ω symmetrizes with respect to a change of sign of the real parts of the frequencies (denoted by ω A , ω B , and ω C ) followed by complex conjugation. While ωC is assumed to be real, the frequencies ωA and ωB can be either real or complex. In the former case, the quadratic response function is purely real or purely imaginary (depending on the combination of A, B and C ), and the building blocks are computed according to standard response theory.