When ω O = 0 (as is the case for Ô = ĥpso K ) Equations ( ) and ( ) may diverge in the case where [A -ω f 1] is singular, i.e., if the solution vector has a component in the direction of the right and left eigenvectors. To avoid these unphysical divergences, the eigenvector derivatives E K f (ω f , 0) and ĒK f (-ω f , 0) are projected onto the orthogonal complement of the undifferentiated eigenvectors, as indicated by the superscript ⊥. Definitions of the remaining CC building blocks can be found, e.g., in Refs. 31, 34, 39, and 41. Since it will be relevant for the discussion of the results in the next sections, we also report here the exact sum-over-states expression for the B K term