Highly correlated ab initio wave functions within the UCCSD(T)-F12 approach have been used to map the potential energy surfaces (PESs) describing the reactivity of the CN(-) (X(1)Σ(+)) anion with neutral atoms present in interstellar media (F, Cl, O, and S). With the H atom, for comparison, the reaction [CN(-)((1)Σ(+)) + H((2)S)] evolves along the PES of the X(2)Σ(+) electronic ground state of HCN(-) (or HNC(-)) until the crossing with the X(1)Σ(+) electronic ground state of HCN (or HNC), where electron detachment occurs. The process is rather similar to the two halogen atoms F and Cl, with some differences due to the larger electron affinity of the halogens, making possible the existence of ClCN(-) in a (2)Σ(+) state. The reaction of CN(-) with O and S atoms proceeds via a multistep mechanism. The lowest electronic state at long distance, the (3)Π state arising from the [CN(-)((1)Σ(+)) + O/S((3)P)] reaction channel, does not correlate with the X(1)Σ(+) ground state of the XCN(-) anion (X = O or S). This (3)Π state and its bent components cross at medium RXC (RXN) distances the X(1)Σ(+) ground state of XCN(-) or XNC(-), and at shorter distances the X(2)Π state of the neutral XCN or XNC where the extra electron can detach. With both O and S atoms, it is shown that the spin-orbit couplings can efficiently lead the [CN(-)((1)Σ(+)) + O/S((3)P)] reaction toward the stable X(1)Σ(+) ground state of XCN(-) and XNC(-).