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- (X1Sigma+) anion with neutral atoms present in interstellar media ; F, Cl, O and S. With H atom, for comparison, the reaction [CN-(1Sigma+) + H(2S)] evolves along the PES of the X2Sigma+ electronic ground state of HCN- (or HNC-) until the crossing with the X1Sigma+ electronic ground state of HCN (or HNC), where electron detachment occurs. The process is rather similar with 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 2Sigma+ state. The reaction of CN- with O and S atoms proceeds via a multi-step mechanism: the lowest electronic state at long distance, the 3Pi state arising from the [CN-(1Sigma+) + O/S(3P)] reaction channel, does not correlate with the X1Sigma+ ground state of the XCN- anion (X=O or S). This 3Pi state and its bent components are crossing at medium R(XC) / (R(XN)) distances the X1Sigma+ ground state of XCN- or XNC-, and at shorter distances the X2Pi 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-(1Sigma+) + O/S(3P)] reaction toward the stable X1Sigma+ ground state of XCN- and XNC-.