The rate coefficients of reactions that occur on potential energy surfaces without a barrier often exhibit a negative temperature dependence at low temperatures. Generally, this behavior is modeled with either the Harcourt-Essen equation, k(T)=AT(-m), or a "negative" activation energy, k(T)=AT(m) exp{Delta E/k(B)T}. Neither of these expressions is consistent with the Wigner threshold law. The general expression k(T)=(1+T/T-W)(-m)Sigma(l=0)(infinity)A(l)(1+T/T-W)(-l)(T/T-W)(l) is proposed where the relative angular momentum of the reacting species is l, T-W and m are independent parameters to be extracted from the data, and the amplitude of each partial wave is A(l). This expression may be approximated by k(T)=A(0)(1+T/T-W)(-m) exp[(T/T-W)/(1+T/T-W)]. For CN+O-2--> NCO+O and CO+NO the above expression reproduces the rate data, the branching ratio to the CO+NO channel, and the reactive cross section for the NCO+O channel. The rate coefficient for the NCO+O channel is given by k(cm(3) s(-1))=1.79x10(-10)(+T/21.7)(-1.38){exp[(T/21.7)/(1+T/21.7)]-1}+4.62x10(-12) exp[(T/21.7)/(1+T/21.7)] while for CO+NO we obtain k(cm(3) s(-1))=1.79x10(-10)(1+T/21.7)(-1.38). An analytic form of the C-O bonding potential and the electric dipole-quadrupole interaction is used to show that the quantum threshold region extends up to 7 K. These results demonstrate the need of a complete quantum treatment for reactions that proceed on potential surfaces without a barrier.