10 tailed analysis of the low energy resonance features in the F + H$_{2}$ reaction was presented by Castillo et al. in 1996 [70]. They demonstrated that several resonances that appear in the energy dependence of the cumulative reaction probability for the F + H$_{2}$ reaction arise due to the van der Waals interaction potential in the product HF + H channel. In particular, the origin of the reso- nances has been attributed to the van der Waals potential associated with the HF( v ′ = 3 , j ′ = 0 − 3) channels. A large number of experimental and theoretical papers has appeared which examined various aspects of these reso- nance features [11, 70–72, 75–80]. Among these studies, the work of Takayanagi and Kurosaki [71] deserves spe- cial attention. They showed that for F + H$_{2}$, F + HD and F + D$_{2}$ reactions reactive scattering resonances oc- cur due to the decay of quasibound states of the van der Waals potential in the entrance channel of the reaction. These Feshbach resonances are associated with the decay of quasibound states of adiabatic potentials correspond- ing to F · · · H$_{2}$( v = 0 , j = 0 , 1), F · · · HD( v = 0 , j = 0 − 2), and F · · · D$_{2}$( v = 0 , j = 0 − 2) complexes, obtained by diagonalizing the J = 0 Hamiltonian in a basis set of the asymptotic ro-vibrational states of the reactant molecules. 10 −7 10 −6 10 −5 10 −4 10 −3 10 −2 10 −1 Kinetic energy (eV) 10 −6 10 −4 10 −2 10 0 10 2 v’=0 v’=1 v’=2 Cross section (10 −16  cm 2 ) FIG. 9: J = 0 cross sections for F + H 2 ( v = 0 , j = 0) → HF( v $^{′}$) + H reaction for v ′ = 0 − 2 as functions of the incident kinetic energy. Reproduced with permission from Balakrish- nan and Dalgarno [11]. In the Wigner threshold regime, the reactivity of the F + H$_{2}$ system is an order of magnitude greater than that of the F + HD reaction. A rigorous analysis of the scattering resonances in the F + HD reaction was recently presented by De Fazio et al. [80], who provided a detailed characterization of the resonances supported by the entrance and exit channels of the van der Waals potential and discussed the effect of higher total angular momenta on the position and lifetime of the resonances. Stereodynamical aspects of the F + H$_{2}$ collision and the effect of polarization of the H$_{2}$ molecule on the outcome of the reaction at low energies were recently explored by Aldegunde et al. [77]. They argued that a reactant polarization scheme can be ex- ploited to control state-to-state dynamics of the reaction. Balakrishnan and Dalgarno [11] showed that quasi- bound states of the F + H$_{2}$ van der Waals complex have a dramatic effect on the reactivity in the Wigner thresh- old regime. They found that the F + H$_{2}$( v = 0 , j = 0) reaction has a rate coefficient of 1 . 25 × 10 $_{−}$12 cm 3 s $_{−}$1 in the zero-temperature limit. Their calculation was based on the widely used PES of Stark and Werner [89] for the F + H$_{2}$ system. The relatively large value of the zero-temperature rate coefficient is due to the presence of a small narrow energy barrier for the reaction so that tunneling of the H atom is efficient. The vibrational level resolved cross sections for the F + H$_{2}$( v = 0 , j = 0) reaction are shown in Fig. 9 for the total angular momentum quantum number J = 0. The v ′ = 2 level is the dominant channel at low energies in agreement with the behavior at higher energies. 1. Reactions at zero temperature To explore the role of tunneling in chemical reactions at cold and ultracold temperatures Bodo, Gianturco, and Dalgarno [73] investigated the dynamics of the F + D$_{2}$ system at low and ultra-low energies. They found that compared to the F + H$_{2}$ reaction, the reactivity of F + D$_{2}$ is significantly suppressed in the Wigner regime with an HF/DF ratio of about 100. This is illustrated in Fig. 11 where the J = 0 cumulative reaction probability and cross sections for the F + H$_{2}$ and F + D$_{2}$ reactions are plotted as functions of the incident kinetic energy from the Wigner limit to 0.01 eV. Subsequent calculations showed that at low energies the F + HD reaction is dominated by the formation of the HF product with an HF/DF branching ratio of about 5.5 [74]. The formation of the DF product is suppressed because tunneling of the heavier D atom is less efficient. In earlier quantum calculations, Baer and coworkers [90, 91] reported HF/DF branching ratios ranging from 1.5 at 450 K to 6.0 at 100 K. Their low temperature value is in close agreement with the zero-temperature limit obtained by Balakrishnan and Dalgarno [74]. Fig. 10 compares the J = 0 cross sections for the F + H$_{2}$( v = 0 , j = 0) and F + HD( v = 0 , j = 0) reactions over a kinetic energy range of 10 $_{−}$7 to 1.0 eV. The dramatic suppression of the F + D$_{2}$ reaction in the Wigner regime cannot be explained based on tunneling alone. A closer examination of the reaction probabilities for the F + H$_{2}$ and F + D$_{2}$ reaction revealed that an un- usual enhancement of the reactivity occurs for the F + H$_{2}$ reaction at about 3 × 10 $_{−}$5 eV [75] (see the upper panel