Table 1: Efficiency of various open-ended and double-ended saddle-point searching algorithms. The first four columns show results on four different systems using the latest version of ART nouveau as described by Machado et al. [30]. The next four columns are results taken from Olsen et al. [59] for their own implementation of ART nouveau and the dimer method. Two columns present results using improved version of the dimer method coupled to ab initio force calculations for small organic molecules [60, 61]. The last column presents results for the growing string method (GSM), a double-ended saddle search algorithm [62]. These systems are characterized as a function of their boundary condition—bulk, surface, isolated, or solution—and the effective number of degrees of freedom of each system. A comparison is made on the average number of force evaluations necessary to go from local minimum to a nearby saddle point for a successful search, . More important, when evaluating the efficiency of the method, is the number of force evaluations required to find a first-order saddle point, taking into account the lost events, . ^{1}Effective number of degrees of freedom. ^{2}Starting near the saddle point and not from a minimum. ^{3}Approximate number extracted from Figure 4 of [61] starting near the saddle point, not from a minimum.