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, 𝑓 . 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, 𝑓 𝑠 . 1Effective number of degrees of freedom. 2Starting near the saddle point and not from a minimum. 3Approximate number extracted from Figure 4 of [61] starting near the saddle point, not from a minimum.

Algo. ART nouveau ART 𝑛 (Olsen) Dimer method Improved dimer GSM
Ref. Machado et al. [30] Olsen et al. [59] [60] [61] [62]

Systema-Si VSi C20 SiC Pt(111) Pt(111) Pt(111) Pt(111) C 6 H 1 0 PHBH/H2O V O 𝑥 /SiO2
BC Bulk Bulk Isol. Surf. Surf. Surf. Surf. Surf. Isol. Sol. Isol.
Pot. SW DFT DFT DFT Morse Morse Morse MorseDFT QM/MM DFT
DOF 3000 121 60 2221 3 525 3 52548 144 121
𝑓 235 210 322 262 145 372 204 335 3842 4253 330
𝑓 𝑠 670 302 718 728 145 2163 204 2148