Benchmarking optimization methods for finding minimum energy paths

Model System

The test problem is a 7 atoms island on the (111) surface of an FCC metal. All saddle points lead from this close packed heptamer (shown in red) to some adjacent state. All the atoms in this simulation are identical. The interaction between the atoms is a very simple pairwise additive Morse potential.

V(r) = A [ e-2 a ( R - R0 ) - 2 e- a ( R - R0 ) ]

This potential is shifted by V(RC) where RC = 9.5 Å is the cutoff distance. The parameters for the Morse potential were chosen to reproduce diffusion barriers on Pt surfaces.

A = 0.7102 eV
a = 1.6047 Å-1
R0 = 2.8970 Å

The surface is simulated with a 6 layer slab, each layer containing 56 atoms. The mimimum energy lattice constant for the FCC solid is used, 2.74412 Å. The bottom three layers in the slab are frozen. A total of 7 + 165 = 175 atoms are free to move.

The configurations of the low energy saddles leading from the compact island (in our local con format) are available here. In this file, each process has three configurations. The 5th lowest energy process, for example, would be a process connecting min05a.con and min05b.con through the saddle sp05.con. For each con file, there is also an eps file which shows a top view of the island. The path.dat files have a list of energy values along the minimum energy path for each process.

Compiled Results

CI NEB sd qm fire cg lbfgs(lineopt) lbfgs(hess) glbfgs(lineopt) glbfgs(hess) rk4
FC (0.01) 412 190 77 111 108 351 100 49  ??
FC (0.001) 737 354 116 169 154 428 147 73  ??
CI-DNEB sd qm fire cg lbfgs(lineopt) lbfgs(hess) glbfgs(lineopt) glbfgs(hess) rk4
FC (0.01) 411 194 78 108 115  ?? 104 47  ??
FC (0.001) 727 351 117 145 151  ?? 160 74  ??
CI Old String sd qm fire cg lbfgs(lineopt) lbfgs(hess) glbfgs(lineopt) glbfgs(hess) rk4
FC (0.01) 410 190 92 143 144 81 93 42 786
FC (0.001) 725 334 146 208 219 195 144 63 1230
Old String sd qm fire cg lbfgs(lineopt) lbfgs(hess) glbfgs(lineopt) glbfgs(hess) rk4
FC (0.01) 421 194 82 126 168 140 100 41 900
FC (0.001) 775 358 148 202 264 338 159 61 1376