Lennard-Jones 38 transition-state separation

SystemLennard-Jones

Atoms38

Runs51

Cap250000 force calls

The main metric is Force calls. Scoring rules.

Charts

Success rate on Lennard-Jones 38 transition-state separation, in rank order. The rate is the share of runs that finished. 2 ranked rows did not record a success rate and are not drawn. PDF.

Dolan-Moré profile for Band / NEB on Lennard-Jones 38 transition-state separation. The curve is the fraction of starts whose cost is at most tau times the best finite cost in this family. Tau is 1, 2, 4, 8, and 16. An unsolved start stays in the denominator and does not cross a finite tau. Dolan, E. D. and Moré, J. J., Math. Program. 91:201-213, 2002. Colored lines are the six largest areas. The other curves are gray. PDF.

Dolan-Moré profile for Minimum mode on Lennard-Jones 38 transition-state separation. The curve is the fraction of starts whose cost is at most tau times the best finite cost in this family. Tau is 1, 2, 4, 8, and 16. An unsolved start stays in the denominator and does not cross a finite tau. Dolan, E. D. and Moré, J. J., Math. Program. 91:201-213, 2002. Colored lines are the six largest areas. The other curves are gray. PDF.

Force calls on each recorded start for Lennard-Jones 38 transition-state separation. The box is the quartiles of those counts. A blue point is a success and a vermillion cross is a recorded failure (768). The horizontal position is the recorded count. The vertical offset only keeps marks from covering one another. PDF.

eOn on Lennard-Jones 38 transition-state separation. Each point is one recorded version of one method. Versions run left to right in numeric order. PAR-2 is omitted where that row has none. No line is drawn across a missing value. PDF.

Performance profile. Higher means more starts solved within that cost ratio. Colored lines are the six largest areas. Thin lines are the other 29.

• eOn (develop 500350d9) · Lanczos improved
• eOn (3.5.0) · Lanczos improved
• Eon svn (r2549) · Lanczos improved L-BFGS
• Eon svn (r2549) · Lanczos L-BFGS
• eOn (3.5.0) · Lanczos
• eOn (develop 500350d9) · Lanczos

Cost distribution of 37 ranked rows. Logarithmic bins, from 502.784 to 500000.

Performance profile SVG Cost and success SVG

Performance profile. Select the plot for the full SVG.

Cost and success. Select the plot for the full SVG.

A shorter bar is a lower cost on a log scale shared by the codes of this problem.

Leaderboard

A shorter bar is a lower cost on the log scale for that problem. Select a column heading to sort.

Rank	Code	Best	Median	Success	PAR-2
1	Eon svn	502.784	681.784	100.0%	502.784
2	eOn	520.333	44040.5	100.0%	520.333
3	OPTIM	2885	2885	100.0%	2885
4	Sella	31447.3	31447.3	100.0%	31447.3
5	pele	52961.9	52961.9	94.1%	52961.9
6	COMPASS	100831	100831	80.4%	100831
7	rgsaddle	266216	417164	47.1%	266216
8	geodesic	412102	412455	17.6%	412102
9	ASE	444244	444244	11.8%	444244
10	TSASE	451753	475877	9.8%	451753
11	LAMMPS	451959	475980	9.8%	451959

The tables below list every ranked row, by method family and overall.

A run short of the full set, or a run that is not the stock method, stays off the ranked table.

Band / NEB

Band / NEB. One row is one code, one version, and one method. A lower cost is better. PAR-2 counts a finished run as the calls it used and a failed run as twice the cap. An archived row shows the average it published, and its PAR-2 applies that rule to the failures the entry records. Hessians is the mean analytic Hessian count. FD calls is that count times one force call per coordinate.

Rank	Row	Cost	Unit	Hessians	FD calls	Runs
1	eOn (develop 500350d9) · energy-weighted CI-NEB	15260.3	force calls	0	0	51
2	Sella (2.6.0) · Sella+NEB	31447.3	force calls	0	0	51
3	eOn (develop 500350d9) · CI-NEB lj/cut	38080.5	force calls	0	0	51
4	eOn (develop 500350d9) · CI-NEB ljcluster	50000.5	force calls	0	0	51
5	eOn (develop 500350d9) · doubly nudged CI-NEB	72306.9	force calls	0	0	51
6	eOn (develop 500350d9) · OCI-NEB	95094.3	force calls	0	0	51
7	rgsaddle (0.2.2) · CI-NEB energy-weighted	266216	force calls	0	0	51
8	eOn (3.5.0) · doubly nudged CI-NEB	363362	force calls	0	0	51
9	Eon svn (r2549) · Doubly nudged CI-NEB	373102	force calls	0	0	51
10	Eon svn (r2549) · CI-NEB	402321	force calls	0	0	51
11	eOn (3.5.0) · CI-NEB lj/cut	402340	force calls	0	0	51
12	rgsaddle (0.2.2) · CI-NEB	402545	force calls	0	0	51
13	rgsaddle (0.2.2) · OCI-NEB	402564	force calls	0	0	51
14	geodesic (1.0.0) · CI-NEB-LBFGS geodesic	412102	force calls	0	0	51
15	geodesic (1.0.0) · CI-NEB geodesic	412455	force calls	0	0	51
16	rgsaddle (0.2.2) · IDPP CI-NEB	431764	force calls	0	0	51
17	rgsaddle (0.2.2) · S-IDPP CI-NEB	441455	force calls	0	0	51
18	ASE (3.29.0) · NEB-FIRE	444244	force calls	0	0	51
19	TSASE (1.0) · CI-NEB	451753	force calls	0	0	51
20	LAMMPS (30 Sep 2026) · CI-NEB-quickmin	451959	force calls	0	0	51
21	LAMMPS (30 Sep 2026) · CI-NEB-fire	500000	force calls	0	0	51
22	TSASE (1.0) · NEB	500000	force calls	0	0	51
23	geodesic (1.0.0) · NEB-FIRE geodesic	500000	force calls	0	0	51
24	rgsaddle (0.2.2) · NEB	500000	force calls	0	0	51

Minimum mode

Minimum mode. One row is one code, one version, and one method. A lower cost is better. PAR-2 counts a finished run as the calls it used and a failed run as twice the cap. An archived row shows the average it published, and its PAR-2 applies that rule to the failures the entry records. Hessians is the mean analytic Hessian count. FD calls is that count times one force call per coordinate.

Rank	Row	Cost	Unit	Hessians	FD calls	Runs
1	Eon svn (r2549) · Lanczos improved L-BFGS	502.784	force calls	0	0	51
2	eOn (3.5.0) · Lanczos improved	520.333	force calls	0	0	51
3	Eon svn (r2549) · Lanczos L-BFGS	524.667	force calls	0	0	51
4	eOn (develop 500350d9) · Lanczos improved	536.667	force calls	0	0	51
5	eOn (3.5.0) · Lanczos	564.647	force calls	0	0	51
6	eOn (develop 500350d9) · Lanczos	573.745	force calls	0	0	51
7	Eon svn (r2549) · Dimer L-BFGS	681.784	force calls	0	0	51
8	eOn (develop 500350d9) · dimer	3236.35	force calls	0	0	51
9	eOn (3.5.0) · dimer	108356	force calls	0	0	51

Connect / double-ended

Connect / double-ended. One row is one code, one version, and one method. A lower cost is better. PAR-2 counts a finished run as the calls it used and a failed run as twice the cap. An archived row shows the average it published, and its PAR-2 applies that rule to the failures the entry records. Hessians is the mean analytic Hessian count. FD calls is that count times one force call per coordinate.

Rank	Row	Cost	Unit	Hessians	FD calls	Runs
1	OPTIM · DNEB + hybrid eigenvector following + Djikstra shortest path	2885	force calls	0	0	51
2	pele · DNEB + hybrid eigenvector following	52961.9	force calls	0	0	51
3	COMPASS (1.0.0) · COMPASS	100831	force calls	0	0	51
4	eOn (3.6.0) · LBFGS	343644	force calls	0	0	51

Overall

One row is one code, one version, and one method. A lower cost is better. PAR-2 counts a finished run as the calls it used and a failed run as twice the cap. An archived row shows the average it published, and its PAR-2 applies that rule to the failures the entry records. Hessians is the mean analytic Hessian count. FD calls is that count times one force call per coordinate. The per-image mean divides the total by the number of moving images.

Row	Family	Family rank	Unit	PAR-2	Published	Median calls	Mean calls	Per-image mean	Hessians	FD calls	Failures	Runs
Eon svn (r2549) · Lanczos improved L-BFGS	Minimum mode	1	force calls	502.784		418	502.784	100.557	0	0	crash 0, divergence 0, cap 0, wrong_stationary 0	51
eOn (3.5.0) · Lanczos improved	Minimum mode	2	force calls	520.333		422	520.333	104.067	0	0	crash 0, divergence 0, cap 0, wrong_stationary 0	51
Eon svn (r2549) · Lanczos L-BFGS	Minimum mode	3	force calls	524.667		467	524.667	104.933	0	0	crash 0, divergence 0, cap 0, wrong_stationary 0	51
eOn (develop 500350d9) · Lanczos improved	Minimum mode	4	force calls	536.667		419	536.667	107.333	0	0	crash 0, divergence 0, cap 0, wrong_stationary 0	51
eOn (3.5.0) · Lanczos	Minimum mode	5	force calls	564.647		482	564.647	112.929	0	0	crash 0, divergence 0, cap 0, wrong_stationary 0	51
eOn (develop 500350d9) · Lanczos	Minimum mode	6	force calls	573.745		482	573.745	114.749	0	0	crash 0, divergence 0, cap 0, wrong_stationary 0	51
Eon svn (r2549) · Dimer L-BFGS	Minimum mode	7	force calls	681.784		451	681.784	136.357	0	0	crash 0, divergence 0, cap 0, wrong_stationary 0	51
OPTIM · DNEB + hybrid eigenvector following + Djikstra shortest path	Connect / double-ended	1	force calls	2885	2885	2565	2885		0	0	0 failed	51
eOn (develop 500350d9) · dimer	Minimum mode	8	force calls	3236.35		568	3236.35	647.271	0	0	crash 0, divergence 0, cap 0, wrong_stationary 0	51
eOn (develop 500350d9) · energy-weighted CI-NEB	Band / NEB	1	force calls	15260.3		2437	15260.3	3052.07	0	0	crash 0, divergence 0, cap 0, wrong_stationary 0	51
Sella (2.6.0) · Sella+NEB	Band / NEB	2	force calls	31447.3		32178	31447.3	6289.47	0	0	crash 0, divergence 0, cap 0, wrong_stationary 0	51
eOn (develop 500350d9) · CI-NEB lj/cut	Band / NEB	3	force calls	38080.5		14257	38080.5	7616.11	0	0	crash 0, divergence 0, cap 0, wrong_stationary 0	51
eOn (develop 500350d9) · CI-NEB ljcluster	Band / NEB	4	force calls	50000.5		14887	40196.5	8039.31	0	0	crash 0, divergence 0, cap 2, wrong_stationary 0	51
pele · DNEB + hybrid eigenvector following	Connect / double-ended	2	force calls	52961.9	25022	20638	25022		0	0	3 failed, class not recorded	51
eOn (develop 500350d9) · doubly nudged CI-NEB	Band / NEB	5	force calls	72306.9		20757	52699.1	10539.8	0	0	crash 0, divergence 0, cap 4, wrong_stationary 0	51
eOn (develop 500350d9) · OCI-NEB	Band / NEB	6	force calls	95094.3		38397	65682.5	13136.5	0	0	crash 0, divergence 0, cap 6, wrong_stationary 0	51
COMPASS (1.0.0) · COMPASS	Connect / double-ended	3	force calls	100831		4031	4586.12	917.224	0	0	crash 0, divergence 0, cap 9, wrong_stationary 1	51
eOn (3.5.0) · dimer	Minimum mode	9	force calls	108356		568	1200.33	240.067	0	0	crash 0, divergence 11, cap 0, wrong_stationary 0	51
rgsaddle (0.2.2) · CI-NEB energy-weighted	Band / NEB	7	force calls	266216		10000	6803.94	1360.79	0	0	crash 0, divergence 0, cap 27, wrong_stationary 0	51
eOn (3.6.0) · LBFGS	Connect / double-ended	4	force calls	343644		44412	40738.4	8147.67	0	0	crash 0, divergence 34, cap 0, wrong_stationary 0	51
eOn (3.5.0) · doubly nudged CI-NEB	Band / NEB	8	force calls	363362		5002	4245.53	849.106	0	0	crash 0, divergence 37, cap 0, wrong_stationary 0	51
Eon svn (r2549) · Doubly nudged CI-NEB	Band / NEB	9	force calls	373102		5007	4283.76	856.753	0	0	crash 0, divergence 38, cap 0, wrong_stationary 0	51
Eon svn (r2549) · CI-NEB	Band / NEB	10	force calls	402321		5007	4385.63	877.125	0	0	crash 0, divergence 41, cap 0, wrong_stationary 0	51
eOn (3.5.0) · CI-NEB lj/cut	Band / NEB	11	force calls	402340		5002	4400.43	880.086	0	0	crash 0, divergence 41, cap 0, wrong_stationary 0	51
rgsaddle (0.2.2) · CI-NEB	Band / NEB	12	force calls	402545		10000	8309.86	1661.97	0	0	crash 0, divergence 0, cap 37, wrong_stationary 4	51
rgsaddle (0.2.2) · OCI-NEB	Band / NEB	13	force calls	402564		10000	8470.33	1694.07	0	0	crash 0, divergence 0, cap 38, wrong_stationary 3	51
geodesic (1.0.0) · CI-NEB-LBFGS geodesic	Band / NEB	14	force calls	412102		10000	8401.49	1680.3	0	0	crash 0, divergence 0, cap 38, wrong_stationary 4	51
geodesic (1.0.0) · CI-NEB geodesic	Band / NEB	15	force calls	412455		10000	8769.92	1753.98	0	0	crash 0, divergence 0, cap 38, wrong_stationary 4	51
rgsaddle (0.2.2) · IDPP CI-NEB	Band / NEB	16	force calls	431764		10000	8882.94	1776.59	0	0	crash 0, divergence 0, cap 41, wrong_stationary 3	51
rgsaddle (0.2.2) · S-IDPP CI-NEB	Band / NEB	17	force calls	441455		10000	8880.2	1776.04	0	0	crash 0, divergence 0, cap 41, wrong_stationary 4	51
ASE (3.29.0) · NEB-FIRE	Band / NEB	18	force calls	444244		40001	38362.8	7672.56	0	0	crash 0, divergence 0, cap 45, wrong_stationary 0	51
TSASE (1.0) · CI-NEB	Band / NEB	19	force calls	451753		10000	9690.35	1938.07	0	0	crash 0, divergence 1, cap 43, wrong_stationary 2	51
LAMMPS (30 Sep 2026) · CI-NEB-quickmin	Band / NEB	20	force calls	451959		9982	9982	1996.4	0	0	crash 0, divergence 45, cap 0, wrong_stationary 1	51
LAMMPS (30 Sep 2026) · CI-NEB-fire	Band / NEB	21	force calls	500000		8120	8114.78	1622.96	0	0	crash 0, divergence 36, cap 0, wrong_stationary 15	51
TSASE (1.0) · NEB	Band / NEB	22	force calls	500000		10000	9720.22	1944.04	0	0	crash 0, divergence 3, cap 44, wrong_stationary 4	51
geodesic (1.0.0) · NEB-FIRE geodesic	Band / NEB	23	force calls	500000		10000	10000	2000	0	0	crash 0, divergence 0, cap 51, wrong_stationary 0	51
rgsaddle (0.2.2) · NEB	Band / NEB	24	force calls	500000		10000	9773.86	1954.77	0	0	crash 0, divergence 3, cap 45, wrong_stationary 3	51