Lennard-Jones 38 clusters

SystemLennard-Jones

Atoms38

Runs1000

Cap10000 force calls

The main metric is Force calls. Scoring rules.

Charts

Success rate on Lennard-Jones 38 clusters, in rank order. The rate is the share of runs that finished. 17 ranked rows did not record a success rate and are not drawn. PDF.

Dolan-Moré profile for Minimizers on Lennard-Jones 38 clusters. 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 clusters. The box is the quartiles of those counts. A blue point is a success and a vermillion cross is a recorded failure (10441). The horizontal position is the recorded count. The vertical offset only keeps marks from covering one another. PDF.

rgmin on Lennard-Jones 38 clusters. 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.

ASE on Lennard-Jones 38 clusters. 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 51.

• rgmin (0.4.0) · NEWTON
• rgmin (0.4.1) · NEWTON
• rgmin (0.4.0) · DOGLEG
• rgmin (0.4.1) · DOGLEG
• rgmin (0.4.0) · LBFGS
• rgmin (0.4.1) · LBFGS

Cost distribution of 74 ranked rows. Logarithmic bins, from 79 to 20000.

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	unknown	79	79	100.0%	79
2	rgmin	81.881	928.197	100.0%	81.881
3	TSASE	166	257.2	100.0%	166
4	OPTIM	176	223.171	100.0%	176
5	pele	179	288.145	100.0%	179
6	eOn	180.137	180.137	100.0%	180.137
7	Eon svn	181	635	100.0%	181
8	DL-FIND	231.908	3048.62	99.8%	231.908
9	GMIN	301.399	301.399	99.7%	301.399
10	ASE	374.645	656	99.9%	374.645
11	vc-SQNM	598.05	598.05	98.9%	598.05
12	Sella	710.089	710.089	100.0%	710.089
13	LAMMPS	1123.81	4361.3	99.7%	1123.81
14	pysisyphus	15124.7	16094.8	25.4%	15124.7

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.

Files with no per-start harness record stay off the ranked table.

These archived rows differ from the table of J. Chem. Theory Comput. 10, 5476 (2014) that prints them, and each ranks on its archived values: eOn (r2025) · FIRE (Table 1 prints 645, 207 and 2963 calls, this file has 731, 227 and 2918, and no archived file has the printed values. The cause is not established).

Minimizers

Minimizers. 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	Newtons Method maxstep=0.25	79	force calls	0	0	1000
2	rgmin (0.4.0) · DOGLEG	81.881	force calls	80.881	9220.43	1000
3	rgmin (0.4.1) · DOGLEG	81.881	force calls	80.881	9220.43	1000
4	tsase-SDLBFGS maxstep=0.1 optimizer='maxatom'	166	force calls	0	0	1000
5	rgmin (0.4.0) · NEWTON	166.337	force calls	65.649	7483.99	1000
6	rgmin (0.4.1) · NEWTON	166.337	force calls	65.649	7483.99	1000
7	OPTIM · L-BFGS	176	force calls	0	0	1000
8	pele-lbfgs-M100-maxstep0.2	179	force calls	0	0	1000
9	eOn (3.6.0) · LBFGS	180.137	force calls	0	0	1000
10	eOn (r2025) · eon-lbfgs	181	force calls	0	0	1000
11	rgmin (0.4.0) · LBFGS	197.228	force calls	0	0	1000
12	rgmin (0.4.1) · LBFGS	197.228	force calls	0	0	1000
13	pele · lbfgs_scipy	230	force calls	0	0	1000
14	DL-FIND (0.0.3) · L-BFGS	231.908	force calls	0	0	1000
15	TSASE (1.0) · SDLBFGS	257.2	force calls	0	0	1000
16	pele (0.1.2) · MYLBFGS	268.036	force calls	0	0	1000
17	OPTIM (svn-snapshot) · L-BFGS	270.341	force calls	0	0	1000
18	pele (0.1.2) · LBFGS	288.145	force calls	0	0	1000
19	GMIN (df8da5992675) · LBFGS	301.399	force calls	0	0	1000
20	ASE (3.6.1) · L-BFGS M=5 maxstep=0.2	374.645	force calls	0	0	1000
21	ASE (3.6.0) · L-BFGS Line Search M=5 maxstep=0.2	417	force calls	0	0	1000
22	eOn (r2025) · Conjugate Gradients	453	force calls	0	0	1000
23	ase-BFGS maxstep=0.1	482.537	force calls	0	0	1000
24	ASE (3.29.0) · LBFGS	532.882	force calls	0	0	1000
25	eOn (r2025) · eon-sd-twopoint	539	force calls	0	0	1000
26	ASE (3.29.0) · BFGSLineSearch	580.893	force calls	0	0	1000
27	vc-SQNM (1.3) · ASE-SQNM	598.05	force calls	0	0	1000
28	vc-SQNM (1.3) · SQNM	598.05	force calls	0	0	1000
29	rgmin (0.4.0) · BB	639.474	force calls	0	0	1000
30	rgmin (0.4.1) · BB	639.474	force calls	0	0	1000
31	ASE (3.6.0) · FIRE	656	force calls	0	0	1000
32	rgmin (0.4.0) · CG	669.237	force calls	0	0	1000
33	rgmin (0.4.1) · CG	669.237	force calls	0	0	1000
34	ASE (3.29.0) · BFGS	706.622	force calls	0	0	1000
35	pele-fire	709	force calls	0	0	1000
36	Sella (2.6.0) · Sella	710.089	force calls	0	0	1000
37	ASE (3.29.0) · PreconLBFGS	728.405	force calls	0	0	1000
38	eOn (r2025) · FIRE	731	force calls	0	0	1000
39	rgmin (0.4.0) · FIRE	769.36	force calls	0	0	1000
40	rgmin (0.4.1) · FIRE	769.36	force calls	0	0	1000
41	ASE (3.29.0) · FIRE	802.368	force calls	0	0	1000
42	rgmin (0.4.0) · FIRE2	845.947	force calls	0	0	1000
43	rgmin (0.4.1) · FIRE2	845.947	force calls	0	0	1000
44	rgmin (0.4.0) · BFGS	1010.45	force calls	0	0	1000
45	rgmin (0.4.1) · BFGS	1010.45	force calls	0	0	1000
46	LAMMPS (30 Sep 2026) · Hessian-free truncated Newton	1123.81	force calls	0	0	1000
47	ASE (3.29.0) · PreconFIRE	1850.86	force calls	0	0	1000
48	rgmin (0.4.0) · QUICKMIN	1933	force calls	0	0	1000
49	rgmin (0.4.1) · QUICKMIN	1933	force calls	0	0	1000
50	rgmin (0.4.1) · DIIS	1967.42	force calls	0	0	1000
51	pele (0.1.2) · FIRE	2141.38	force calls	0	0	1000
52	rgmin (0.4.1) · SR1	2185.66	force calls	0	0	1000
53	rgmin (0.4.1) · SR2	2298.44	force calls	0	0	1000
54	ase-Precon-LBFGS maxstep=0.1	2686	force calls	0	0	1000
55	DL-FIND (0.0.3) · conjugate gradient	3048.62	force calls	0	0	1000
56	DL-FIND (0.0.3) · steepest descent	3093.74	force calls	0	0	1000
57	LAMMPS (30 Sep 2026) · Quickmin	3138.21	force calls	0	0	1000
58	eOn (r2025) · QuickMin	3901.97	force calls	0	0	1000
59	LAMMPS (30 Sep 2026) · conjugate gradient	4361.3	force calls	0	0	1000
60	LAMMPS (30 Sep 2026) · FIRE	5844.9	force calls	0	0	1000
61	eOn (r2025) · eon-sd	6350.5	force calls	0	0	1000
62	rgmin (0.4.0) · SD	8392.75	force calls	0	0	1000
63	rgmin (0.4.1) · SD	8392.75	force calls	0	0	1000
64	rgmin (0.4.1) · ADAM	13835.7	force calls	0	0	1000
65	LAMMPS (30 Sep 2026) · steepest descent	14468.2	force calls	0	0	1000
66	pysisyphus (0.1.dev1) · conjugate gradient	15124.7	force calls	0	0	1000
67	pysisyphus (0.1.dev1) · steepest descent	16094.8	force calls	0	0	1000
68	rgmin (0.4.0) · ADAM	16420.2	force calls	0	0	1000
69	rgmin (0.4.0) · SR1	19908.9	force calls	0	0	1000
70	rgmin (0.4.0) · DIIS	19945	force calls	0	0	1000
71	TSASE (1.0) · MDMin	20000	force calls	0	0	1000
72	pele (0.1.2) · steepest descent	20000	force calls	0	0	1000
73	pysisyphus (0.1.dev1) · L-BFGS	20000	force calls	0	0	1000
74	rgmin (0.4.0) · SR2	20000	force calls	0	0	1000

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.

Row	Family	Family rank	Unit	PAR-2	Published	Median calls	Mean calls	Hessians	FD calls	Failures	Runs
Newtons Method maxstep=0.25	Minimizers	1	force calls	79	79		79	0	0	0 failed	1000
rgmin (0.4.0) · DOGLEG	Minimizers	2	force calls	81.881		79	81.881	80.881	9220.43	crash 0, divergence 0, cap 0, wrong_stationary 0	1000
rgmin (0.4.1) · DOGLEG	Minimizers	3	force calls	81.881		79	81.881	80.881	9220.43	crash 0, divergence 0, cap 0, wrong_stationary 0	1000
tsase-SDLBFGS maxstep=0.1 optimizer='maxatom'	Minimizers	4	force calls	166	166		166	0	0	0 failed	1000
rgmin (0.4.0) · NEWTON	Minimizers	5	force calls	166.337		64	66.649	65.649	7483.99	crash 0, divergence 0, cap 0, wrong_stationary 5	1000
rgmin (0.4.1) · NEWTON	Minimizers	6	force calls	166.337		64	66.649	65.649	7483.99	crash 0, divergence 0, cap 0, wrong_stationary 5	1000
OPTIM · L-BFGS	Minimizers	7	force calls	176	176	166	176	0	0	0 failed	1000
pele-lbfgs-M100-maxstep0.2	Minimizers	8	force calls	179	179		179	0	0	0 failed	1000
eOn (3.6.0) · LBFGS	Minimizers	9	force calls	180.137		171	180.137	0	0	crash 0, divergence 0, cap 0, wrong_stationary 0	1000
eOn (r2025) · eon-lbfgs	Minimizers	10	force calls	181	181		181	0	0	0 failed	1000
rgmin (0.4.0) · LBFGS	Minimizers	11	force calls	197.228		170	177.367	0	0	crash 0, divergence 0, cap 0, wrong_stationary 1	1000
rgmin (0.4.1) · LBFGS	Minimizers	12	force calls	197.228		170	177.367	0	0	crash 0, divergence 0, cap 0, wrong_stationary 1	1000
pele · lbfgs_scipy	Minimizers	13	force calls	230	230		230	0	0	0 failed	1000
DL-FIND (0.0.3) · L-BFGS	Minimizers	14	force calls	231.908		184	202.105	0	0	crash 0, divergence 0, cap 1, wrong_stationary 1	1000
TSASE (1.0) · SDLBFGS	Minimizers	15	force calls	257.2		169	177.96	0	0	crash 0, divergence 0, cap 0, wrong_stationary 4	1000
pele (0.1.2) · MYLBFGS	Minimizers	16	force calls	268.036		235	248.224	0	0	crash 0, divergence 0, cap 0, wrong_stationary 1	1000
OPTIM (svn-snapshot) · L-BFGS	Minimizers	17	force calls	270.341		217	230.724	0	0	crash 0, divergence 0, cap 0, wrong_stationary 2	1000
pele (0.1.2) · LBFGS	Minimizers	18	force calls	288.145		235	248.601	0	0	crash 0, divergence 0, cap 0, wrong_stationary 2	1000
GMIN (df8da5992675) · LBFGS	Minimizers	19	force calls	301.399		223	242.093	0	0	crash 0, divergence 0, cap 0, wrong_stationary 3	1000
ASE (3.6.1) · L-BFGS M=5 maxstep=0.2	Minimizers	20	force calls	374.645	355		355	0	0	1 failed, class not recorded	1000
ASE (3.6.0) · L-BFGS Line Search M=5 maxstep=0.2	Minimizers	21	force calls	417	417		417	0	0	0 failed	1000
eOn (r2025) · Conjugate Gradients	Minimizers	22	force calls	453	453		453	0	0	0 failed	1000
ase-BFGS maxstep=0.1	Minimizers	23	force calls	482.537	463		463	0	0	1 failed, class not recorded	1000
ASE (3.29.0) · LBFGS	Minimizers	24	force calls	532.882		257	344.881	0	0	crash 0, divergence 0, cap 7, wrong_stationary 6	1000
eOn (r2025) · eon-sd-twopoint	Minimizers	25	force calls	539	539		539	0	0	0 failed	1000
ASE (3.29.0) · BFGSLineSearch	Minimizers	26	force calls	580.893		551	561.466	0	0	crash 0, divergence 0, cap 0, wrong_stationary 1	1000
vc-SQNM (1.3) · ASE-SQNM	Minimizers	27	force calls	598.05		365.5	382.068	0	0	crash 0, divergence 0, cap 0, wrong_stationary 11	1000
vc-SQNM (1.3) · SQNM	Minimizers	28	force calls	598.05		365.5	382.068	0	0	crash 0, divergence 0, cap 0, wrong_stationary 11	1000
rgmin (0.4.0) · BB	Minimizers	29	force calls	639.474		471.5	521.461	0	0	crash 0, divergence 0, cap 0, wrong_stationary 6	1000
rgmin (0.4.1) · BB	Minimizers	30	force calls	639.474		471.5	521.461	0	0	crash 0, divergence 0, cap 0, wrong_stationary 6	1000
ASE (3.6.0) · FIRE	Minimizers	31	force calls	656	656		656	0	0	0 failed	1000
rgmin (0.4.0) · CG	Minimizers	32	force calls	669.237		538	591.346	0	0	crash 0, divergence 0, cap 0, wrong_stationary 4	1000
rgmin (0.4.1) · CG	Minimizers	33	force calls	669.237		538	591.346	0	0	crash 0, divergence 0, cap 0, wrong_stationary 4	1000
ASE (3.29.0) · BFGS	Minimizers	34	force calls	706.622		414.5	489.938	0	0	crash 0, divergence 0, cap 3, wrong_stationary 11	1000
pele-fire	Minimizers	35	force calls	709	709		709	0	0	0 failed	1000
Sella (2.6.0) · Sella	Minimizers	36	force calls	710.089		692.5	710.089	0	0	crash 0, divergence 0, cap 0, wrong_stationary 0	1000
ASE (3.29.0) · PreconLBFGS	Minimizers	37	force calls	728.405		652.5	690.119	0	0	crash 0, divergence 0, cap 0, wrong_stationary 2	1000
eOn (r2025) · FIRE	Minimizers	38	force calls	731	731		731	0	0	0 failed	1000
rgmin (0.4.0) · FIRE	Minimizers	39	force calls	769.36		625.5	711.609	0	0	crash 0, divergence 0, cap 0, wrong_stationary 3	1000
rgmin (0.4.1) · FIRE	Minimizers	40	force calls	769.36		625.5	711.609	0	0	crash 0, divergence 0, cap 0, wrong_stationary 3	1000
ASE (3.29.0) · FIRE	Minimizers	41	force calls	802.368		604	706.005	0	0	crash 0, divergence 0, cap 0, wrong_stationary 5	1000
rgmin (0.4.0) · FIRE2	Minimizers	42	force calls	845.947		639.5	730.952	0	0	crash 0, divergence 0, cap 0, wrong_stationary 6	1000
rgmin (0.4.1) · FIRE2	Minimizers	43	force calls	845.947		639.5	730.952	0	0	crash 0, divergence 0, cap 0, wrong_stationary 6	1000
rgmin (0.4.0) · BFGS	Minimizers	44	force calls	1010.45		970	1010.45	0	0	crash 0, divergence 0, cap 0, wrong_stationary 0	1000
rgmin (0.4.1) · BFGS	Minimizers	45	force calls	1010.45		970	1010.45	0	0	crash 0, divergence 0, cap 0, wrong_stationary 0	1000
LAMMPS (30 Sep 2026) · Hessian-free truncated Newton	Minimizers	46	force calls	1123.81		974	1066.61	0	0	crash 0, divergence 0, cap 0, wrong_stationary 3	1000
ASE (3.29.0) · PreconFIRE	Minimizers	47	force calls	1850.86		1562	1816.59	0	0	crash 0, divergence 0, cap 0, wrong_stationary 2	1000
rgmin (0.4.0) · QUICKMIN	Minimizers	48	force calls	1933		1598	1897.22	0	0	crash 0, divergence 0, cap 0, wrong_stationary 2	1000
rgmin (0.4.1) · QUICKMIN	Minimizers	49	force calls	1933		1598	1897.22	0	0	crash 0, divergence 0, cap 0, wrong_stationary 2	1000
rgmin (0.4.1) · DIIS	Minimizers	50	force calls	1967.42		1652	1930.92	0	0	crash 0, divergence 0, cap 0, wrong_stationary 2	1000
pele (0.1.2) · FIRE	Minimizers	51	force calls	2141.38		739	1325.29	0	0	crash 0, divergence 0, cap 7, wrong_stationary 41	1000
rgmin (0.4.1) · SR1	Minimizers	52	force calls	2185.66		1728	2093.01	0	0	crash 0, divergence 0, cap 2, wrong_stationary 4	1000
rgmin (0.4.1) · SR2	Minimizers	53	force calls	2298.44		1837.5	2230.07	0	0	crash 0, divergence 0, cap 5, wrong_stationary 1	1000
ase-Precon-LBFGS maxstep=0.1	Minimizers	54	force calls	2686	2686		2686	0	0	0 failed	1000
DL-FIND (0.0.3) · conjugate gradient	Minimizers	55	force calls	3048.62		2554	2958.62	0	0	crash 0, divergence 0, cap 9, wrong_stationary 0	1000
DL-FIND (0.0.3) · steepest descent	Minimizers	56	force calls	3093.74		2577	2993.74	0	0	crash 0, divergence 0, cap 10, wrong_stationary 0	1000
LAMMPS (30 Sep 2026) · Quickmin	Minimizers	57	force calls	3138.21		2545	3020.94	0	0	crash 0, divergence 5, cap 0, wrong_stationary 4	1000
eOn (r2025) · QuickMin	Minimizers	58	force calls	3901.97	3523		3523	0	0	23 failed, class not recorded	1000
LAMMPS (30 Sep 2026) · conjugate gradient	Minimizers	59	force calls	4361.3		1550.5	2810.32	0	0	crash 0, divergence 1, cap 148, wrong_stationary 3	1000
LAMMPS (30 Sep 2026) · FIRE	Minimizers	60	force calls	5844.9		413	421.053	0	0	crash 0, divergence 224, cap 0, wrong_stationary 49	1000
eOn (r2025) · eon-sd	Minimizers	61	force calls	6350.5	4901		4901	0	0	96 failed, class not recorded	1000
rgmin (0.4.0) · SD	Minimizers	62	force calls	8392.75		6099	6350.19	0	0	crash 0, divergence 0, cap 200, wrong_stationary 3	1000
rgmin (0.4.1) · SD	Minimizers	63	force calls	8392.75		6099	6350.19	0	0	crash 0, divergence 0, cap 200, wrong_stationary 3	1000
rgmin (0.4.1) · ADAM	Minimizers	64	force calls	13835.7		10000	8365.68	0	0	crash 0, divergence 0, cap 547, wrong_stationary 0	1000
LAMMPS (30 Sep 2026) · steepest descent	Minimizers	65	force calls	14468.2		10000	8298.19	0	0	crash 0, divergence 0, cap 617, wrong_stationary 0	1000
pysisyphus (0.1.dev1) · conjugate gradient	Minimizers	66	force calls	15124.7		10000	7655.12	0	0	crash 0, divergence 0, cap 745, wrong_stationary 1	1000
pysisyphus (0.1.dev1) · steepest descent	Minimizers	67	force calls	16094.8		10000	8144.78	0	0	crash 0, divergence 0, cap 795, wrong_stationary 0	1000
rgmin (0.4.0) · ADAM	Minimizers	68	force calls	16420.2		10000	9110.16	0	0	crash 0, divergence 0, cap 731, wrong_stationary 0	1000
rgmin (0.4.0) · SR1	Minimizers	69	force calls	19908.9		10000	8133.1	0	0	crash 0, divergence 196, cap 799, wrong_stationary 0	1000
rgmin (0.4.0) · DIIS	Minimizers	70	force calls	19945		10000	9836.21	0	0	crash 0, divergence 0, cap 964, wrong_stationary 32	1000
TSASE (1.0) · MDMin	Minimizers	71	force calls	20000		10000	10000	0	0	crash 0, divergence 0, cap 1000, wrong_stationary 0	1000
pele (0.1.2) · steepest descent	Minimizers	72	force calls	20000		10000	10000	0	0	crash 0, divergence 0, cap 1000, wrong_stationary 0	1000
pysisyphus (0.1.dev1) · L-BFGS	Minimizers	73	force calls	20000		10000	10000	0	0	crash 0, divergence 0, cap 1000, wrong_stationary 0	1000
rgmin (0.4.0) · SR2	Minimizers	74	force calls	20000		10000	9990.45	0	0	crash 0, divergence 1, cap 999, wrong_stationary 0	1000

Not scored

• eOn: no per-start record
• eOn: no per-start record
• eOn: no per-start record
• eOn: no per-start record
• eOn: no per-start record
• eOn: no per-start record
• eOn: no per-start record
• Eon svn: no per-start record
• Eon svn: no per-start record
• Eon svn: no per-start record
• Eon svn: no per-start record
• Eon svn: no per-start record
• Eon svn: no per-start record
• Eon svn: no per-start record
• pele: no per-start record
• pele: no per-start record
• pele: no per-start record
• pele: no per-start record
• pele: no per-start record
• pele: no per-start record
• pele: no per-start record

Success on this problem: harness force calls under the cap, the force norm at the stop, and vibrational Hessian index 0.

The six rigid modes of the free cluster are removed before the count.

A curvature counts as negative only below -max(force_norm, 1e-8*||H||_F, 1e-6).

Energy and Kabsch RMSD are not applied: this file has no energy_tol, rmsd_tol, or per-start reference.