CrystalFp: comparative test results

Version	Description
1	First experiment, no cutoff distance
2	Second experiment, cutoff=10
3	Cutoff = 5
4	Cutoff = 3 (minimum possible value)
5	Cutoff = 30 (more than every free cutoff distance)

Au₈Pd₄

Atom types:	Au	Pd
Atom count:	8	4
Structures:	259
Theor. dim.:	39
Intr. dim.:	15.20000

Version	Dimensions	Actual cutoff	Computed cutoff	Raw intrinsic dimension (old)	Intrinsic dimension (old)	Sigma mult.	Shift	Raw intrinsic dimension	Intrinsic dimension
4	180	3.0000	13.1925	1.9236	5.4258	1.0000	0.0000	1.8977	5.1110
3	300	5.0000	13.1925	3.1287	9.0803	1.1859	0.0183	3.4941	10.1000
2	600	10.0000	13.1925	3.4214	10.0130	1.4709	0.0526	3.8826	11.4303
1	792	13.1925	13.1925	3.6382	10.7167	1.5558	0.0668	4.3820	13.2152
5	1800	30.0000	13.1925	4.1807	12.5327	1.6124	0.0883	4.7852	14.7213

Ca at 160GPa

Atom types:	Ca
Atom count:	16
Structures:	243
Theor. dim.:	51
Intr. dim.:	68.45801

Version	Dimensions	Actual cutoff	Computed cutoff	Raw intrinsic dimension (old)	Intrinsic dimension (old)	Sigma mult.	Shift	Raw intrinsic dimension	Intrinsic dimension
4	60	3.0000	15.5247	3.6405	10.2435	1.0000	0.0000	5.0747	15.0558
3	100	5.0000	15.5247	7.4742	24.0608	1.0398	0.0305	8.6180	29.3890
2	200	10.0000	15.5247	11.2724	42.9385	1.0495	0.0507	12.0201	47.2766
1	310	15.5247	15.5247	11.9542	46.8540	1.0519	0.0575	12.2788	48.7660
5	600	30.0000	15.5247	13.3867	55.0270	1.0484	0.0630	14.3875	60.8993

Ca at 300GPa

Atom types:	Ca
Atom count:	16
Structures:	228
Theor. dim.:	51
Intr. dim.:	43.59908

Version	Dimensions	Actual cutoff	Computed cutoff	Raw intrinsic dimension (old)	Intrinsic dimension (old)	Sigma mult.	Shift	Raw intrinsic dimension	Intrinsic dimension
4	60	3.0000	15.6613	3.3408	9.5660	1.0000	0.0000	3.9434	11.6018
3	100	5.0000	15.6613	6.2810	20.0756	1.0598	0.0329	6.0101	18.9526
2	200	10.0000	15.6613	8.2047	29.0075	1.0887	0.0574	8.8194	31.5341
1	313	15.6613	15.6613	8.6072	31.0458	1.0921	0.0651	9.3341	34.3826
5	600	30.0000	15.6613	9.3068	34.5565	1.0920	0.0711	9.9195	37.9589

Carbon 0GPa 8 atoms

Atom types:	C
Atom count:	8
Structures:	2694
Theor. dim.:	27
Intr. dim.:	30.68134

Version	Dimensions	Actual cutoff	Computed cutoff	Raw intrinsic dimension (old)	Intrinsic dimension (old)	Sigma mult.	Shift	Raw intrinsic dimension	Intrinsic dimension
4	60	3.0000	21.4254	4.1962	11.3048	1.2229	-0.0531	4.2658	11.8116
3	100	5.0000	21.4254	5.9086	17.0171	1.1175	-0.0278	6.1651	17.6423
2	200	10.0000	21.4254	7.6156	22.8642	1.0430	-0.0097	7.7013	22.6661
1	429	21.4254	21.4254	8.7361	26.6645	1.0077	-0.0018	8.9492	26.9745
5	600	30.0000	21.4254	8.8152	26.9347	1.0000	0.0000	9.1764	27.7823

CH₂ 800GPa

Atom types:	C	H
Atom count:	6	12
Structures:	946
Theor. dim.:	57
Intr. dim.:	68.8177

Version	Dimensions	Actual cutoff	Computed cutoff	Raw intrinsic dimension (old)	Intrinsic dimension (old)	Sigma mult.	Shift	Raw intrinsic dimension	Intrinsic dimension
4	180	3.0000	7.5728	8.7975	25.8612	1.1035	-0.0429	9.1000	27.3217
3	300	5.0000	7.5728	12.1405	42.0940	1.0501	-0.0230	12.8924	45.0016
1	453	7.5728	7.5728	13.5489	49.2181	1.0348	-0.0134	14.0960	51.7864
2	600	10.0000	7.5728	14.5962	54.5822	1.0196	-0.0086	14.8214	56.1189
5	1800	30.0000	7.5728	16.0679	61.8660	1.0000	0.0000	16.2680	65.0863

GaAs 8 atoms

Atom types:	Ga	As
Atom count:	4	4
Structures:	2997
Theor. dim.:	27
Intr. dim.:	28.98297

Version	Dimensions	Actual cutoff	Computed cutoff	Raw intrinsic dimension (old)	Intrinsic dimension (old)	Sigma mult.	Shift	Raw intrinsic dimension	Intrinsic dimension
4	180	3.0000	20.8210	3.6944	9.5759	1.9211	-0.1239	3.7910	9.9716
3	300	5.0000	20.8210	7.5434	21.1069	1.3980	-0.0514	6.1599	16.8885
2	600	10.0000	20.8210	9.3622	27.5956	1.1325	-0.0171	7.7905	22.0129
1	1248	20.8210	20.8210	10.3875	31.3947	1.0272	-0.0033	8.8924	25.6632
5	1800	30.0000	20.8210	10.7463	32.7154	1.0000	0.0000	9.2306	26.8159

H₂O

Atom types:	H	O
Atom count:	8	4
Structures:	949
Theor. dim.:	39
Intr. dim.:	99.96788

Version	Dimensions	Actual cutoff	Computed cutoff	Raw intrinsic dimension (old)	Intrinsic dimension (old)	Sigma mult.	Shift	Raw intrinsic dimension	Intrinsic dimension
4	180	3.0000	9.1283	7.3566	21.9211	1.0331	-0.0554	8.7139	26.7070
3	300	5.0000	9.1283	15.0186	54.3507	1.0246	-0.0273	15.7558	59.6162
1	549	9.1283	9.1283	16.2232	60.3653	1.0226	-0.0113	17.4254	70.4236
2	600	10.0000	9.1283	16.2437	60.4828	1.0117	-0.0112	19.0706	82.8335
5	1800	30.0000	9.1283	19.5645	87.1742	1.0000	0.0000	20.3680	93.9843

H 300GPa 12 atoms

Atom types:	H
Atom count:	12
Structures:	205
Theor. dim.:	39
Intr. dim.:	11.31231

Version	Dimensions	Actual cutoff	Computed cutoff	Raw intrinsic dimension (old)	Intrinsic dimension (old)	Sigma mult.	Shift	Raw intrinsic dimension	Intrinsic dimension
4	60	3.0000	6.3956	2.7761	8.6186	1.0972	-0.0239	2.2807	7.0394
3	100	5.0000	6.3956	3.3101	10.4547	1.0638	-0.0141	2.7200	8.4967
1	128	6.3956	6.3956	3.4517	10.9519	1.0447	-0.0107	2.9147	9.1544
2	200	10.0000	6.3956	3.5460	11.2857	1.0252	-0.0060	3.1230	9.8664
5	600	30.0000	6.3956	4.0273	13.0217	1.0000	0.0000	3.3909	10.7954

H 500GPa 16 atoms

Atom types:	H
Atom count:	16
Structures:	337
Theor. dim.:	51
Intr. dim.:	36.07003

Version	Dimensions	Actual cutoff	Computed cutoff	Raw intrinsic dimension (old)	Intrinsic dimension (old)	Sigma mult.	Shift	Raw intrinsic dimension	Intrinsic dimension
4	60	3.0000	9.0923	4.8585	15.0257	1.0479	-0.0252	5.2147	17.4846
3	100	5.0000	9.0923	6.0064	19.4918	1.0261	-0.0144	6.4038	21.9929
1	182	9.0923	9.0923	7.8501	27.1659	1.0127	-0.0070	8.0702	28.7220
2	200	10.0000	9.0923	8.0635	28.1000	1.0111	-0.0060	8.3279	29.8095
5	600	30.0000	9.0923	8.5719	30.3691	1.0000	0.0000	9.0615	32.9810

H 500GPa 8 atoms

Atom types:	H
Atom count:	8
Structures:	312
Theor. dim.:	27
Intr. dim.:	10.95844

Version	Dimensions	Actual cutoff	Computed cutoff	Raw intrinsic dimension (old)	Intrinsic dimension (old)	Sigma mult.	Shift	Raw intrinsic dimension	Intrinsic dimension
4	60	3.0000	5.0686	3.6648	10.6952	1.1240	-0.0279	2.0856	5.7531
3	100	5.0000	5.0686	4.3999	13.3577	1.0666	-0.0152	2.5997	7.2968
1	101	5.0686	5.0686	4.4152	13.4155	1.0646	-0.0146	2.8044	7.9274
2	200	10.0000	5.0686	5.1120	16.0258	1.0272	-0.0061	3.1247	8.9332
5	600	30.0000	5.0686	6.0166	19.4534	1.0000	0.0000	3.5684	10.3677

Lennard Jones atoms (a)

Atom types:	Li	H
Atom count:	4	8
Structures:	1993
Theor. dim.:	39
Intr. dim.:	5.841494

Version	Dimensions	Actual cutoff	Computed cutoff	Raw intrinsic dimension (old)	Intrinsic dimension (old)	Sigma mult.	Shift	Raw intrinsic dimension	Intrinsic dimension
4	180	3.0000	27.7744	1.7836	3.9206	1.0000	0.0000	0.6946	1.8315
3	300	5.0000	27.7744	2.2914	5.4611	1.0170	0.0200	1.2829	3.4209
2	600	10.0000	27.7744	2.7114	6.7548	1.0651	0.0480	1.7033	4.5792
1	1665	27.7744	27.7744	2.7314	6.8170	1.0489	0.0634	1.9939	5.3912
5	1800	30.0000	27.7744	2.7429	6.8526	1.0475	0.0640	2.0117	5.4413

Lennard Jones atoms

Atom types:	Li	H
Atom count:	4	8
Structures:	1949
Theor. dim.:	39
Intr. dim.:	5.484571

Version	Dimensions	Actual cutoff	Computed cutoff	Raw intrinsic dimension (old)	Intrinsic dimension (old)	Sigma mult.	Shift	Raw intrinsic dimension	Intrinsic dimension
4	180	3.0000	27.7744	1.7904	4.7234	1.0000	0.0000	0.6863	1.6988
3	300	5.0000	27.7744	2.2879	6.0634	1.0157	0.0200	1.2762	3.1989
2	600	10.0000	27.7744	2.7279	7.2682	1.0619	0.0481	1.6969	4.2926
1	1665	27.7744	27.7744	2.7421	7.3073	1.0449	0.0635	1.9785	5.0360
5	1800	30.0000	27.7744	2.7563	7.3466	1.0436	0.0641	2.0133	5.1285

MgNH with energy < 2.5eV

Atom types:	Mg	N	H
Atom count:	4	4	4
Structures:	2212
Theor. dim.:	39
Intr. dim.:	14.53835

Version	Dimensions	Actual cutoff	Computed cutoff	Raw intrinsic dimension (old)	Intrinsic dimension (old)	Sigma mult.	Shift	Raw intrinsic dimension	Intrinsic dimension
4	360	3.0000	17.1311	7.1503	21.0912	1.0000	0.0000	2.8042	7.5220
3	600	5.0000	17.1311	9.7674	29.9358	1.2385	0.0582	2.9294	7.8729
2	1200	10.0000	17.1311	13.0961	42.2854	1.2447	0.0893	3.6612	9.9517
1	2058	17.1311	17.1311	14.6603	49.5621	1.2402	0.1015	4.0640	11.1170
5	3600	30.0000	17.1311	15.9010	55.5371	1.2266	0.1063	4.3810	12.0454

MgNH

Atom types:	Mg	N	H
Atom count:	4	4	4
Structures:	6979
Theor. dim.:	39
Intr. dim.:	67.76572

Version	Dimensions	Actual cutoff	Computed cutoff	Raw intrinsic dimension (old)	Intrinsic dimension (old)	Sigma mult.	Shift	Raw intrinsic dimension	Intrinsic dimension
4	360	3.0000	26.4909	7.0418	19.5341	1.2115	-0.1001	7.0895	19.7849
3	600	5.0000	26.4909	9.8019	30.5290	1.1118	-0.0451	10.3068	32.4519
2	1200	10.0000	26.4909	12.8018	44.1158	1.0422	-0.0159	13.6733	48.1615
1	3180	26.4909	26.4909	16.1287	59.2944	1.0017	-0.0006	16.0344	59.0682
5	3600	30.0000	26.4909	16.1745	59.2429	1.0000	0.0000	16.2340	59.9375

MgO 32 atoms

Atom types:	Mg	O
Atom count:	16	16
Structures:	967
Theor. dim.:	99
Intr. dim.:	11.5388

Version	Dimensions	Actual cutoff	Computed cutoff	Raw intrinsic dimension (old)	Intrinsic dimension (old)	Sigma mult.	Shift	Raw intrinsic dimension	Intrinsic dimension
4	180	3.0000	27.3328	2.4746	6.8488	1.0000	0.0000	1.3831	3.7783
3	300	5.0000	27.3328	5.4258	15.8700	1.0373	0.0414	2.6062	7.2625
2	600	10.0000	27.3328	6.5976	19.7168	1.0447	0.0641	3.6163	10.2508
1	1641	27.3328	27.3328	7.7255	23.5946	1.0317	0.0760	3.7404	10.6252
5	1800	30.0000	27.3328	7.8504	24.0356	1.0311	0.0766	3.8617	10.9930

MgO full

Atom types:	Mg	O
Atom count:	16	16
Structures:	1331
Theor. dim.:	99
Intr. dim.:	19.65137

Version	Dimensions	Actual cutoff	Computed cutoff	Raw intrinsic dimension (old)	Intrinsic dimension (old)	Sigma mult.	Shift	Raw intrinsic dimension	Intrinsic dimension
4	180	3.0000	27.3328	3.0934	7.9734	1.0000	0.0000	1.3353	3.2947
3	300	5.0000	27.3328	7.3923	21.4098	1.0609	0.0392	4.9877	13.5028
2	600	10.0000	27.3328	9.0553	27.9182	1.0630	0.0610	5.2226	14.2313
1	1641	27.3328	27.3328	10.9539	35.9905	1.0509	0.0729	6.8297	19.5031
5	1800	30.0000	27.3328	10.9630	36.0307	1.0503	0.0735	6.7445	19.2102

Na 140GPa 8 atoms

Atom types:	Na
Atom count:	8
Structures:	161
Theor. dim.:	27
Intr. dim.:	25.91837

Version	Dimensions	Actual cutoff	Computed cutoff	Raw intrinsic dimension (old)	Intrinsic dimension (old)	Sigma mult.	Shift	Raw intrinsic dimension	Intrinsic dimension
4	60	3.0000	7.7783	3.0461	9.7152	1.1050	-0.0786	4.8849	14.0359
3	100	5.0000	7.7783	4.8455	15.6936	1.0793	-0.0457	6.2327	18.5881
1	156	7.7783	7.7783	6.0604	19.8282	1.0487	-0.0257	6.8258	20.7293
2	200	10.0000	7.7783	6.3119	20.6954	1.0387	-0.0171	7.3936	22.8739
5	600	30.0000	7.7783	7.3348	24.2658	1.0000	0.0000	7.8095	24.5125

Urea 0GPa

Atom types:	N	H	C	O
Atom count:	4	8	2	2
Structures:	819
Theor. dim.:	51
Intr. dim.:	25.76689

Version	Dimensions	Actual cutoff	Computed cutoff	Raw intrinsic dimension (old)	Intrinsic dimension (old)	Sigma mult.	Shift	Raw intrinsic dimension	Intrinsic dimension
4	600	3.0000	11.7571	4.1139	12.0776	1.1626	-0.0551	1.9417	5.5706
3	1000	5.0000	11.7571	5.6706	17.4630	1.0940	-0.0309	4.1819	12.3880
2	2000	10.0000	11.7571	7.1606	22.7433	1.0353	-0.0114	6.0900	18.5790
1	2350	11.7571	11.7571	7.2576	23.0960	1.0261	-0.0090	6.3389	19.4158
5	6000	30.0000	11.7571	7.9974	25.8022	1.0000	0.0000	7.4433	23.2187

GaAs 8 atoms (old)

Atom types:	Ga	As
Atom count:	4	4
Structures:	120
Theor. dim.:	27
Intr. dim.:	17.86204

Version	Dimensions	Actual cutoff	Computed cutoff	Raw intrinsic dimension (old)	Intrinsic dimension (old)	Sigma mult.	Shift	Raw intrinsic dimension	Intrinsic dimension
4	180	3.0000	26.3748	1.5538	5.5814	1.4160	-0.1213	1.5702	5.6818
3	300	5.0000	26.3748	2.8015	9.5244	1.2366	-0.0520	2.6776	9.7676
2	600	10.0000	26.3748	3.7979	12.7878	1.1211	-0.0202	3.5117	12.8924
1	1581	26.3748	26.3748	4.7752	16.0960	1.0099	-0.0011	4.3324	16.0094
5	1800	30.0000	26.3748	4.8004	16.1830	1.0000	0.0000	4.3813	16.1963

MgSiO₃ Postperovskite 120GPa

Atom types:	Mg	Si	O
Atom count:	4	4	12
Structures:	610
Theor. dim.:	63
Intr. dim.:	60.45808

Version	Dimensions	Actual cutoff	Computed cutoff	Raw intrinsic dimension (old)	Intrinsic dimension (old)	Sigma mult.	Shift	Raw intrinsic dimension	Intrinsic dimension
4	360	3.0000	8.9750	6.9258	21.4983	1.0000	0.0000	7.6703	24.0133
3	600	5.0000	8.9750	9.7926	32.3801	1.0617	0.0303	10.4871	34.9233
1	1074	8.9750	8.9750	12.9204	45.6372	1.0723	0.0542	12.8922	45.6059
2	1200	10.0000	8.9750	13.6988	49.3007	1.0736	0.0568	13.2939	47.5439
5	3600	30.0000	8.9750	15.2460	57.3971	1.0562	0.0727	14.7881	55.2216

GaAs random

Atom types:	Ga	As
Atom count:	4	4
Structures:	3020
Theor. dim.:	27
Intr. dim.:	29.32768

Version	Dimensions	Actual cutoff	Computed cutoff	Raw intrinsic dimension (old)	Intrinsic dimension (old)	Sigma mult.	Shift	Raw intrinsic dimension	Intrinsic dimension
4	180	3.0000	20.8210	3.3001	8.9260	1.8954	-0.1221	2.1440	7.1382
3	300	5.0000	20.8210	5.6116	14.7681	1.3884	-0.0508	5.3103	18.1681
2	600	10.0000	20.8210	6.8171	18.0590	1.1300	-0.0169	6.7043	23.2271
1	1248	20.8210	20.8210	7.7044	23.5258	1.0269	-0.0032	7.7021	26.9312
5	1800	30.0000	20.8210	8.9519	26.6949	1.0000	0.0000	7.9918	28.0201

MgNH random

Atom types:	Mg	N	H
Atom count:	4	4	4
Structures:	1674
Theor. dim.:	39
Intr. dim.:	63.74314

Version	Dimensions	Actual cutoff	Computed cutoff	Raw intrinsic dimension (old)	Intrinsic dimension (old)	Sigma mult.	Shift	Raw intrinsic dimension	Intrinsic dimension
4	360	3.0000	20.1948	6.0499	18.3547	1.3864	-0.0772	6.1489	20.0166
3	600	5.0000	20.1948	10.7144	36.8741	1.1705	-0.0350	10.4641	35.7284
2	1200	10.0000	20.1948	13.4432	49.1151	1.0608	-0.0124	13.6617	48.9582
1	2424	20.1948	20.1948	15.4819	58.0170	1.0132	-0.0026	15.2457	56.3338
5	3600	30.0000	20.1948	15.7575	59.3525	1.0000	0.0000	15.6961	58.5725