Table 1 Test root mean squared errors (RMSE) energies (E) in meV/atom, forces (F) in meV/Å are reported for different models with cutoffs rcut

From: Machine learning of charges and long-range interactions from energies and forces

  

ACE

χ + η(ACE)

3G-HDNNP

4G-HDNNP

CACE-SR

CACE-LR

 

rcut

6 Å

6 Å

4.23 Å

4.23 Å

4.23 Å

4.23 Å

\({{{\rm{C}}}}_{10}{{{\rm{H}}}}_{2}/{{{\rm{C}}}}_{10}{{{\rm{H}}}}_{3}^{+}\)

E

0.76

0.75

2.045

1.194

1.27

0.73

 

F

37.22

35.16

231.0

78.00

91.0

36.9

 

rcut

6 Å

6 Å

5.29 Å

5.29 Å

5.29 Å

-

\({{{\rm{Ag}}}}_{3}^{+/-}\)

E

809.62

0.21

320.2

1.323

0.162

-

 

F

285.81

23.10

1913

31.69

29.0

-

 

rcut

6 Å

6 Å

5.29 Å

5.29 Å

5.29 Å

5.29 Å

\({{{\rm{Na}}}}_{8/9}{{{\rm{Cl}}}}_{8}^{+}\)

E

1.55

0.71

2.042

0.481

1.58

0.21

 

F

41.72

12.35

76.67

32.78

48.8

9.78

 

rcut

6 Å

6 Å

-

4.23 Å

5.5 Å

5.5 Å

Au2-MgO(001)

E

2.56

1.63

-

0.219

2.25

0.073

 

F

88.70

50.27

-

66.00

59.3

7.91

  1. The 3G-HDNNP and 4G-HDNNP values are from ref. 12. The values for the atomic cluster expansion (ACE) model and the charge constrained model (χ + η(ACE)) are from ref. 46. CACE-SR and CACE-LR stand for short-ranged and long-ranged Cartesian atomic cluster expansion (CACE) models. Short-ranged CACE with embedded charge states was used for the \({{{\rm{Ag}}}}_{3}^{+/-}\) system.