si.pdf

Supplementary Material for OrbNet Denali: A machine learning potential

for biological and organic chemistry with semi-empirical cost and DFT

accuracy

Anders S. Christensen,

Sai Krishna Sirumalla,

Zhuoran Qiao,

Michael B. O’Connor,

Daniel G. A. Smith,

Feizhi Ding,

Peter J. Bygrave,

Animashree Anandkumar,

3, 4

Matthew Welborn,

Frederick R. Manby,

and

Thomas F. Miller III

1, 2

Entos, Inc.

Los Angeles, CA 90027

Division of Chemistry and Chemical Engineering

California Institute of Technology

Pasadena, CA 91125

Division of Engineering and Applied Sciences

California Institute of Technology

Pasadena, CA 91125

NVIDIA

Santa Clara, CA 95051

(*Electronic mail: tom@entos.ai)

(Dated: 21 October 2021)

I. ADDITIONAL GMTKN55 STATISTICS

Indicates equal contribution.

FIG. S1. The figure shows the performance of OrbNet Denali on the GMTKN55 subsets that only contain elements, charge- and spin-states that

are supported by OrbNet Denali, but contain chemistry that is not represented in the training set (for example water clusters, C

molecules,

transition states, etc.). In the left colum, the MAE values are with respect to the CCSD(T) references in the GMTKN55 dataset

while, in the

right column, the MAE values are with respect to

ω

B97X-D3/def2-TZVP reference energies (the same method used to generate the OrbNet

training data). Due to an error in the training of OrbNet Denali 10%, that model does not support lithium and the ALK8 test set is excluded

here.

FIG. S2. The figure shows the performance of OrbNet Denali on the GMTKN55 subsets that only contain elements, charge- and spin-states

that are supported by OrbNet Denali, and where molecules with similar chemistry are found in the training set for OrbNet Denali. In the left

column, the MAE values are with respect to the CCSD(T) references in the GMTKN55 dataset

while, in the right column, the MAE values

are with respect to

ω

B97X-D3/def2-TZVP reference energies (the same method used to generate the OrbNet training data).

TABLE S1. Overview of the mean absolute error (MAE) of every GMTKN55 subset for every method where applicable as discussed in

the text. The reference values are the high-level reference values from the GMTKN55 database.

The MAE values displayed are in units of

kcal/mol, along with the WTMAD-

which is calculated as discussed in the main text.

MAE [kcal/mol]

Subset

ω

B97X-D3

B97-3c OrbNet Denali ANI-1ccx ANI-2x GFN2-xTB GFN1-xTB GFN0-xTB

W4-11

3.52

7.48

G21EA

7.07

8.24

G21IP

3.07

3.69

DIPCS10

5.58

4.16

274.75

301.44

1936.47

PA26

3.32

5.58

5.29

163.05

162.30

938.31

SIE4x4

12.18

22.54

ALKBDE10

5.28

7.90

YBDE18

2.17

5.13

AL2X6

3.07

2.22

14.63

15.18

8.30

HEAVYSB11

2.56

2.51

NBPRC

1.67

1.56

10.27

10.51

10.96

33.00

ALK8

4.07

3.54

60.55

23.91

52.55

97.75

RC21

3.28

6.39

G2RC

4.58

8.34

21.92

29.27

52.60

BH76RC

2.31

3.64

FH51

2.47

4.42

3.58

13.38

11.41

12.05

22.14

TAUT15

1.05

1.71

1.13

2.51

0.98

5.79

3.89

DC13

6.81

11.33

MB16-43

40.75

27.39

DARC

1.27

4.34

1.31

1.13

5.48

17.77

15.82

15.46

RSE43

1.44

3.49

BSR36

4.36

1.90

0.77

2.69

8.85

2.76

2.34

2.03

CDIE20

0.72

1.98

0.61

2.09

3.63

1.80

2.04

2.27

ISO34

1.18

1.87

1.21

1.24

12.94

6.90

6.30

10.15

ISOL24

2.75

5.19

2.64

11.68

10.92

10.78

C60ISO

1.18

6.27

11.82

91.96

44.94

5.80

7.88

11.89

PArel

0.67

1.80

1.60

5.86

4.54

7.09

BH76

2.25

6.89

BHPERI

2.85

4.59

4.72

10.24

9.32

6.84

BHDIV10

1.01

5.80

6.83

8.12

8.40

9.99

INV24

1.63

1.96

4.59

3.32

5.80

5.06

BHROT27

0.47

0.61

0.39

1.42

1.17

2.38

1.68

PX13

3.18

7.08

14.84

13.32

2.74

8.30

17.16

WCPT18

2.14

5.46

4.91

6.13

3.84

5.30

8.40

RG18

0.11

0.12

0.11

0.32

0.44

ADIM6

0.36

0.53

0.40

0.64

0.34

1.15

1.01

0.51

S22

0.36

0.29

0.45

5.00

1.51

0.76

1.33

1.63

S66

0.52

0.32

0.48

2.52

1.11

0.73

1.07

1.29

HEAVY28

0.26

0.80

0.61

0.65

0.91

WATER27

14.23

9.41

2.39

3.05

7.39

17.81

CARBHB12

0.83

2.07

0.91

1.79

0.67

2.32

PNICO23

0.38

1.64

1.71

1.11

2.33

2.00

HAL59

0.34

1.62

2.15

1.28

1.34

1.76

AHB21

3.40

3.27

1.81

2.97

4.68

26.02

CHB6

1.32

1.37

3.58

5.40

3.95

20.51

IL16

2.09

2.34

4.60

4.32

5.69

55.34

IDISP

2.78

3.91

2.61

12.39

20.64

6.78

6.53

13.27

ICONF

0.34

0.38

1.25

1.63

2.63

1.55

ACONF

0.09

0.21

0.06

0.56

0.16

0.19

0.66

0.44

Amino20x4

0.26

0.33

0.35

1.00

0.95

1.11

1.22

PCONF21

0.33

0.83

0.47

3.18

2.20

1.76

2.17

1.99

MCONF

0.48

0.33

0.42

0.92

0.82

1.72

1.44

1.34

SCONF

0.30

0.77

0.32

1.58

2.47

1.64

2.50

2.10

UPU23

0.94

0.51

0.87

2.91

1.24

3.74

BUT14DIOL

0.41

0.40

0.61

1.42

1.25

0.95

0.60

WTMAD-1 [arb. units]

3.37

5.76

7.19

14.12

13.56

12.00

14.72

24.83

WTMAD-2 [arb. units]

5.87

10.22

9.84

23.80

24.11

18.89

22.63

37.99

TABLE S2. Overview of the mean absolute error (MAE) of every GMTKN55 subset for every method where applicable as discussed in the

text. The reference energies are calculated at the

ω

B97X-D3 level of theory The MAE values displayed are in units of kcal/mol, along with

the WTMAD-

which is calculated as discussed in the main text.

MAE [kcal/mol]

SUBSET

B97-3c

Denali Denali 10% ANI-1ccx ANI-2x GFN2-xTB GFN1-xTB GFN0-xTB

W4-11

7.77

G21EA

2.16

G21IP

2.87

DIPCS10

2.63

279.84

306.53

1941.57

PA26

2.57

5.06

5.80

166.38

165.62

941.63

SIE4x4

10.82

ALKBDE10

4.71

YBDE18

3.81

AL2X6

1.55

11.56

13.98

8.24

HEAVYSB11

2.10

NBPRC

2.92

9.23

14.87

10.41

10.53

33.40

ALK8

6.34

63.24

22.58

53.20

98.41

RC21

4.43

G2RC

5.75

19.71

25.91

53.23

BH76RC

2.58

FH51

4.02

1.33

4.36

11.15

9.81

10.67

22.15

TAUT15

1.15

0.27

0.45

1.84

1.26

5.25

3.54

DC13

11.15

MB16-43

28.97

RSE43

2.06

BSR36

2.47

3.97

4.64

1.68

4.48

6.39

4.13

5.97

CDIE20

1.65

0.82

1.24

2.48

4.14

1.14

1.42

2.43

ISO34

1.56

0.32

0.87

1.78

12.07

6.52

6.40

10.20

ISOL24

5.43

1.17

1.39

11.37

10.03

10.79

C60ISO

19.66

2.08

2.61

105.51

58.49

19.34

21.43

25.43

PArel

1.59

1.58

3.20

6.04

4.82

7.40

BH76

5.28

BHPERI

7.34

3.09

2.87

12.22

11.29

9.53

BHDIV10

5.86

6.95

7.24

8.58

9.10

10.54

INV24

2.79

4.72

6.59

4.05

5.78

6.06

BHROT27

0.60

0.29

0.51

1.61

1.40

2.77

2.05

PX13

3.90

18.02

18.56

15.72

3.41

6.98

17.15

WCPT18

4.33

6.00

6.05

6.56

3.88

5.36

7.94

RG18

0.17

0.16

0.38

0.45

ADIM6

0.89

0.07

0.11

1.00

0.70

1.51

1.37

0.87

S22

0.30

0.41

0.59

5.36

1.62

1.01

1.64

1.94

S66

0.47

0.32

0.46

3.03

0.97

1.17

1.56

1.70

HEAVY28

0.86

0.57

0.71

0.89

WATER27

5.26

14.28

13.02

14.20

15.49

24.07

CARBHB12

1.27

0.78

1.51

2.45

1.05

3.06

PNICO23

1.55

1.84

2.15

1.04

2.30

2.18

HAL59

1.69

2.09

2.45

1.28

1.29

1.84

AHB21

0.97

2.60

1.96

4.79

5.10

23.89

CHB6

1.01

3.45

5.44

4.41

21.31

IL16

0.81

3.10

6.80

6.33

7.30

53.26

IDISP

4.18

0.69

3.02

11.52

18.43

8.11

7.04

14.43

ICONF

0.49

1.08

2.73

1.61

2.72

1.54

ACONF

0.26

0.07

0.11

0.56

0.16

0.18

0.62

0.41

Amino20x4

0.32

0.16

0.36

1.09

0.93

1.15

1.25

PCONF21

0.92

0.29

0.86

3.27

2.26

1.63

2.04

1.78

MCONF

0.36

0.10

0.30

1.18

0.93

1.97

1.85

1.61

SCONF

0.53

0.15

0.19

1.51

2.21

1.39

2.25

1.85

UPU23

0.54

0.62

0.84

2.12

1.21

4.49

BUT14DIOL

0.11

0.07

0.22

1.01

1.03

1.43

1.20

0.65

WTMAD-1 [arb. units]

4.98

6.42

7.40

15.82

13.23

12.32

15.06

25.89

WTMAD-2 [arb. units]

8.84

8.40

11.41

27.44

22.52

20.19

23.79

39.72

TABLE S3. Overview of which GMTKN55 subsets are supported by OrbNet Denali, ANI-1ccx, ANI-2x, and the GFN

-xTB methods. For

OrbNet Denali, the allowed subsets are those that only contain singlet-state molecules with the elements H, Li, B, C, N, O, F, Na, Mg, Si, P, S,

Cl, K, Ca, Br, and I. For ANI-1ccx

and ANI-2x

only neutral single-state molecules containing the elements H, C, N, O (for ANI-1ccx) or H,

C, N, O, F, Cl, S (for ANI-2x) are allowed. For the GFN

-xTB family of methods, only singlet-state molecules are allowed in this list.