Supporting Information Towards Predicting Efficiency of Organic Solar Cells via Machine Learning and Improved Descriptors Harikrishna Sahu, Weining Rao, Alessandro Troisi,∗ and Haibo Ma∗
Dr. H. Sahu, W. Rao, Prof. H. Ma Key Laboratory of Mesoscopic Chemistry of MOE School of Chemistry and Chemical Engineering Nanjing University, Nanjing 210023, China E-mail:
[email protected] Prof. A. Troisi Department of Chemistry, University of Liverpool L69 7DZ Liverpool, United Kingdom E-mail:
[email protected]
Page 1 of 46
List of Figures
S1
Correlations between the energy of charge transfer state (ECT ) and the energetic difference DA ) at the donor-acceptor interface. . . . . . of HOMO of donor and LUMO of acceptor (EHL
14
S2
Correlation between vertical IP(v) and energy of HOMO (EHOMO ) of donor molecules. . .
14
S3
∆H (a), ∆L (b), Eg (c) and IP(v) (d) calculated by the M06-2X versus B3LYP functionals using the ground state geometries obtained at the M06-2X/6-31G(d) level. . . . . . . . . .
S4
15
Tanimoto (a) and Euclidean (c) distances of the chemical fingerprints and the normalized features for 30 closet data points to each sample in the testing set, respectively. The differences of PCE (∆PCE ) of testing samples with respect to the corresponding 30 closest training data points are shown in (b, Tanimoto distance) and (d, Euclidean distance). Indextesting set and Indextraining set are indexes of donor molecules in training and testing sets, respectively. Tanimoto distances are calculated by using the default set of parameters for generating fingerprints as implemented in RDKit package. [185] . . . . . . . . . . . . . . . . . . . . . .
19
S5
∆L (a) and ∆H (b) of the donor molecules. . . . . . . . . . . . . . . . . . . . . . . . . . .
21
S6
∆H versus ∆L of the donor molecules. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
S7
Correlations of the HOMO-LUMO gap and number of unsaturated atoms in the main conD ) versus ∆ and ∆ of the donor molecules. . . . . . . . . . . . . . . . jugation path (Natom H L
S8
Correlation between experimental absorption coefficients (ε) and oscillator strengths ( fosc ) of the main electronic transition for 82 donor molecules. . . . . . . . . . . . . . . . . . .
S9
23
24
Correlations of experimental absorption coefficients (ε) and calculated oscillator strengths ( fosc ) of the main electronic transition versus ∆H and ∆L of 82 donor molecules. . . . . . .
25
S10 Chemical structures of donor molecules chosen for electronic coupling calculations. . . . .
26
S11 Correlations of JSC and VOC versus ∆H and ∆L of donor molecules. . . . . . . . . . . . . .
29
S12 Theoretically predicted versus experimental PCE for the testing set (30 molecules) (a) and all data points using the leave-one-out cross-validation technique (b) for the LR model. Inset shows probability density of prediction errors. . . . . . . . . . . . . . . . . . . . . . 2
31
S13 Theoretically predicted versus experimental PCE for the testing set (30 molecules) (a) and all data points using the leave-one-out cross-validation technique (b) for the k-NN model. Inset shows probability density of prediction errors. . . . . . . . . . . . . . . . . . . . . .
31
S14 Theoretically predicted versus experimental PCE for the testing set (30 molecules) (a) and all data points using the leave-one-out cross-validation technique (b) for the ANN model. Inset shows probability density of prediction errors. . . . . . . . . . . . . . . . . . . . . .
32
S15 Theoretically predicted versus experimental PCE for the testing set (30 molecules) (a) and all data points using the leave-one-out cross-validation technique (b) for the RF model. Inset shows probability density of prediction errors. . . . . . . . . . . . . . . . . . . . . .
3
32
List of Tables S1
D , E and E represent Experimentally estimated VOC , JSC , FF and PCE of SM-OPVs. Natom H L
the number of unsaturated atoms in the main conjugation path, energy of highest occupied molecular orbital (HOMO) and energy of lowest unoccupied molecular orbital (LUMO) of donor molecules. ∆H (∆L ) is the energetic difference between HOMO and HOMO-1 (LUMO+1 and LUMO) orbitals. EH and EL of PC71 BM (PC61 BM) are -6.69 (-6.90) and -2.54 (-2.60) eV, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S2
Division of the dataset to 8 groups of each having a specific range of PCE. Npoints represents the number data points in a group. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
S3
5
20
Electronic coupling values for hole transport (t H→H /t effHT ) and exciton dissociation (t L→L /t effED ) rates between two adjacent molecules in dimer and donor-PC71 BM interface, respectively. Chemical structures of donor molecules i, ii, iii and iv are shown in Figure S9. Electronic coupling calculated using M06-2X and B3LYP/PBE0 functionals are outside and inside the parentheses. Coupling values are in meV. . . . . . . . . . . . . . . . . . . . . . . . . . .
S4
28
Performance of models obtained by 10-fold cross-validation over 250 data points using different ML algorithms. MAPE, RMSE, r and Pout represent mean absolute percentage error, root mean square error, Pearson’s correlation coefficient and percentage of number points outside a cutoff value, respectively. Values outside and inside parentheses are obtained for the stratified sampling and convenience (raw data)/random (shuffling of the raw data) sampling methods, respectively. Hyperparameters of each model are optimized separately to get the optimum results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
30
D , E and E represent the number of unsaturated Table S1 Experimentally estimated VOC , JSC , FF and PCE of SM-OPVs. Natom H L
atoms in the main conjugation path, energy of highest occupied molecular orbital (HOMO) and energy of lowest unoccupied molecular orbital (LUMO) of donor molecules. ∆H (∆L ) is the energetic difference between HOMO and HOMO-1 (LUMO+1 and LUMO) orbitals. EH and EL of PC71 BM (PC61 BM) are -6.69 (-6.90) and -2.54 (-2.60) eV, respectively. S No.
Acceptor
VOC (V)
JSC (mA/cm2 )
FF
PCE (%)
D Natom
EH
EL
∆H (eV)
∆L (eV)
1
PC71 BM
0.89
15.70
0.72
9.84
130
-5.94
-2.39
0.22
0.01
[1]
2
PC71 BM
0.93
14.10
0.75
9.54
68
-6.20
-2.05
0.33
0.06
[2]
3
PC71 BM
0.92
15.45
0.683
9.45
130
-6.02
-2.40
0.17
0.01
[1]
4
PC71 BM
0.89
14.21
0.76
9.36
68
-6.12
-2.01
0.39
0.05
[3]
5
PC71 BM
0.97
13.45
0.71
9.01
68
-6.23
-2.07
0.34
0.07
[4]
6
PC61 BM
0.80
16.82
0.68
9.00
86
-5.83
-2.44
0.33
0.50
[5]
7
PC71 BM
0.87
14.30
0.72
8.95
99
-5.83
-2.11
0.13
0.06
[6]
8
PC71 BM
0.89
13.39
0.75
8.91
99
-5.84
-2.10
0.14
0.07
[7]
9
PC71 BM
0.89
13.60
0.74
8.90
68
-6.10
-2.02
0.37
0.05
[8]
10
PC71 BM
0.84
14.62
0.74
8.85
99
-5.77
-2.05
0.17
0.01
[9]
11
PC71 BM
0.89
13.06
0.75
8.54
64
-5.89
-2.07
0.40
0.05
[10]
12
PC71 BM
0.91
12.93
0.71
8.50
74
-6.12
-2.03
0.37
0.06
[11]
13
PC71 BM
0.91
13.85
0.70
8.46
44
-6.30
-2.32
0.52
0.33
[12]
14
PC71 BM
0.89
12.25
0.76
8.27
64
-5.89
-2.07
0.40
0.05
[7]
15
PC71 BM
0.87
13.40
0.72
8.24
64
-5.87
-2.10
0.40
0.06
[10]
16
PC71 BM
0.89
12.60
0.73
8.23
90
-6.02
-1.97
0.24
0.03
[13]
17
PC71 BM
0.82
14.30
0.70
8.13
82
-5.89
-2.46
0.54
0.21
[14]
18
PC61 BM
0.78
16.76
0.62
8.04
78
-5.78
-2.40
0.37
0.51
[15]
19
PC71 BM
0.94
12.17
0.70
8.02
68
-6.12
-2.01
0.39
0.05
[16]
20
PC71 BM
0.90
12.48
0.72
8.02
90
-6.02
-1.97
0.24
0.03
[17]
21
PC71 BM
0.90
13.33
0.67
8.02
60
-6.17
-2.35
0.38
0.17
[18]
22
PC71 BM
0.82
14.19
0.69
7.95
102
-5.74
-2.27
0.27
0.27
[19]
23
PC71 BM
0.88
14.07
0.66
7.91
62
-6.30
-2.26
0.45
0.03
[20]
24
PC71 BM
0.90
12.20
0.70
7.85
74
-6.21
-2.05
0.32
0.07
[11]
25
PC71 BM
0.98
12.23
0.66
7.83
52
-5.94
-2.10
0.25
0.25
[21]
26
PC71 BM
0.86
12.31
0.74
7.83
58
-6.17
-2.03
0.35
0.05
[22]
27
PC71 BM
0.97
11.48
0.70
7.81
84
-6.12
-2.20
0.17
0.29
[23]
Page 5 of 46
Ref.
28
PC71 BM
0.91
13.84
0.63
7.81
72
-6.05
-2.69
0.49
0.45
[24]
29
PC71 BM
0.92
12.95
0.65
7.80
68
-6.12
-2.01
0.39
0.05
[25]
30
PC71 BM
0.95
11.86
0.70
7.79
64
-6.12
-2.04
0.49
0.06
[26]
31
PC71 BM
0.93
11.42
0.7279
7.75
72
-6.69
-2.54
0.22
0.04
[27]
32
PC61 BM
0.78
13.71
0.73
7.74
80
-5.86
-2.19
0.28
0.05
[28]
33
PC71 BM
0.92
11.73
0.71
7.72
78
-6.12
-2.01
0.39
0.05
[25]
34
PC71 BM
0.94
12.40
0.66
7.70
70
-6.14
-2.16
0.41
0.24
[29]
35
PC71 BM
0.81
13.77
0.68
7.62
69
-6.09
-2.28
0.39
0.01
[30]
36
PC71 BM
0.90
13.12
0.66
7.61
54
-6.18
-2.30
0.57
0.24
[18]
37
PC71 BM
0.93
13.1
0.654
7.6
74
-6.69
-2.54
0.37
0.03
[31]
38
PC71 BM
0.90
14.51
0.582
7.55
59
-6.26
-2.27
0.52
0.04
[32]
39
PC71 BM
0.94
12.10
0.68
7.55
44
-6.34
-2.18
0.52
0.30
[12]
40
PC71 BM
0.80
14.93
0.64
7.47
74
-5.77
-2.32
0.56
0.37
[14]
41
PC71 BM
0.91
11.90
0.69
7.44
54
-6.44
-2.39
0.84
0.05
[33]
42
PC71 BM
1.04
12.06
0.6
7.37
64
-6.69
-2.54
0.33
0.01
[34]
43
PC71 BM
0.76
14.83
0.65
7.35
62
-6.04
-2.20
0.54
0.14
[35]
44
PC61 BM
0.73
13.60
0.73
7.30
86
-5.87
-2.30
0.17
0.14
[36]
45
PC71 BM
0.99
11.98
0.62
7.24
46
-6.69
-2.54
0.37
1.44
[37]
46
PC71 BM
0.93
11.75
0.68
7.21
68
-6.12
-2.01
0.39
0.05
[38]
47
PC71 BM
0.77
15.3
0.64
7.21
78
-6.69
-2.54
0.17
0.29
[39]
48
PC61 BM
0.84
12.27
0.70
7.20
80
-6.04
-2.26
0.18
0.06
[28]
49
PC71 BM
0.92
12.12
0.64
7.18
58
-6.19
-2.04
0.35
0.05
[25]
50
PC71 BM
0.85
12.36
0.69
7.14
32
-6.69
-2.54
0.48
0.71
[40]
51
PC71 BM
0.94
10.64
0.72
7.12
70
-6.19
-1.94
0.32
0.04
[41]
52
PC71 BM
0.93
11.03
0.70
6.97
56
-6.12
-2.02
0.36
0.05
[42]
53
PC71 BM
0.90
10.98
0.70
6.89
112
-6.02
-1.98
0.18
0.01
[43]
54
PC71 BM
0.88
10.71
0.72
6.86
110
-5.91
-2.32
0.07
0.25
[44]
55
PC71 BM
0.86
11.56
0.69
6.86
48
-6.04
-2.14
0.46
0.29
[45]
56
PC71 BM
0.87
11.78
0.67
6.84
99
-5.84
-2.13
0.14
0.09
[6]
57
PC71 BM
0.93
13.61
0.54
6.83
64
-6.01
-2.37
0.15
0.01
[46]
58
PC61 BM
0.71
16.00
0.64
6.83
80
-5.70
-2.37
0.43
0.50
[47]
59
PC71 BM
0.92
11.05
0.66
6.75
66
-6.13
-2.02
0.56
0.12
[48]
Page 6 of 46
60
PC71 BM
0.89
10.50
0.72
6.73
46
-6.42
-2.26
0.66
0.03
[33]
61
PC71 BM
0.9
12.43
0.629
6.71
52
-6.43
-2.32
0.54
0.11
[49]
62
PC71 BM
0.78
14.40
0.59
6.70
48
-6.05
-2.33
0.40
0.36
[50]
63
PC71 BM
0.79
12.88
0.66
6.68
64
-5.91
-1.99
0.56
0.04
[51]
64
PC71 BM
0.89
10.90
0.69
6.67
134
-5.83
-2.12
0.08
0.04
[7]
65
PC71 BM
0.90
11.54
0.66
6.67
34
-6.27
-2.23
0.81
0.72
[52]
66
PC71 BM
0.85
13.38
0.59
6.59
76
-5.85
-2.48
0.56
0.50
[24]
67
PC71 BM
0.77
12.74
0.68
6.59
52
-6.01
-1.93
0.38
0.05
[53]
68
PC71 BM
0.78
13.42
0.62
6.59
48
-5.97
-2.10
0.54
0.27
[45]
69
PC71 BM
0.80
14.12
0.61
6.52
50
-5.85
-2.05
0.33
0.23
[54]
70
PC71 BM
0.94
10.65
0.651
6.49
84
-6.05
-1.83
0.28
0.09
[55]
71
PC71 BM
0.84
11.94
0.65
6.47
49
-5.93
-2.01
0.61
0.14
[56]
72
PC71 BM
0.91
11.00
0.64
6.40
54
-5.91
-1.99
0.47
0.12
[57]
73
PC71 BM
0.95
12.40
0.55
6.40
70
-5.79
-2.06
0.41
0.09
[58]
74
PC71 BM
0.96
11.87
0.56
6.38
58
-6.24
-2.06
0.32
0.07
[59]
75
PC61 BM
0.91
10.78
0.65
6.38
58
-6.19
-2.04
0.35
0.05
[60]
76
PC71 BM
0.86
10.80
0.68
6.37
64
-6.22
-2.26
0.43
0.02
[20]
77
PC61 BM
0.71
15.60
0.58
6.30
86
-5.81
-2.23
0.24
0.08
[36]
78
PC71 BM
0.90
10.50
0.67
6.30
62
-5.87
-1.76
0.48
0.25
[61]
79
PC71 BM
0.88
10.30
0.70
6.30
72
-5.93
-1.74
0.30
0.33
[62]
80
PC61 BM
0.75
12.90
0.65
6.30
67
-5.89
-2.32
0.32
0.21
[63]
81
PC71 BM
0.943
11.08
0.62
6.28
54
-6.14
-2.31
0.55
0.32
[64]
82
PC71 BM
0.78
13.18
0.61
6.27
79
-6.69
-2.54
0.11
0.05
[65]
83
PC71 BM
0.90
11.03
0.66
6.26
68
-6.06
-2.01
0.41
0.05
[38]
84
PC71 BM
0.79
14.21
0.56
6.23
74
-6.22
-2.44
0.41
0.03
[66]
85
PC71 BM
0.73
14.90
0.57
6.20
48
-5.88
-2.05
0.63
0.25
[67]
86
PC71 BM
0.92
9.80
0.69
6.20
62
-5.93
-1.71
0.47
0.34
[29]
87
PC71 BM
1.01
14.36
0.427
6.17
49
-6.69
-2.54
0.48
0.10
[68]
88
PC71 BM
0.85
10.79
0.67
6.15
52
-6.13
-2.07
0.46
0.05
[69]
89
PC71 BM
0.92
11.45
0.58
6.11
54
-6.34
-2.29
0.52
0.09
[30]
90
PC71 BM
0.99
11.18
0.56
6.11
52
-6.69
-2.54
0.43
0.02
[34]
91
PC61 BM
0.92
13.98
0.47
6.10
51
-6.09
-2.01
0.46
0.06
[70]
Page 7 of 46
92
PC61 BM
0.76
13.50
0.59
6.10
67
-5.96
-2.32
0.27
0.19
[63]
93
PC71 BM
0.89
10.68
0.65
6.07
26
-6.69
-2.54
0.62
1.60
[40]
94
PC71 BM
0.88
11.42
0.61
6.05
52
-5.74
-1.72
0.12
0.27
[71]
95
PC71 BM
1.03
9.5
0.616
6.04
64
-6.20
-1.85
0.48
0.21
[55]
96
PC71 BM
0.97
12.54
0.508
6.02
44
-6.69
-2.54
0.88
0.33
[72]
97
PC71 BM
0.90
10.00
0.69
6.00
42
-6.39
-2.29
0.76
0.15
[73]
98
PC71 BM
0.78
13.92
0.55
6.00
62
-5.87
-1.91
0.39
0.49
[74]
99
PC71 BM
0.82
11.13
0.66
5.98
55
-5.57
-1.92
0.71
0.18
[75]
100
PC71 BM
0.92
11.28
0.60
5.94
41
-6.65
-2.90
0.87
0.24
[76]
101
PC61 BM
0.80
12.17
0.62
5.93
72
-5.96
-2.05
0.21
0.22
[77]
102
PC71 BM
0.96
12.00
0.53
5.89
60
-5.78
-2.02
0.52
0.09
[58]
103
PC71 BM
0.66
15.35
0.58
5.88
66
-5.93
-1.94
0.08
0.11
[78]
104
PC71 BM
0.69
13.60
0.64
5.87
74
-6.04
-2.20
0.21
0.17
[79]
105
PC61 BM
0.80
11.51
0.64
5.84
52
-6.08
-2.01
0.53
0.08
[80]
106
PC61 BM
0.71
13.60
0.60
5.80
67
-5.88
-2.27
0.30
0.17
[63]
107
PC61 BM
0.75
12.60
0.62
5.80
86
-5.92
-2.44
0.16
0.22
[63]
108
PC61 BM
0.84
11.97
0.58
5.79
62
-5.96
-2.04
0.21
0.21
[81]
109
PC71 BM
0.85
10.48
0.66
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PC61 BM
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12.60
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5.70
67
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0.28
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PC71 BM
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10.44
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PC71 BM
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PC71 BM
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PC71 BM
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PC71 BM
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15.43
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PC71 BM
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0.69
5.60
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0.15
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PC71 BM
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0.09
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PC61 BM
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11.40
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0.86
10.40
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PC61 BM
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12.70
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PC71 BM
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PC71 BM
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PC71 BM
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10.50
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PC71 BM
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PC71 BM
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11.86
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PC71 BM
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0.555
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0.25
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PC71 BM
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PC71 BM
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PC71 BM
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12.98
0.49
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0.07
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PC71 BM
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10.90
0.61
5.03
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13.39
0.56
5.03
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0.16
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PC61 BM
0.70
11.50
0.63
5.03
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0.04
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8.27
0.69
4.99
64
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PC71 BM
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10.93
0.57
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PC71 BM
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0.61
4.97
55
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0.18
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PC71 BM
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10.82
0.56
4.96
38
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1.45
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PC61 BM
0.80
8.56
0.72
4.93
59
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0.06
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PC61 BM
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10.81
0.56
4.92
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0.20
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PC71 BM
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0.53
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32
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1.38
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14
0.34
4.86
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0.74
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PC61 BM
1.08
14.00
0.32
4.84
51
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PC71 BM
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10.51
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0.56
4.80
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PC61 BM
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11.88
0.50
4.78
80
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0.47
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PC71 BM
0.98
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0.56
4.76
22
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0.00
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PC71 BM
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10.52
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13.60
0.48
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11.2
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PC61 BM
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0.60
4.70
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PC71 BM
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7.44
0.69
4.68
68
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0.31
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PC71 BM
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0.63
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28
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1.45
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PC71 BM
0.92
11.21
0.44
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34
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1.84
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PC71 BM
0.97
10.32
0.46
4.65
56
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PC71 BM
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10.63
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4.65
32
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PC71 BM
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11.90
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10.25
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12.60
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0.71
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10.20
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0.73
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PC61 BM
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0.51
4.46
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0.08
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4.43
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0.53
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PC71 BM
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13.10
0.52
4.40
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1.27
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PC61 BM
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11.70
0.50
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PC71 BM
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10.24
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10.08
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0.66
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11.17
0.56
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1.02
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10.83
0.51
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0.03
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PC71 BM
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10.76
0.44
4.24
35
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1.19
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PC71 BM
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0.42
4.22
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0.26
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0.58
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PC71 BM
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10.11
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6.30
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[122]
250
PC71 BM
0.93
8.19
0.461
3.51
52
-5.85
-1.76
0.16
0.27
[164]
251
PC71 BM
0.89
8.80
0.45
3.50
60
-6.04
-2.04
0.48
0.25
[168]
Page 12 of 46
252
PC71 BM
0.90
7.91
0.49
3.45
32
-6.13
-1.72
1.00
1.32
[169]
253
PC61 BM
0.98
10.06
0.49
3.40
37
-6.87
-2.36
0.58
0.11
[170]
254
PC61 BM
0.92
8.77
0.42
3.40
47
-5.90
-1.73
0.10
0.99
[123]
255
PC71 BM
0.91
7.01
0.57
3.34
54
-6.15
-1.97
0.41
0.06
[117]
256
PC71 BM
0.87
7.21
0.53
3.30
56
-5.93
-2.04
0.50
0.04
[51]
257
PC61 BM
0.88
7.02
0.53
3.27
37
-6.34
-2.06
0.75
0.22
[159]
258
PC71 BM
0.78
10.18
0.49
3.26
61
-6.15
-1.83
0.48
0.24
[171]
259
PC71 BM
0.83
8.13
0.48
3.24
58
-6.12
-1.98
0.40
0.31
[172]
260
PC61 BM
0.83
8.20
0.65
3.23
43
-6.24
-2.32
0.84
0.13
[146]
261
PC71 BM
0.80
8.37
0.51
3.20
68
-5.85
-1.86
0.33
0.66
[135]
262
PC71 BM
0.96
8.52
0.39
3.19
62
-6.69
-2.54
0.27
0.26
[151]
263
PC61 BM
0.91
6.84
0.52
3.14
54
-6.15
-1.97
0.41
0.06
[117]
264
PC71 BM
0.66
8.23
0.56
3.09
74
-5.86
-2.03
0.18
0.19
[88]
265
PC61 BM
0.78
7.10
0.55
3.07
71
-5.96
-2.06
0.27
0.17
[159]
266
PC71 BM
0.90
7.34
0.46
3.04
32
-6.06
-1.69
1.63
1.72
[173]
267
PC61 BM
0.36
15.00
0.50
2.70
22
-5.70
-1.73
1.51
1.66
[174]
268
PC61 BM
0.94
8.24
0.34
2.59
25
-6.45
-1.87
1.46
0.74
[175]
269
PC71 BM
0.84
8
0.38
2.56
66
-6.69
-2.54
0.19
0.22
[176]
270
PC71 BM
0.87
5.96
0.49
2.52
50
-6.69
-2.54
0.23
0.27
[176]
271
PC61 BM
0.79
6.10
0.49
2.50
42
-5.70
-1.89
1.81
0.00
[177]
272
PC61 BM
0.58
7.00
0.57
2.30
18
-6.01
-1.36
1.66
1.76
[178]
273
PC61 BM
0.97
3.36
0.57
2.10
30
-6.20
-1.93
2.18
0.00
[179]
274
PC61 BM
0.76
6.30
0.38
1.76
40
-6.24
-2.05
0.37
1.47
[180]
275
PC61 BM
0.76
6.30
0.36
1.74
20
-6.36
-2.04
1.42
2.07
[181]
276
PC61 BM
0.90
5.30
0.32
1.54
25
-6.55
-1.94
1.42
0.75
[181]
277
PC61 BM
0.75
4.14
0.44
1.34
33
-5.77
-1.79
0.89
1.97
[182]
278
PC61 BM
0.80
4.43
0.34
1.17
25
-5.90
-1.67
1.16
1.99
[182]
279
PC61 BM
0.84
2.96
0.40
1.00
24
-5.76
-1.68
1.41
1.90
[183]
280
PC61 BM
0.47
1.90
0.52
0.50
26
-5.66
-2.11
1.57
2.02
[184]
Page 13 of 46
2.5 r = 0.87
ECT
2.4
2.3
2.2 3.3
3.4
3.5
DA HL
3.6
3.7
3.8
E
Figure S1 Correlations between the energy of charge transfer state (ECT ) and the energetic difference of HOMO of donor and DA ) at the donor-acceptor interface. LUMO of acceptor (EHL
7.5
r = 0.97
IP (eV)
7.0
6.5
6.0 5.5
6.0
6.5 -EHOMO (eV)
7.0
Figure S2 Correlation between vertical IP(v) and energy of HOMO (EHOMO ) of donor molecules.
Page 14 of 46
1.6
r = 0.99
0.8 0.4 0
b
1.6
∆L (eV)
1.2
∆H (eV)
2
a
r = 0.99
1.2 0.8 0.4
0
0.4
0.8
1.2
0
1.6
0
0.4 0.8 1.2 1.6
∆H (eV) 6.8
c r = 0.75
700
2.4
∆L (eV)
IP (eV)
Eg (nm)
800
2
600 500
d r = 0.95
6.3 5.8 5.3
400 400
450
500
550
600
650
Eg (nm)
4.8
6
6.3
6.6
6.9
7.2
IP (eV)
Figure S3 ∆H (a), ∆L (b), Eg (c) and IP(v) (d) calculated by the M06-2X versus B3LYP functionals using the ground state
geometries obtained at the M06-2X/6-31G(d) level.
Page 15 of 46
ML techniques and optimization of their hyperparameters We have used k-Nearest Neighbors (k-NN), linear regression (LR), artificial neural networks (ANN), random forest (RF) and gradient boosting regression tree (GB) techniques to build models. To find best hyperparameters of each model, 10-fold cross-validation was employed to evaluate the performance of each parameter combination on 250 data points (training and validating sets). The predictive power of each model is estimated over testing set (30 data points, unseen data completely different from the training and validating sets) by mean absolute percentage error (MAPE) = s root mean square error (RMSE) =
100 N |Pk − Ak | ∑ Ak , N k=1
2 ∑N k=1 (Ak − Pk ) , N
× (Pk − Pk ) ∑N k=1 (Ak − Ak )q Pearson’s correlation coefficient (r) = q 2 2 ∑N ∑N k=1 (Ak − Ak ) × k=1 (Pk − Pk )
(1)
(2) (3)
and the percentage of number points outside a cutoff value (Pout ). Here, Ak and Pk are actual and predicted values, respectively, and Ak /Pk represents the average value of them. A brief description of each ML approach is described below. k-Nearest Neighbors for regression (k-NN): k-NN is a simple non-parametric machine learning algorithm, which involves only in storing the training dataset. It considers k training examples in the feature space closest in distance to the new data point. The prediction is then simply the average of the relevant neighbors. This algorithm is sensitive to the local structure of the data, so we transforms features by scaling each feature so that it is in the given range on the training set, i.e. between zero and one. Optimum performance is achieved for k=3 and weights proportional to the inverse of the distance from the new point. Linear regression (LR): LR is the simplest technique to build models. In this approach, a linear function of the input descriptors is used for prediction. Given a set of descriptors (x[i]s) and a target y, the general equation can be expressed Page 16 of 46
as, yˆ = w[0] × x[0] + . . . + w[p] × x[p] + b,
(4)
where w and b are parameters of the model learned by minimizing the mean squared error between predictions and targets for the training set. Artificial neural networks (ANN): ANN is a nonlinear machine learning technique where the complex relationships between inputs and outputs can be modeled. In this approach, the input and output layers are connected by single or multiple hidden layers, and each layer consists of a set of elements called neurons. Unlike the LR approach, the process of computing weighted linear summation (equation 4) is carried out multiple times. At the beginning, neurons of the first hidden layer is computed as weighted sum of input descriptors, and then results are used as input for the next hidden layer. A non linear function is applied to the results of each computed hidden unit, h[i] = f unc(w[0, i] × x[0] + w[1, i] × x[1] + . . . + w[p, i] × x[p])
(5)
Finally, the output results are obtained as weighted sums of the last hidden layer, yˆ = v[0] × h[0] + . . . + v[n] × h[n].
(6)
The complexity of an ANN model can be tuned by a number of hyperparameters such as the number of hidden neurons, layers, iterations and the regularizations. This approach is also sensitive to descriptor scaling, which means that all input descriptors should vary in a similar way, and it is necessary to rescale input data before building a model. In this work, ANN is trained using the limited-memory BFGS (L-BFGS) algorithm in combination with the rectified linear unit (relu) as activation function. All other hyperparameters are optimized to get the best result. Random forest (RF): RF is an ensemble of decision trees, where trees are constructed randomly to ensure that each one is different from others. Randomness in building trees is introduced by bootstrapping of the provided dataset Page 17 of 46
and selecting a subset of the descriptors. For each tree, the value of a target variable is predicted by a hierarchy of if/else questions, and the output of the RF model is the mean prediction of the individual trees. Important hyperparameters to train a RF model are number of trees in the forest, maximum number of descriptors, maximum depth of a tree and minimum number of samples required to be at a leaf node. In this work, the mean squared error is used to measure the quality of a split and max descriptors is equal to log2(Ndescriptors ), where Ndescriptors is the total number of descriptors. Other hyperparameters are optimized to achieve optimum outcomes. Gradient boosting regression tree (GB): GB is also an ensemble of decision trees, where the model is built by constructing trees in a forward stage-wise fashion, rectifying the mistakes of the previous one in each stage. Compared to the RF, there is one more important hyperparameters to tune, i.e., the learning rate, which determine the ability to correct the mistakes of a tree from the previous one. In this work, the mean squared error with improvement score by Friedman is used to measure the quality of a split and max descriptors = log2(Ndescriptors ). Other hyperparameters are optimized until we found the best results.
Page 18 of 46
b
a 30
1.2
30
25
1
25
20
0.8
15
0.6
10
0.4
5
0.2
8
6
20
5
4
15
3
10 2
5
1
0
0
5
10
15
20
25
5
30
10
15
20
25
30
Indextesting set
Indextesting set
d
c
0.45
30
∆PCE
Indextraning set
Tanimoto distance
Indextraning set
7
7
30
0.4
0.25
15
0.2 0.15
10
0.1
5
0.05
5
20 4
15 3
10
2
5
1
0
5
10
15
20
25
∆PCE
0.3
20
25
Indextraning set
Indextraning set
0.35
Euclidean distance
6
25
0
30
5
Indextesting set
10
15
20
25
30
Indextesting set
Figure S4 Tanimoto (a) and Euclidean (c) distances of the chemical fingerprints and the normalized features for 30 closet data
points to each sample in the testing set, respectively. The differences of PCE (∆PCE ) of testing samples with respect to the corresponding 30 closest training data points are shown in (b, Tanimoto distance) and (d, Euclidean distance). Indextesting set and Indextraining set are indexes of donor molecules in training and testing sets, respectively. Tanimoto distances are calculated by using the default set of parameters for generating fingerprints as implemented in RDKit package. [185]
Page 19 of 46
Table S2 Division of the dataset to 8 groups of each having a specific range of PCE. Npoints represents the number data points in a group. 1
2
3
4
5
6
7
8
PCE
≤3%
3-4%
4-5%
5-6%
6-7%
7-8%
8-9%
> 9.0
Npoints
14
33
73
64
45
30
16
5
Page 20 of 46
a
∆L (eV)
2.0 1.5 1.0 0.5
∆H (eV)
0.0 2.0
b
1.5 1.0 0.5 0.0 1
50
100
150
200
Index of donor molecules Figure S5 ∆L (a) and ∆H (b) of the donor molecules.
Page 21 of 46
250
2.0
r = 0.43
∆L (eV)
1.5 1.0 0.5 0.0 0.0
0.5
1.0
∆H (eV) Figure S6 ∆H versus ∆L of the donor molecules.
Page 22 of 46
1.5
2.0
ELUMO−EHOMO
a
b
4.6 4.2 3.8 3.4 3.0 140
r = 0.26
c
d r = −0.61
115
NDatom
r = 0.14
r = −0.53
90 65 40 15 0.0
0.5
1.0
1.5
2.0 0.0
∆H (eV)
0.5
1.0
1.5
2.0
∆L (eV)
D ) versus Figure S7 Correlations of the HOMO-LUMO gap and number of unsaturated atoms in the main conjugation path (Natom
∆H and ∆L of the donor molecules.
Page 23 of 46
r = 0.42
-1
ε × 10 (M cm )
1.3
-5
-1
1
0.7
0.4
0.1
0
1
2
3
4
5
6
fosc Figure S8 Correlation between experimental absorption coefficients (ε) and oscillator strengths ( fosc ) of the main electronic
transition for 82 donor molecules.
Page 24 of 46
6
a
b
5
fosc
4
r = −0.30
r = −0.70
3 2 1
ε × 10−5 (M−1 cm−1)
0
c
d
1.3 1
r = −0.22
r = −0.40
0.7 0.4 0.1 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
∆H (eV)
∆L (eV)
Figure S9 Correlations of experimental absorption coefficients (ε) and calculated oscillator strengths ( fosc ) of the main
electronic transition versus ∆H and ∆L of 82 donor molecules.
Page 25 of 46
O
i
S
N
H3C
S
O
S
S
S
S
S
S
N
S H3C
CH3
CH3
CH3
H3C
N
N N
N
N
ii
H3C
S
H3C
F
CH3
F
N
S
S S
S
S
S N
F
S
S
iii
N
S
S F
F
S
S
CH3
O
S S
O S
H3CO
F
O
N
OCH3 O S
OCH3
H3C
H3C
N
S
F
iv
N
N
OCH3
O H3CO
O
S
N
S
O
CH3
H3C
F
OCH3
O
S
S S
S
S
N
S H3C
CH3
S S
CH3
S
H3C
CH3
CH3 S
Figure S10 Chemical structures of donor molecules chosen for electronic coupling calculations.
Page 26 of 46
Electronic coupling calculations Molecular structures of selected donor molecules for the electronic coupling calculation are shown in Figure S9. Dimer of donor molecules and donor-PC71 BM complex structures were optimized at the M06-2X/631G(d) level. The details of the coupling calculations are described below. Calculation of t H→H /t L→L : The transfer integral can be obtained by the following equation, KS Vij = hφi |FKS |φ j i = ∑ ci,µ c j,ν Fµν ,
(7)
µν
where φi and φ j are HOMO (LUMO) of isolated molecules i and j, respectively, and ci,µ and c j,ν are the coefficients for atomic basis functions µ on molecule i and ν on molecule j. The Kohn-Sham Fock matrix (FKS ) for the total system can be evaluated as FKS = SCεC−1 ,
(8)
where S is the intermolecular overlap matrix, and C and ε are the molecular orbital coefficients and eigenvalues of the total system, respectively. Spacial overlap is calculated as Oi j = ∑ ci,µ c j,ν Sµν .
(9)
µν
The two-by-two matrices H and O are calculated using equations equations 7 and 9, respectively, where H=
Vii Vij Vji Vjj
and O=
Oii Oij Oji Ojj
.
Electronic coupling values are off-diagonal terms of the O−1/2 HO−1/2 .
Page 27 of 46
Calculation of the effective electronic coupling (t effHT /t effED ): When ∆H /∆L is small, it is essential to consider an adequate description for the initial/final state of interacting molecules as orbitals other than HOMO/LUMO of individual molecules may also contribute to the HOMO/LUMO of the total system. To calculate the effective coupling, a similar method is applied as reported by Br´edas and coworkers. [186] The HOMO (LUMO) of the total system can be written as a combination of orbitals localized on two interacting molecules, |ΨDimer H/L i = ∑ ck ψk k
(10)
= ∑ ci,µ ψi,µ + ∑ c j,ν ψ j,ν µ
ν
= |Ψi i + |Ψ j i, where ci,µ and c j,ν are the coefficients for atomic basis functions µ on molecule i and ν on molecule j. Ψi and Ψ j , localized on two individual molecules i and j are more appropriate description of the initial and final states, which are determined by the electronic Hamiltonian of the total system. Now, the effective transfer integral can be obtained by the following equation, ef f
Vij
= hΨi |FKS |Ψ j i.
(11)
Similar to t H→H /t L→L , a standard symmetric orthogonalization process is applied to obtain t effHT /t effED . Table S3 Electronic coupling values for hole transport (t H→H /t effHT ) and exciton dissociation (t L→L /t effED ) rates between two adjacent molecules in dimer and donor-PC71 BM interface, respectively. Chemical structures of donor molecules i, ii, iii and iv are shown in Figure S9. Electronic coupling calculated using M06-2X and B3LYP/PBE0 functionals are outside and inside the parentheses. Coupling values are in meV. coupling
i
ii
iii
iv
t H→H
57.10 (-53.63/-51.87)
-39.53 (-34.62/-33.69)
64.48 (55.95/54.72)
-19.84 (-9.61/-10.86)
t effHT
151.83 (138.69/146.28)
145.52 (125.91/130.73)
253.63 (221.477/229.78)
248.96 (225.37/232.59)
t L→L
11.16 (10.10/9.96)
8.70 (10.67/10.11)
t effED
255.34 (170.47/203.61)
41.83 (10.07/28.88)
Page 28 of 46
b
VOC (V)
JSC (mA/cm2)
18 a 15 12 9 6 3 0 c 1.1
r = −0.38
r = −0.23
d
0.9 0.7 0.5 0.3 0.0
r = −0.06
0.5
1.0
r = −0.19
1.5
2.0 0.0
0.5
∆H (eV)
1.0
1.5
∆L (eV)
Figure S11 Correlations of JSC and VOC versus ∆H and ∆L of donor molecules.
Page 29 of 46
2.0
Table S4 Performance of models obtained by 10-fold cross-validation over 250 data points using different ML algorithms. MAPE, RMSE, r and Pout represent mean absolute percentage error, root mean square error, Pearson’s correlation coefficient and percentage of number points outside a cutoff value, respectively. Values outside and inside parentheses are obtained for the stratified sampling and convenience (raw data)/random (shuffling of the raw data) sampling methods, respectively. Hyperparameters of each model are optimized separately to get the optimum results. ML techniques
MAPE (%)
RMSE (%)
r
Pout in % (± 1.5/± 2.5)
LR
22.9 (27.6/23.5)
1.24 (1.34/1.25)
0.68 (0.51/0.63)
22.4/4.4
k-NN
20.2 (31.0/20.2)
1.19 (1.48/1.19)
0.72 (0.49/0.69)
18.8/5.6
ANN
20.1 (27.6/21.5)
1.13 (1.29/1.17)
0.74 (0.54/0.69)
20.8/1.6
RF
21.3 (29.6/21.6)
1.12 (1.31/1.13)
0.75 (0.54/0.71)
20.8/1.6
GB
19.3 (29.1/20.6)
1.06 (1.29/1.11)
0.77 (0.55/0.73)
17.6/1.2
Page 30 of 46
8
a
b
r = 0.66
r = 0.67
6 4
16 12 8 4 0 -3 -2 -1 0 1 2 3
Count (%)
PCE (%)
10
2 0
Error (%)
0
2
4
6
8
Predicted PCE (%)
10 0
2
4
6
8
Predicted PCE (%)
10
Figure S12 Theoretically predicted versus experimental PCE for the testing set (30 molecules) (a) and all data points using the
leave-one-out cross-validation technique (b) for the LR model. Inset shows probability density of prediction errors.
8
a
b
r = 0.71
r = 0.74
6 4
20 15 10 5 0-4 -3 -2 -1 0 1 2 3 4
Count (%)
PCE (%)
10
2 0
Error (%)
0
2
4
6
8
Predicted PCE (%)
10 0
2
4
6
8
Predicted PCE (%)
10
Figure S13 Theoretically predicted versus experimental PCE for the testing set (30 molecules) (a) and all data points using the
leave-one-out cross-validation technique (b) for the k-NN model. Inset shows probability density of prediction errors.
Page 31 of 46
8
a
b
r = 0.68
r = 0.73
6 4
Count (%)
PCE (%)
10
15 10 5 0-4 -3 -2 -1 0 1 2 3 4
2 0
Error (%)
0
2
4
6
8
Predicted PCE (%)
10 0
2
4
6
8
Predicted PCE (%)
10
Figure S14 Theoretically predicted versus experimental PCE for the testing set (30 molecules) (a) and all data points using the
leave-one-out cross-validation technique (b) for the ANN model. Inset shows probability density of prediction errors.
8
a
b
r = 0.78
r = 0.75
6 4
Count (%)
PCE (%)
10
16 12 8 4 0-4 -3 -2 -1 0 1 2 3 4
2 0
Error (%)
0
2
4
6
8
Predicted PCE (%)
10 0
2
4
6
8
Predicted PCE (%)
10
Figure S15 Theoretically predicted versus experimental PCE for the testing set (30 molecules) (a) and all data points using the
leave-one-out cross-validation technique (b) for the RF model. Inset shows probability density of prediction errors.
Page 32 of 46
How to use the python scripts (“script.py” and “predictnew.py”) The “script.py” can reproduce the data reported in Table 1 and S4. It will generate three files, namely “Testing 30.dat”, “k10-cv 250.dat” and “LOO-cv 280.dat” for the 30 data points (testing set), 250 data points (10-fold cross-validation) and all 280 data points (leave-one-out cross-validation), respectively. The PCE of new molecules can be estimated using “predictnew.py” from properties of D/A molecules calculated at the M06-2X/6-31G(d) level. Two comma separated values (csv) files are provided along with the scripts: • TandV.csv • Testing.csv “TandV.csv” and “Testing.csv” contain data for the training/validating and testing sets, respectively. To predict the PCE, properties D/A molecules are needed to feed in the “Testing.csv” file in the following order, each separated by a comma: 1. Serial number (In “TandV.csv” and “Testing.csv” files, the first column is the serial number of D/A systems as reported in Table S1.) 2. Experimentally estimated PCE (Keep it blank for new candidate materials) 3. Polarizability (Bohr3 ) 4. ∆A L (eV) 5. ∆L (eV) D 6. Natom
7. Eg (nm) 8. λh (eV) 9. IP(v) (eV) DA (eV) 10. EHL
11. ∆H (eV) Page 33 of 46
12. Ebind (eV) DA (eV) 13. ELL
14. ∆ge (Debye) 15. ET1 (eV) The user should install Python 3.6 and scikit-learn software package before running the script. The script and data files should be kept in the same folder. The “predictnew.py” will generate a file (“Predicted PCE.dat”) with the predicted PCE using various ML-models.
Page 34 of 46
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