Supporting information for: Systematic Improvement of Density ...
Supporting information for: Systematic Improvement of Density-Functionals Through Parameter-Free Hybridization Schemes Éric Brémond,∗,† Marika Savarese,† Ángel José Pérez-Jiménez,‡ Juan Carlos Sancho-García,‡ and Carlo Adamo∗,¶,§,† CompuNet, Istituto Italiano di Tecnologia, via Morego 30, I-16163 Genoa, Italy, Departamento de Química Física, Universidad de Alicante, E-03080 Alicante, Spain, Institut de Recherche de Chimie Paris, IRCP CNRS UMR-8247, École Nationale Supérieure de Chimie de Paris, Chimie ParisTech, 11 rue P. et M. Curie, F-75231 Paris Cedex 05, France, and Institut Universitaire de France, 103 Boulevard Saint Michel, F-75005 Paris, France E-mail: [email protected]; [email protected]
∗
To whom correspondence should be addressed Istituto Italiano di Tecnologia ‡ Universidad de Alicante ¶ Chimie ParisTech § Institut Universitaire de France †
S1
Atomization Energies 50 PURE HYB0 QIDH 34.52
40 35 30
6.66
BLY P
6.79
12.27
15.24 5.54 4.26
1 PW9
4.90
TPSS
9.39 6.90
12.78
PBE h
4.59 4.17
9.95
TCA
8.06 10.35 5.98
mol PBE
APB E
4.68
8.02 8.06
13.53
E revP B
6.41
8.64
9.04
PBE sol
0
5.55 4.32
10 5
17.13
18.50 14.66
20 15
21.00
25
PBE
Mean Absolute Deviation (kcal mol−1 )
45
Figure S1: Mean absolute deviations for the AE6 test set as function of the pure densityfunctionals hybridized according to the HYB0 and QIDH models. All the reactions are evaluated with the quadruple-ζ def2-QZVP basis set.
S2
0
S3 18.26
15.29
21.40
35
30
25 9.61 7.96
5.74
8.47
4.70 4.89 5.04
2.78 3.96
5.35 5.03 5.41
2.77 4.33
9.78
3.86 7.30 6.14
40
4.76 7.37 5.90
G2/55
8.38 2.95 4.72
0
7.53 3.11 4.36
6.57 9.52 6.88
19.80
40
6.93 10.75 7.87
5.58 4.30
6.63 7.77 6.25
4.09 4.29
13.92
5.90 6.00 6.74
6.30 4.86 6.12
4.54 7.32 6.79
3.51
8.37
G1/31
BLY P
1
PW9
TPSS
h
PBE
8.82
6.01 6.08 6.29
6.16 5.00 5.68
15
TCA
8.57 7.45 6.67
9.93
4.74 6.87 6.20
17.34
45
mol
5.29 5.69
10.76 7.02
6.85
3.16
7.44
9.34
45
PBE
E
5
APB
10
BE
45 41.43
20
revP
15
9.42
25 22.29
5 2.87 4.43
20
sol
20 8.23
25
PBE
5 3.00 4.12
10
17.39
Mean Absolute Deviation (kcal mol−1 ) 10
5.28 4.32
Mean Absolute Deviation (kcal mol−1 ) 15
PBE
Mean Absolute Deviation (kcal mol−1 )
50
PURE HYB0 QIDH
35
30
0
G2/148
40
35
30
Figure S2: Mean absolute deviations for the G1/31, G2/55 and G2/148 test sets as function of the pure density-functionals hybridized according to the HYB0 and QIDH models. All the reactions are evaluated with the triple-ζ 6-311+G(3df, 2pd ) basis set.
Noncovalent Binding Energies 6 PURE HYB0 QIDH 4.35
5 4.00
4.5
3.62
4
0.85
1.07
2.00 1.92 0.98
0.89
0.88
0.86
0.86
1.06
1.20
1.5
0.86
2
1
2.96 2.66
2.86 2.73
2.15 2.06
2.41 2.35 1.99 1.87
2.5
2.49 2.40
3
3.20
3.5
2.18 2.09
Mean Absolute Deviation (kcal mol−1 )
5.5
BLY P
1 PW9
TPSS
PBE h
TCA
mol PBE
APB E
E revP B
PBE sol
0
PBE
0.5
Figure S3: Mean absolute deviations for the S22/full test set as function of the pure densityfunctionals hybridized according to the HYB0 and QIDH models. All the reactions are evaluated with the triple-ζ cc-pVTZ basis set.
S4
0
S5 1.24
0.73
1.13
0.82
2.17 2.20
2.40 2.39
3.67
3.26 3.05
3.14 3.11
4.27 1.22
0.70
1.18
0.78
0.71
1.05
2.78 2.61
3.09 2.91
4.64
4.44 3.93
4.23 3.99
3.62 3.38
6.07
5.74
dispersion dominant
BLY P
1
PW9
TPSS
h
PBE
0.82
1.01
2.69 2.67
0.99
3.51 3.28
5
TCA
mol
6
PBE
0.97
2.64 2.61
6
E
1.63
5.11
1.24 0.73
1.03 0.89 1.13
1.13 0.96 0.62
0.92 0.85 1.00
1.94
1.17 1.04 1.69
1.12 0.96 0.61
1.05 0.89 0.67
0.54
1.93
2.73
2.40 1.97 1.72
6
APB
1.41
4.25 3.78
4
BE
5
revP
1 0.44
1.91 1.88
2
0.47
2 1.69 1.77
0.90 0.86 0.94
2
sol
1 0.80
Mean Absolute Deviation (kcal mol−1 ) 3
PBE
3
0.84
3 3.17 2.95
4
2.45 2.43
Mean Absolute Deviation (kcal mol−1 ) 1
PBE
Mean Absolute Deviation (kcal mol−1 )
7
H-bond dominant PURE HYB0 QIDH
5
4
0
0
mixed
Figure S4: Mean absolute deviations for the S22/full subsets — hydrogen bond dominant (S22/HB), dispersion dominant (S22/DD) and mixed interactions (S22/MX) — as function of the pure density-functionals hybridized according to the HYB0 and QIDH models. All the reactions are evaluated with the triple-ζ cc-pVTZ basis set.
Basis set Convergence
PBE revPBE
1.38 0.79
1.37 0.83
1.20 0.62
0.84
1
1.20
1.5
1.33
2
0.86
Mean Absolute Deviation (kcal mol−1 )
2.5
0.5
X-V QZ RIJ COS
RIJ
VQZ
K-a VTZ
Z -VT RIJ C
OSX
VTZ
0
Figure S5: Mean absolute deviations for the S22/full test set as function of the size of the correlation consistent basis sets (aug)-cc-pVnZ. All the reactions are evaluated with the QIDH double-hybrid density-functional model.
S6
Barrier Heights PURE HYB0 QIDH 10.30
12
7.73
8.48
8.18
8.27 7.36
6.50
8
7.30
7.55
8.25
10
3.27
3.83
PW9
1
1.00
1.12
1.49
TPSS
1.14
PBE h
BLY P
4.05
3.64 1.73
TCA
1.30
PBE
mol
1.26
APB E
2.76
2.86
3.06 1.30
E revP B
PBE sol
PBE
0
1.17
2
1.33
2.58
4
5.26
6 3.65
Mean Absolute Deviation (kcal mol−1 )
14
Figure S6: Mean absolute deviations for the DBH24/08 test set as function of the pure density-functionals hybridized according to the HYB0 and QIDH models. All the reactions are evaluated with the triple-ζ aug-cc-pVTZ basis set.
S7
3.65
2.09
3.13
5.28
PBE
0
2.99
P B3LY
SX N12-
F M06H
M06
H -QID
PBE
2-SX
4.23
3.15 4.40
2.50 5.14
2.19
4.32 1.17
3.86
0.86
0.56 4.40 1.31
1.51 2.04 2.59
MN1
LYP
0.91 2.00 2.99
B2-P
X
M11
2-PL YP
0
2.44
2
ω B97
1.87
4
0.54
6
3.93 1.12
1.17
8
0.66
0.68
10
2.12
G2/148 DBH24/08 S22/full
12
mPW
Mean Absolute Deviation (kcal mol−1 )
Cumulative Performances
Figure S7: Cumulative mean absolute deviations for the PBE-based HYB0 and QIDH models (red fonts), and for some standard and modern density-functionals. The performances are evaluated on the G2/148 (blue) atomization energy dataset, on the DBH24/08 (magenta) barrier height dataset, and on the S22/full (green) nonbonded interaction dataset. All the reactions of the G2/148, DBH24/08 and S22/full test sets are evaluated with the 6-311+G(3df, 2pd ), aug-cc-pVTZ and cc-pVTZ basis sets respectively.
S8
Computational Methods All the computations were done with the Gaussian program package S1 except for resolution of identity-based calculations which were done with the Orca software S2 making use of the RIJCOSX S3,S4 approach. The semilocal density-functionals and their respective single and double hybridization forms which were not commercialized with Gaussian’09 were fully implemented within the software. An ultrafine integration grid was set for meta-GGA-based computations. The Ahlrichs quadruple-ζ and the Pople triple-ζ 6-311+G(3df, 2pd ) basis sets were used to to evaluate atomization energies of systems included in the AE6 S5 and G2/148 S6–S8 datasets respectively, while the Dunning triple-ζ aug-cc-pVTZ and cc-pVTZ basis sets were employed to compute the barrier height energies and the weakly binding energies of complexes involved in the DBH24/08 S9 and S22 S10,S11 datasets respectively.
References (S1) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, Ö.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 09 Revision D.01. 2009; Gaussian Inc. Wallingford
S9
CT. (S2) Neese, F. WIREs Comput. Mol. Sci. 2012, 2, 73–78. (S3) Neese, F. J. Comput. Chem 2003, 24, 1740–1747. (S4) Neese, F.; Wennmohs, F.; Hansen, A.; Becker, U. Chem. Phys. 2009, 356, 98–109. (S5) Lynch, B. J.; Truhlar, D. G. J. Phys. Chem. A 2003, 107, 8996–8999. (S6) Pople, J. A.; Head-Gordon, M.; Fox, D. J.; Raghavachari, K.; Curtiss, L. A. J. Chem. Phys. 1989, 90, 5622–5629. (S7) Curtiss, L. A.; Raghavachari, K.; Trucks, G. W.; Pople, J. A. J. Chem. Phys. 1991, 94, 7221–7230. (S8) Curtiss, L. A.; Raghavachari, K.; Redfern, P. C.; Pople, J. A. J. Chem. Phys. 1997, 106, 1063–1079. (S9) Zheng, J.; Zhao, Y.; Truhlar, D. G. J. Chem. Theory Comput. 2009, 5, 808–821. (S10) Jurecka, P.; Sponer, J.; Cerny, J.; Hobza, P. Phys. Chem. Chem. Phys. 2006, 8, 1985–1993. (S11) Marshall, M. S.; Burns, L. A.; Sherrill, C. D. J. Chem. Phys. 2011, 135, 194102.
S10
∗
To whom correspondence should be addressed Istituto Italiano di Tecnologia ‡ Universidad de Alicante ¶ Chimie ParisTech § Institut Universitaire de France †
S1
Atomization Energies 50 PURE HYB0 QIDH 34.52
40 35 30
6.66
BLY P
6.79
12.27
15.24 5.54 4.26
1 PW9
4.90
TPSS
9.39 6.90
12.78
PBE h
4.59 4.17
9.95
TCA
8.06 10.35 5.98
mol PBE
APB E
4.68
8.02 8.06
13.53
E revP B
6.41
8.64
9.04
PBE sol
0
5.55 4.32
10 5
17.13
18.50 14.66
20 15
21.00
25
PBE
Mean Absolute Deviation (kcal mol−1 )
45
Figure S1: Mean absolute deviations for the AE6 test set as function of the pure densityfunctionals hybridized according to the HYB0 and QIDH models. All the reactions are evaluated with the quadruple-ζ def2-QZVP basis set.
S2
0
S3 18.26
15.29
21.40
35
30
25 9.61 7.96
5.74
8.47
4.70 4.89 5.04
2.78 3.96
5.35 5.03 5.41
2.77 4.33
9.78
3.86 7.30 6.14
40
4.76 7.37 5.90
G2/55
8.38 2.95 4.72
0
7.53 3.11 4.36
6.57 9.52 6.88
19.80
40
6.93 10.75 7.87
5.58 4.30
6.63 7.77 6.25
4.09 4.29
13.92
5.90 6.00 6.74
6.30 4.86 6.12
4.54 7.32 6.79
3.51
8.37
G1/31
BLY P
1
PW9
TPSS
h
PBE
8.82
6.01 6.08 6.29
6.16 5.00 5.68
15
TCA
8.57 7.45 6.67
9.93
4.74 6.87 6.20
17.34
45
mol
5.29 5.69
10.76 7.02
6.85
3.16
7.44
9.34
45
PBE
E
5
APB
10
BE
45 41.43
20
revP
15
9.42
25 22.29
5 2.87 4.43
20
sol
20 8.23
25
PBE
5 3.00 4.12
10
17.39
Mean Absolute Deviation (kcal mol−1 ) 10
5.28 4.32
Mean Absolute Deviation (kcal mol−1 ) 15
PBE
Mean Absolute Deviation (kcal mol−1 )
50
PURE HYB0 QIDH
35
30
0
G2/148
40
35
30
Figure S2: Mean absolute deviations for the G1/31, G2/55 and G2/148 test sets as function of the pure density-functionals hybridized according to the HYB0 and QIDH models. All the reactions are evaluated with the triple-ζ 6-311+G(3df, 2pd ) basis set.
Noncovalent Binding Energies 6 PURE HYB0 QIDH 4.35
5 4.00
4.5
3.62
4
0.85
1.07
2.00 1.92 0.98
0.89
0.88
0.86
0.86
1.06
1.20
1.5
0.86
2
1
2.96 2.66
2.86 2.73
2.15 2.06
2.41 2.35 1.99 1.87
2.5
2.49 2.40
3
3.20
3.5
2.18 2.09
Mean Absolute Deviation (kcal mol−1 )
5.5
BLY P
1 PW9
TPSS
PBE h
TCA
mol PBE
APB E
E revP B
PBE sol
0
PBE
0.5
Figure S3: Mean absolute deviations for the S22/full test set as function of the pure densityfunctionals hybridized according to the HYB0 and QIDH models. All the reactions are evaluated with the triple-ζ cc-pVTZ basis set.
S4
0
S5 1.24
0.73
1.13
0.82
2.17 2.20
2.40 2.39
3.67
3.26 3.05
3.14 3.11
4.27 1.22
0.70
1.18
0.78
0.71
1.05
2.78 2.61
3.09 2.91
4.64
4.44 3.93
4.23 3.99
3.62 3.38
6.07
5.74
dispersion dominant
BLY P
1
PW9
TPSS
h
PBE
0.82
1.01
2.69 2.67
0.99
3.51 3.28
5
TCA
mol
6
PBE
0.97
2.64 2.61
6
E
1.63
5.11
1.24 0.73
1.03 0.89 1.13
1.13 0.96 0.62
0.92 0.85 1.00
1.94
1.17 1.04 1.69
1.12 0.96 0.61
1.05 0.89 0.67
0.54
1.93
2.73
2.40 1.97 1.72
6
APB
1.41
4.25 3.78
4
BE
5
revP
1 0.44
1.91 1.88
2
0.47
2 1.69 1.77
0.90 0.86 0.94
2
sol
1 0.80
Mean Absolute Deviation (kcal mol−1 ) 3
PBE
3
0.84
3 3.17 2.95
4
2.45 2.43
Mean Absolute Deviation (kcal mol−1 ) 1
PBE
Mean Absolute Deviation (kcal mol−1 )
7
H-bond dominant PURE HYB0 QIDH
5
4
0
0
mixed
Figure S4: Mean absolute deviations for the S22/full subsets — hydrogen bond dominant (S22/HB), dispersion dominant (S22/DD) and mixed interactions (S22/MX) — as function of the pure density-functionals hybridized according to the HYB0 and QIDH models. All the reactions are evaluated with the triple-ζ cc-pVTZ basis set.
Basis set Convergence
PBE revPBE
1.38 0.79
1.37 0.83
1.20 0.62
0.84
1
1.20
1.5
1.33
2
0.86
Mean Absolute Deviation (kcal mol−1 )
2.5
0.5
X-V QZ RIJ COS
RIJ
VQZ
K-a VTZ
Z -VT RIJ C
OSX
VTZ
0
Figure S5: Mean absolute deviations for the S22/full test set as function of the size of the correlation consistent basis sets (aug)-cc-pVnZ. All the reactions are evaluated with the QIDH double-hybrid density-functional model.
S6
Barrier Heights PURE HYB0 QIDH 10.30
12
7.73
8.48
8.18
8.27 7.36
6.50
8
7.30
7.55
8.25
10
3.27
3.83
PW9
1
1.00
1.12
1.49
TPSS
1.14
PBE h
BLY P
4.05
3.64 1.73
TCA
1.30
PBE
mol
1.26
APB E
2.76
2.86
3.06 1.30
E revP B
PBE sol
PBE
0
1.17
2
1.33
2.58
4
5.26
6 3.65
Mean Absolute Deviation (kcal mol−1 )
14
Figure S6: Mean absolute deviations for the DBH24/08 test set as function of the pure density-functionals hybridized according to the HYB0 and QIDH models. All the reactions are evaluated with the triple-ζ aug-cc-pVTZ basis set.
S7
3.65
2.09
3.13
5.28
PBE
0
2.99
P B3LY
SX N12-
F M06H
M06
H -QID
PBE
2-SX
4.23
3.15 4.40
2.50 5.14
2.19
4.32 1.17
3.86
0.86
0.56 4.40 1.31
1.51 2.04 2.59
MN1
LYP
0.91 2.00 2.99
B2-P
X
M11
2-PL YP
0
2.44
2
ω B97
1.87
4
0.54
6
3.93 1.12
1.17
8
0.66
0.68
10
2.12
G2/148 DBH24/08 S22/full
12
mPW
Mean Absolute Deviation (kcal mol−1 )
Cumulative Performances
Figure S7: Cumulative mean absolute deviations for the PBE-based HYB0 and QIDH models (red fonts), and for some standard and modern density-functionals. The performances are evaluated on the G2/148 (blue) atomization energy dataset, on the DBH24/08 (magenta) barrier height dataset, and on the S22/full (green) nonbonded interaction dataset. All the reactions of the G2/148, DBH24/08 and S22/full test sets are evaluated with the 6-311+G(3df, 2pd ), aug-cc-pVTZ and cc-pVTZ basis sets respectively.
S8
Computational Methods All the computations were done with the Gaussian program package S1 except for resolution of identity-based calculations which were done with the Orca software S2 making use of the RIJCOSX S3,S4 approach. The semilocal density-functionals and their respective single and double hybridization forms which were not commercialized with Gaussian’09 were fully implemented within the software. An ultrafine integration grid was set for meta-GGA-based computations. The Ahlrichs quadruple-ζ and the Pople triple-ζ 6-311+G(3df, 2pd ) basis sets were used to to evaluate atomization energies of systems included in the AE6 S5 and G2/148 S6–S8 datasets respectively, while the Dunning triple-ζ aug-cc-pVTZ and cc-pVTZ basis sets were employed to compute the barrier height energies and the weakly binding energies of complexes involved in the DBH24/08 S9 and S22 S10,S11 datasets respectively.
References (S1) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, Ö.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 09 Revision D.01. 2009; Gaussian Inc. Wallingford
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CT. (S2) Neese, F. WIREs Comput. Mol. Sci. 2012, 2, 73–78. (S3) Neese, F. J. Comput. Chem 2003, 24, 1740–1747. (S4) Neese, F.; Wennmohs, F.; Hansen, A.; Becker, U. Chem. Phys. 2009, 356, 98–109. (S5) Lynch, B. J.; Truhlar, D. G. J. Phys. Chem. A 2003, 107, 8996–8999. (S6) Pople, J. A.; Head-Gordon, M.; Fox, D. J.; Raghavachari, K.; Curtiss, L. A. J. Chem. Phys. 1989, 90, 5622–5629. (S7) Curtiss, L. A.; Raghavachari, K.; Trucks, G. W.; Pople, J. A. J. Chem. Phys. 1991, 94, 7221–7230. (S8) Curtiss, L. A.; Raghavachari, K.; Redfern, P. C.; Pople, J. A. J. Chem. Phys. 1997, 106, 1063–1079. (S9) Zheng, J.; Zhao, Y.; Truhlar, D. G. J. Chem. Theory Comput. 2009, 5, 808–821. (S10) Jurecka, P.; Sponer, J.; Cerny, J.; Hobza, P. Phys. Chem. Chem. Phys. 2006, 8, 1985–1993. (S11) Marshall, M. S.; Burns, L. A.; Sherrill, C. D. J. Chem. Phys. 2011, 135, 194102.
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