Prepared for Journal of Chemical Physics
July 4, 2012
SUPPLEMENTARY MATERIAL FOR
What are the Most Efficient Basis Set Strategies
for Correlated Wave Function Calculations
of Reaction Energies and Barrier Heights?
Ewa Papajak and Donald G. Truhlar
Department of Chemistry and Minnesota Supercomputing Institute, University of
Minnesota,
Minneapolis, MN 55455-0431 USA
Tables S1–S3 are the full versions of tables VIII – X in the paper, including all the
methods invoving cc-pVXZ, aug-ccc-pVXZ, and seasonal basis sets.
Table 4 contains complete results for cc-pVXZ-F12 basis sets.
TABLES:
TABLE S1. Mean unsigned errors on TK48 data in kcal/mol with respect to the complete
basis set CCSD(T) limit and best available estimates in order of increasing cost.
TABLE S2. Mean unsigned errors on ATK9 data in kcal/mol with respect to the
complete basis set CCSD(T) limit and best available estimates in order of increasing cost.
TABLE S3. Mean unsigned errors on NTK39 data in kcal/mol with respect to the
complete basis set CCSD(T) limit and Weizmann results in order of increasing cost.
S-2
TABLE S1. Mean unsigned errors in kcal/mol on TK48 data with respect to the complete
basis set CCSD(T) limit and best available estimates in order of increasing cost.
Methoda
MP2-F12
CCSD(T)-F12a
diffuse
diffuse


–
D
–
–
jun
D
–
–
jul
D
–
–
–
–
–
D
–
–
jun
D
aug
D
–
–
–
–
jul
D
–
T
–
–
may
T
–
–
jun
T
–
–
aug
D
–
D
jul
T
–
–
aug
D
jun
D
–
T
–
D
may
T
–
D
–
T
jun
D
jun
T
–
D
aug
D
jul
D
may
T
jun
D
–
–
aug
D
jun
T
jun
D
jul
T
–
D
–
T
jul
D
may
T
jul
D
jul
T
jun
D
jun
T
jul
D
jul
T
jul
D
aug
T
–
–
–
T
aug
D
may
T
aug
D
jun
T
aug
D
jul
T
aug
D
aug
T
–
D
aug
T
jun
D
aug
T
jul
D
–
–
–
T
–
Q
–
–
aug
T
aug
D
apr
Q
–
–
may
Q
–
–
–
–
may
T
may
T
–
T
cost
CCSD(T)/CBS
Errorb
BE
Errorc
38
42
47
58
74
85
104
108
117
129
143
150
159
166
175
182
187
189
191
203
203
208
212
221
224
233
253
300
311
320
332
352
358
374
404
449
483
503
514
550
553
566
3.84
3.07
2.77
2.23
0.68
2.74
0.45
3.18
2.73
2.71
0.49
2.69
0.31
1.01
0.40
1.16
0.41
0.34
0.29
0.32
0.27
0.41
1.17
0.30
0.27
0.28
0.26
2.68
1.18
0.29
0.25
0.24
0.42
0.28
0.25
1.09
2.93
0.24
2.68
2.70
0.20
0.25
3.99
3.23
2.92
2.19
0.79
2.88
0.52
3.36
2.88
2.86
0.69
2.84
0.52
1.12
0.67
1.18
0.67
0.53
0.54
0.45
0.52
0.66
1.20
0.56
0.50
0.53
0.50
2.83
1.21
0.51
0.47
0.46
0.69
0.53
0.51
1.14
3.12
0.47
2.83
2.85
0.50
0.57
S-3
apr
jun
apr
jul
may
apr
may
jun
may
jun
jun
jun
jul
–
jul
apr
jun
aug
may
jun
aug
jul
apr
may
–
aug
apr
jun
may
jun
apr
may
aug
jun
aug
apr
may
jun
–
apr
may
jun
–
apr
may
jun
–
may
Q
T
Q
T
Q
Q
Q
Q
Q
T
Q
Q
T
–
Q
Q
Q
T
Q
Q
T
T
Q
Q
–
T
Q
Q
Q
Q
Q
Q
T
Q
Q
Q
Q
Q
–
Q
Q
Q
–
Q
Q
Q
–
Q
–
–
jun
–
–
jul
jun
–
jul
may
–
jun
may
jun
–
aug
jul
–
aug
aug
may
jun
–
–
jul
jun
may
–
may
may
jun
jun
jul
jun
–
jul
jul
jul
aug
aug
aug
aug
–
–
–
–
apr
apr
D
T
D
T
D
D
D
–
D
T
D
D
T
T
–
D
D
T
D
D
T
T
T
T
T
T
T
T
T
T
T
T
T
T
–
T
T
T
T
T
T
T
Q
Q
Q
Q
Q
Q
572
578
588
599
608
618
624
625
654
682
683
699
703
711
715
717
729
749
753
828
853
860
963
999
1009
1011
1067
1074
1103
1178
1225
1261
1309
1336
1409
1523
1559
1634
2036
2550
2586
2661
4215
4728
4764
4839
4898
5447
0.41
0.22
0.28
0.20
0.43
0.26
0.27
2.70
0.25
0.14
0.42
0.27
0.13
0.14
2.69
0.25
0.24
0.20
0.23
0.22
0.11
0.13
0.20
0.21
0.15
0.11
0.13
0.21
0.11
0.11
0.12
0.09
0.12
0.09
2.69
0.12
0.10
0.10
0.14
0.13
0.10
0.11
0.63
0.10
0.11
0.11
0.09
0.06
0.69
0.55
0.55
0.53
0.70
0.54
0.54
2.85
0.53
0.47
0.70
0.54
0.46
0.44
2.84
0.51
0.52
0.55
0.49
0.49
0.47
0.43
0.57
0.58
0.41
0.43
0.52
0.57
0.50
0.50
0.48
0.46
0.42
0.46
2.84
0.47
0.45
0.44
0.41
0.45
0.43
0.43
0.89
0.49
0.50
0.49
0.50
0.47
S-4
jun
–
jun
–
–
–
Q
–
Q
–
–
–
apr
may
may
jun
jul
aug
Q
Q
Q
Q
Q
Q
5522
5663
6288
7127
9188
18190
0.06
0.04
0.04
0.04
0.05
0.05
0.47
0.45
0.45
0.44
0.44
0.43
a for single-level calculations only one basis set is listed; for dual-level calculations using
eq 3, first two columns (MP2-F12 basis set) list X bases, while third and fourth
(CCSD(T)-F12a basis set) list Y bases used. In all cases basis sets with tight d functions
on third row atoms (+d) were used.
b error with respect to the CCSD(T)-F12a/apr-cc-pV(5+d)Z values.
c error with respect to the Best Estimate: W3.2 and W4 values for DBH24 data and
CCSDT(2)Q/CBS (T,Q-extrapolation) values for the methanol reactions.
S-5
TABLE S2. Mean unsigned errors in kcal/mol on ATK9 data with respect to the
complete basis set CCSD(T) limit and best available estimates in order of increasing cost.
Methoda
MP2-F12
CCSD(T)-F12a
diffuse
diffuse


–
D
–
–
jun
D
–
–
jul
D
–
–
–
–
–
D
–
–
jun
D
aug
D
–
–
jul
D
–
T
–
–
may
T
–
–
jun
T
–
–
aug
D
–
D
jul
T
–
–
aug
D
jun
D
–
T
–
D
may
T
–
D
–
T
jun
D
jun
T
–
D
aug
D
jul
D
may
T
jun
D
aug
D
jun
T
jun
D
jul
T
–
D
–
T
jul
D
may
T
jul
D
jul
T
jun
D
jun
T
jul
D
jul
T
jul
D
aug
T
–
–
–
T
aug
D
may
T
aug
D
jun
T
aug
D
jul
T
aug
D
aug
T
–
D
aug
T
jun
D
aug
T
jul
D
–
–
–
T
–
Q
–
–
aug
T
aug
D
apr
Q
–
–
may
Q
–
–
–
–
may
T
cost
CCSD(T)/CBS
Errorb
BE
Errorc
38
42
47
58
74
85
104
108
117
129
143
150
159
166
175
182
187
189
191
203
203
208
212
221
224
233
253
300
311
320
332
352
358
374
404
449
483
503
514
550
553
5.92
2.26
1.05
5.79
1.37
1.09
0.42
3.46
1.09
1.03
0.72
0.92
0.42
3.40
0.56
3.82
0.60
0.52
0.35
0.45
0.26
0.60
3.72
0.44
0.25
0.35
0.28
0.98
3.82
0.36
0.28
0.25
0.68
0.29
0.28
3.50
2.22
0.28
0.87
0.99
0.24
6.03
2.15
0.94
5.90
1.26
0.98
0.38
3.56
0.98
0.92
0.65
0.81
0.46
3.52
0.48
3.93
0.53
0.39
0.30
0.39
0.21
0.53
3.83
0.37
0.22
0.29
0.22
0.87
3.93
0.31
0.22
0.22
0.61
0.26
0.23
3.62
2.32
0.24
0.76
0.88
0.18
S-6
may
apr
jun
apr
jul
may
apr
may
jun
may
jun
jun
jun
jul
–
jul
apr
jun
aug
may
jun
aug
jul
apr
may
–
aug
apr
jun
may
jun
apr
may
aug
jun
aug
apr
may
jun
–
apr
may
jun
–
apr
may
jun
–
T
Q
T
Q
T
Q
Q
Q
Q
Q
T
Q
Q
T
–
Q
Q
Q
T
Q
Q
T
T
Q
Q
–
T
Q
Q
Q
Q
Q
Q
T
Q
Q
Q
Q
Q
–
Q
Q
Q
–
Q
Q
Q
–
–
–
–
jun
–
–
jul
jun
–
jul
may
–
jun
may
jun
–
aug
jul
–
aug
aug
may
jun
–
–
jul
jun
may
–
may
may
jun
jun
jul
jun
–
jul
jul
jul
aug
aug
aug
aug
–
–
–
–
apr
T
D
T
D
T
D
D
D
–
D
T
D
D
T
T
–
D
D
T
D
D
T
T
T
T
T
T
T
T
T
T
T
T
T
T
–
T
T
T
T
T
T
T
Q
Q
Q
Q
Q
566
572
578
588
599
608
618
624
625
654
682
683
699
703
711
715
717
729
749
753
828
853
860
963
999
1009
1011
1067
1074
1103
1178
1225
1261
1309
1336
1409
1523
1559
1634
2036
2550
2586
2661
4215
4728
4764
4839
4898
0.42
0.61
0.44
0.29
0.36
0.65
0.27
0.23
0.97
0.24
0.16
0.65
0.23
0.09
0.18
0.95
0.29
0.22
0.43
0.23
0.21
0.14
0.11
0.34
0.44
0.15
0.15
0.15
0.43
0.08
0.08
0.16
0.09
0.18
0.08
0.98
0.20
0.12
0.11
0.20
0.22
0.14
0.14
2.46
0.16
0.27
0.25
0.18
0.31
0.54
0.33
0.27
0.27
0.58
0.21
0.20
0.87
0.18
0.12
0.58
0.21
0.15
0.12
0.84
0.27
0.17
0.35
0.18
0.19
0.13
0.13
0.28
0.34
0.14
0.12
0.21
0.33
0.10
0.13
0.19
0.08
0.15
0.10
0.87
0.21
0.09
0.11
0.18
0.22
0.12
0.14
2.57
0.14
0.17
0.18
0.29
S-7
may
jun
–
jun
–
–
–
Q
Q
–
Q
–
–
–
apr
apr
may
may
jun
jul
aug
Q
Q
Q
Q
Q
Q
Q
5447
5522
5663
6288
7127
9188
18190
0.06
0.08
0.02
0.03
0.03
0.07
0.05
0.17
0.19
0.13
0.14
0.14
0.18
0.16
a for single-level calculations only one basis set is listed; for dual-level calculations using
eq 3, first two columns (MP2-F12 basis set) list X bases, while third and fourth
(CCSD(T)-F12a basis set) list Y bases used. In all cases basis sets with tight d functions
on third row atoms (+d) were used.
b error with respect to the CCSD(T)-F12a/apr-cc-pV(5+d)Z values.
c error with respect to the Best Estimate: W3.2 and W4 values for DBH24 data and
CCSDT(2)Q/CBS (T,Q-extrapolation) values for the methanol reactions.
S-8
TABLE S3. Mean unsigned errors on NTK39 data in kcal/mol with respect to the
complete basis set CCSD(T) limit and Weizmann results in order of increasing cost.
Methoda
MP2-F12
CCSD(T)-F12a
diffuse
diffuse


–
D
–
–
jun
D
–
–
jul
D
–
–
–
–
–
D
–
–
jun
D
aug
D
–
–
–
–
jul
D
–
T
–
–
may
T
–
–
jun
T
–
–
aug
D
–
D
jul
T
–
–
aug
D
jun
D
–
T
–
D
may
T
–
D
–
T
jun
D
jun
T
–
D
aug
D
jul
D
may
T
jun
D
aug
D
jun
T
jun
D
jul
T
–
D
–
T
jul
D
may
T
jul
D
jul
T
jun
D
jun
T
jul
D
jul
T
jul
D
aug
T
–
–
–
T
aug
D
may
T
aug
D
jun
T
aug
D
jul
T
aug
D
aug
T
–
D
aug
T
jun
D
aug
T
jul
D
–
–
–
T
–
Q
–
–
aug
T
aug
D
apr
Q
–
–
may
Q
–
–
–
–
may
T
cost
CCSD(T)/CBS
Errorb
BE
Errorc
38
42
47
58
74
85
104
108
117
129
143
150
159
166
175
182
187
189
191
203
203
208
212
221
224
233
253
300
311
320
332
352
358
374
404
449
483
503
514
550
553
3.36
3.26
3.17
1.40
0.52
3.11
0.46
3.11
3.11
3.10
0.43
3.10
0.29
0.46
0.36
0.55
0.37
0.30
0.27
0.29
0.28
0.36
0.58
0.27
0.27
0.26
0.26
3.08
0.57
0.27
0.24
0.24
0.36
0.27
0.24
0.54
3.10
0.23
3.10
3.09
0.19
3.52
3.48
3.38
1.33
0.68
3.32
0.56
3.31
3.32
3.31
0.70
3.30
0.55
0.57
0.71
0.55
0.71
0.47
0.59
0.47
0.59
0.69
0.60
0.60
0.57
0.58
0.56
3.28
0.58
0.55
0.53
0.51
0.71
0.59
0.57
0.57
3.30
0.53
3.31
3.30
0.58
S-9
may
apr
jun
apr
jul
may
apr
may
jun
may
jun
jun
jun
jul
–
jul
apr
jun
aug
may
jun
aug
jul
apr
may
–
aug
apr
jun
may
jun
apr
may
aug
jun
aug
apr
may
jun
–
apr
may
jun
–
apr
may
jun
–
T
Q
T
Q
T
Q
Q
Q
Q
Q
T
Q
Q
T
–
Q
Q
Q
T
Q
Q
T
T
Q
Q
–
T
Q
Q
Q
Q
Q
Q
T
Q
Q
Q
Q
Q
–
Q
Q
Q
–
Q
Q
Q
–
–
–
–
jun
–
–
jul
jun
–
jul
may
–
jun
may
jun
–
aug
jul
–
aug
aug
may
jun
–
–
jul
jun
may
–
may
may
jun
jun
jul
jun
–
jul
jul
jul
aug
aug
aug
aug
–
–
–
–
apr
T
D
T
D
T
D
D
D
–
D
T
D
D
T
T
–
D
D
T
D
D
T
T
T
T
T
T
T
T
T
T
T
T
T
T
–
T
T
T
T
T
T
T
Q
Q
Q
Q
Q
566
572
578
588
599
608
618
624
625
654
682
683
699
703
711
715
717
729
749
753
828
853
860
963
999
1009
1011
1067
1074
1103
1178
1225
1261
1309
1336
1409
1523
1559
1634
2036
2550
2586
2661
4215
4728
4764
4839
4898
0.21
0.37
0.17
0.28
0.16
0.37
0.26
0.28
3.10
0.25
0.14
0.37
0.28
0.13
0.14
3.10
0.24
0.25
0.14
0.23
0.22
0.11
0.14
0.17
0.16
0.15
0.10
0.13
0.16
0.12
0.11
0.11
0.09
0.11
0.09
3.09
0.11
0.09
0.09
0.12
0.12
0.10
0.10
0.21
0.08
0.08
0.07
0.07
0.63
0.73
0.61
0.62
0.59
0.73
0.61
0.62
3.30
0.61
0.51
0.73
0.62
0.54
0.51
3.31
0.56
0.60
0.60
0.56
0.56
0.55
0.49
0.64
0.64
0.48
0.51
0.59
0.63
0.59
0.59
0.55
0.55
0.49
0.54
3.30
0.53
0.53
0.52
0.46
0.51
0.50
0.50
0.50
0.57
0.57
0.57
0.55
S-10
may
jun
–
jun
–
–
–
Q
Q
–
Q
–
–
–
apr
apr
may
may
jun
jul
aug
Q
Q
Q
Q
Q
Q
Q
5447
5522
5663
6288
7127
9188
18190
0.05
0.05
0.04
0.04
0.04
0.05
0.05
0.55
0.54
0.53
0.52
0.51
0.50
0.49
a for single-level calculations only one basis set is listed; for dual-level calculations using
eq 3, first two columns (MP2-F12 basis set) list X bases, while third and fourth
(CCSD(T)-F12a basis set) list Y bases used. In all cases basis sets with tight d functions
on third row atoms (+d) were used.
b error with respect to the CCSD(T)-F12a/apr-cc-pV(5+d)Z values.
c error with respect to the Best Estimate: W3.2 and W4 values for DBH24 data and
CCSDT(2)Q/CBS (T,Q-extrapolation) values for the methanol reactions.
S-11
TABLE S4. Mean unsigned errors in kcal/mol on the full database and its two subsets
with respect to the complete basis set CCSD(T) limit and the best available estimates in
order of increasing cost.
TK48
Method and basis set
MP2-F12
CCSD(T)-F12a
cc-pVDZ-F12
–
cc-pVTZ-F12
–
cc-pVQZ-F12
–
–
cc-pVDZ-F12
–
cc-pVTZ-F12
–
cc-pVQZ-F12
cc-pVTZ-F12
cc-pVDZ-F12
cc-pVQZ-F12
cc-pVTZ-F12
cc-pVQZ-F12
cc-pVDZ-F12
CCSD(T)/CBS
Error
2.74
2.68
2.68
0.32
0.13
0.05
0.23
0.11
0.21
BE Error
2.89
2.83
2.83
0.60
0.46
0.45
0.55
0.45
0.53
ATK9
Method and basis set
MP2-F12
CCSD(T)-F12a
cc-pVDZ-F12
–
cc-pVTZ-F12
–
cc-pVQZ-F12
–
–
cc-pVDZ-F12
–
cc-pVTZ-F12
–
cc-pVQZ-F12
cc-pVTZ-F12
cc-pVDZ-F12
cc-pVQZ-F12
cc-pVTZ-F12
cc-pVQZ-F12
cc-pVDZ-F12
CCSD(T)/CBS
Error
1.09
0.97
0.95
0.58
0.27
0.13
0.37
0.22
0.32
BE Error
0.98
0.86
0.85
0.52
0.23
0.19
0.32
0.19
0.26
NTK39
Method and basis set
MP2-F12
CCSD(T)-F12a
cc-pVDZ-F12
–
cc-pVTZ-F12
–
cc-pVQZ-F12
–
–
cc-pVDZ-F12
–
cc-pVTZ-F12
–
cc-pVQZ-F12
cc-pVTZ-F12
cc-pVDZ-F12
cc-pVQZ-F12
cc-pVTZ-F12
cc-pVQZ-F12
cc-pVDZ-F12
CCSD(T)/CBS
Error
3.12
3.07
3.08
0.26
0.09
0.03
0.19
0.09
0.18
BE Error
3.33
3.28
3.29
0.62
0.52
0.51
0.60
0.51
0.60