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Computational Chemistry Comparison and Benchmark DataBase
Release 18October 2016
NIST Standard Reference Database 101
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III.G.1.a.

Comparison of levels of theory for O-H


Click on an entry for a histogram of the values.
The subscript refers to how many bonds of that type have been calculated.
average calculated bond lengths (Å)
Methods with predefined basis sets
semi-empirical AM1 1.0645
110
PM3 1.0736
121
PM6 1.0873
209
composite G2 1.0487
201
G3 1.0143
187
G3B3 1.0639
230
G3MP2 1.0198
16
G4 1.0548
226
CBS-Q 1.0165
170
molecular mechanics DREIDING 0.9811
4

average calculated bond lengths (Å)
Methods with standard basis sets
STO-3G 3-21G 3-21G* 6-31G 6-31G* 6-31G** 6-31+G** 6-311G* 6-311G** 6-31G(2df,p) 6-311+G(3df,2p) 6-311+G(3df,2pd) TZVP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(D+d)Z cc-pV(T+d)Z aug-cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ aug-cc-pCVTZ daug-cc-pVTZ Sadlej_pVTZ
hartree fock HF 1.0649
189
1.0587
227
1.0398
194
1.0305
189
1.0483
250
1.0171
193
1.0486
151
1.0037
195
1.0070
190
1.0146
192
1.0173
107
1.2005
36
1.0348
241
1.0193
192
1.0068
188
0.9616
76
1.0117
182
1.0290
196
0.9630
69
0.9499
1
0.9446
6
0.9401
2
0.9551
3
0.9484
5
0.9469
1
0.9418
3
0.9454
5
ROHF 1.0150
3
1.0492
25
1.0469
26
1.0631
21
1.0543
29
1.0553
24
0.9594
25
0.9606
24
0.9669
20
0.9568
4
0.9502
1
0.9505
1
0.9661
15
1.0396
24
0.9607
22
0.9623
15
0.9596
21
0.9575
20
0.9595
15
    0.9395
1
  0.9458
1
0.9464
1
   
density functional LSDA 1.1204
224
1.0905
227
1.1001
228
1.0837
225
1.0616
226
1.0718
224
1.0662
224
1.0627
227
1.0626
225
1.0685
223
0.9740
3
0.9737
3
1.0854
108
1.0734
223
1.0616
224
0.9871
7
1.0691
210
1.0553
113
0.9878
7
0.9837
1
0.9761
5
0.9706
2
0.9869
2
0.9830
3
0.9910
1
0.9711
3
 
SVWN 1.0378
3
1.1090
225
1.0112
3
0.9910
3
1.0799
226
1.0965
110
1.0619
225
1.0826
110
1.0811
110
1.0914
110
0.9740
3
0.9737
3
1.0713
168
1.0964
111
1.0796
110
0.9736
3
1.0901
103
1.0628
94
0.9741
3
  0.9761
5
0.9706
2
0.9900
1
0.9862
2
0.9910
1
0.9711
3
 
BLYP 1.1307
188
1.0887
194
1.0907
180
1.0742
191
1.0816
262
1.0536
195
1.0439
195
1.0485
179
1.0417
191
1.0506
192
0.9757
3
0.9756
3
1.0907
108
1.0583
190
1.0429
186
0.9752
3
1.0708
92
1.1793
42
0.9755
3
0.9871
1
0.9766
5
0.9717
2
0.9897
2
0.9829
3
0.9890
1
0.9733
3
 
B1B95 1.0966
213
1.0737
218
1.0707
212
1.0633
215
1.0560
211
1.0522
218
1.0498
212
1.0370
211
1.0372
211
1.0504
211
0.9608
3
0.9610
3
1.0740
106
1.0536
215
1.0380
210
0.9771
12
1.0477
193
1.0612
132
0.9772
12
0.9697
1
0.9621
5
0.9572
2
0.9727
2
0.9670
3
0.9715
1
0.9585
3
 
B3LYP 1.1113
188
1.1060
225
1.0705
191
1.0559
194
1.0631
227
1.0402
194
1.0524
228
1.0291
195
1.0480
149
1.0495
235
0.9631
55
1.1980
34
1.0514
237
1.0430
193
1.0297
189
0.9865
71
1.0573
159
1.0584
219
0.9857
69
0.9751
1
0.9664
6
0.9614
2
0.9780
2
0.9703
5
0.9762
1
0.9630
3
0.9684
5
B3LYPultrafine 1.0353
3
1.1910
82
1.0037
3
0.9830
3
1.0691
213
1.1552
54
1.1196
102
1.1248
54
0.9665
3
0.9669
3
0.9653
3
1.1845
36
1.1140
58
1.1028
90
1.0513
120
0.9648
3
1.0934
82
1.0456
223
0.9651
3
  0.9612
2
0.9614
2
  0.9753
1
0.9762
1
0.9629
3
 
B3PW91 1.1137
146
1.0721
191
1.0686
192
1.0531
192
1.0413
192
1.0370
194
1.0340
181
1.0272
195
1.0459
149
1.0340
193
0.9634
3
0.9635
3
1.0749
108
1.0408
191
1.0278
189
0.9632
3
1.0567
92
1.1081
57
0.9635
3
0.9730
1
0.9648
5
0.9600
2
0.9760
2
0.9699
3
0.9748
1
0.9613
3
 
mPW1PW91 1.1108
152
1.0660
193
1.0797
157
1.0513
190
1.0535
192
1.0341
194
1.0265
194
1.0243
195
1.0249
192
1.0326
191
0.9611
3
0.9612
3
1.0724
108
1.0385
191
1.0344
167
0.9609
3
1.0374
162
1.0446
103
0.9612
3
0.9705
1
0.9613
3
0.9578
2
0.9735
2
0.9675
3
0.9719
1
0.9590
3
 
M06-2X 1.1060
114
1.1148
113
1.0834
226
1.1007
113
1.0687
229
1.0802
116
1.0687
115
1.0658
116
1.0653
116
1.0643
130
0.9625
3
0.9626
3
1.0746
108
1.0818
116
1.0538
129
0.9623
3
1.0735
109
1.0381
114
0.9626
3
0.9711
1
0.9646
6
0.9593
2
0.9747
2
0.9691
3
0.9726
1
0.9601
3
 
PBEPBE 1.1376
146
1.1226
216
1.1045
149
1.0932
147
1.0772
214
1.0506
191
1.0644
217
1.0405
192
1.0390
192
1.0906
191
0.9723
57
1.3694
32
1.0876
108
1.0532
192
1.0477
191
0.9906
12
1.0778
121
1.0747
153
0.9907
12
0.9849
1
0.9745
4
0.9705
2
0.9873
2
0.9818
3
0.9886
1
0.9716
3
0.9771
5
PBEPBEultrafine 1.0453
3
1.1976
82
1.0150
3
0.9929
3
1.0856
177
1.1629
54
1.1508
86
1.1338
54
0.9748
3
0.9753
3
0.9737
3
1.1834
36
1.1226
58
1.1111
90
1.0908
89
0.9736
3
1.1021
82
1.1168
107
0.9739
3
  0.9703
2
0.9705
2
  0.9876
1
0.9886
1
0.9716
3
 
PBE1PBE 1.1194
100
1.1084
100
1.1084
100
1.1000
98
1.0669
217
1.0846
100
1.0663
100
1.0652
100
1.0641
100
1.0774
100
0.9619
3
0.9620
3
1.0683
98
1.0810
101
1.0633
100
0.9618
3
1.0732
93
1.0567
89
0.9621
3
  0.9636
5
0.9587
2
0.9770
1
0.9708
2
0.9731
1
0.9599
3
 
HSEh1PBE 1.1261
113
1.1154
225
1.1090
113
1.1018
111
1.0700
219
1.0817
113
1.0613
229
1.0663
114
1.0660
114
1.0774
114
0.9619
3
0.9621
3
1.0755
106
1.0830
114
1.0743
229
0.9617
3
1.0744
107
1.0489
98
0.9620
3
0.9712
1
0.9636
6
0.9587
2
0.9743
2
0.9685
3
0.9728
1
0.9599
3
 
TPSSh 1.3319
27
1.1666
61
1.1647
61
1.1514
61
1.0728
237
1.1357
61
1.0650
237
1.1272
61
1.2747
27
1.0726
231
    1.1198
57
1.1345
62
1.0613
237
1.0334
19
1.1217
55
1.1237
53
1.0364
17
  0.9637
2
0.9639
2
  0.9777
1
0.9786
1
0.9657
3
 
wB97X-D 1.2598
34
1.2398
34
1.0819
263
1.2285
34
1.0629
263
1.2075
34
1.0605
263
1.2052
34
1.0566
263
1.2035
34
    1.0575
263
1.0601
263
1.0561
263
1.0189
21
1.2069
34
1.0558
262
1.0194
21
            0.9585
3
 
B97D3 1.0980
9
1.0687
247
1.0437
9
1.0187
9
1.0490
247
1.0098
9
0.9978
9
0.9930
9
1.0421
247
0.9977
9
    0.9955
9
1.0150
9
0.9953
9
0.9946
8
0.9982
9
1.0417
246
0.9944
8
            0.9668
3
 
STO-3G 3-21G 3-21G* 6-31G 6-31G* 6-31G** 6-31+G** 6-311G* 6-311G** 6-31G(2df,p) 6-311+G(3df,2p) 6-311+G(3df,2pd) TZVP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(D+d)Z cc-pV(T+d)Z aug-cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ aug-cc-pCVTZ daug-cc-pVTZ Sadlej_pVTZ
Moller Plesset perturbation MP2 1.1003
146
1.1029
229
1.0666
191
1.0603
188
1.0874
256
1.0364
195
1.0505
231
1.0703
254
1.0253
192
1.0653
179
0.9594
4
1.1612
35
1.0551
240
1.0386
194
1.0389
183
0.9887
58
1.0457
160
1.0896
161
0.9891
56
0.9733
1
0.9661
6
0.9620
2
0.9691
9
0.9659
10
0.9735
1
0.9635
3
0.9705
5
MP2=FULL 1.1030
143
1.0793
169
1.0874
149
1.0820
147
1.0477
198
1.0417
180
1.0362
177
1.0260
191
1.0431
149
1.0672
158
0.9607
3
0.9598
3
1.1066
110
1.0495
167
1.0389
167
0.9895
55
1.0630
127
1.0551
129
0.9903
50
0.9727
1
0.9645
6
0.9598
2
0.9685
9
0.9648
10
0.9727
1
0.9610
3
0.9700
5
ROMP2 1.0403
20
1.0903
21
1.0903
21
1.0752
21
1.0732
20
1.0580
20
0.9857
21
0.9911
20
0.9872
21
1.0513
21
0.9674
1
0.9666
1
0.9904
16
1.0427
22
0.9870
19
0.9938
2
0.9869
20
0.9970
2
0.9674
1
        0.9707
1
0.9732
1
0.9615
2
 
MP3 1.0293
3
0.9950
3
0.9950
3
0.9788
3
1.0456
180
0.9632
3
1.0591
234
0.9586
3
0.9586
3
0.9594
3
0.9581
3
0.9578
3
1.1271
50
1.1503
51
1.1228
50
0.9570
3
0.9662
3
0.9603
3
0.9578
3
  0.9580
5
0.9552
2
  0.9639
1
0.9659
1
0.9569
3
 
MP3=FULL   1.2553
32
1.2542
32
1.2463
32
1.0716
230
1.2027
34
1.0625
225
1.1975
34
1.1970
34
1.1970
34
    1.1296
49
1.1531
50
1.1236
49
  1.2189
32
1.2089
32
    0.9529
2
0.9529
2
  0.9632
1
0.9652
1
0.9543
3
 
MP4 1.0299
6
1.0964
123
1.0001
10
0.9846
10
1.1073
143
0.9681
4
0.9699
4
0.9618
21
1.0700
113
0.9602
5
0.9634
3
0.9630
3
1.1009
76
1.1189
76
1.0610
124
0.9623
3
1.1141
70
1.1043
60
0.9635
3
0.9735
1
0.9655
4
0.9628
2
0.9737
1
1.7041
5
0.9747
1
0.9659
3
 
MP4=FULL 1.0333
3
1.1573
75
0.9997
3
0.9825
3
1.1299
76
0.9651
3
0.9669
3
0.9627
3
1.0941
77
0.9614
3
0.9624
3
0.9616
3
0.9741
1
1.1203
75
1.1057
70
0.9607
3
1.1113
71
0.9881
58
0.9622
3
  0.9597
2
0.9605
2
  2.7976
2
0.9739
1
0.9632
3
 
B2PLYP 1.1724
64
1.1800
64
1.1764
64
1.1674
64
1.0984
183
1.1466
64
1.1205
65
1.1223
64
1.1204
64
1.1046
81
0.9630
3
0.9629
3
1.1229
64
1.1438
65
1.0800
192
0.9623
3
1.1420
57
1.0801
71
0.9630
3
        0.9726
1
0.9742
1
0.9627
3
 
B2PLYP=FULL 1.1724
64
1.1643
65
1.1785
64
1.1696
64
1.1367
65
1.1463
64
1.1199
65
1.1222
64
1.1202
64
1.1422
64
0.9701
1
0.9698
1
1.1228
64
1.1436
65
1.1189
64
0.9694
1
1.1423
57
1.1162
54
0.9702
1
        0.9724
1
0.9740
1
0.9620
3
 
B2PLYP=FULLultrafine 1.2411
36
1.2333
36
1.2302
36
1.2205
36
1.0494
106
1.1964
36
1.1972
36
1.1922
36
1.1931
36
1.1925
36
    1.1958
36
1.2018
36
1.1925
36
  1.1976
36
1.1929
36
              0.9620
3
 
Configuration interaction CID 1.0262
5
1.0873
139
1.0851
137
1.0777
136
1.0563
171
0.9618
5
0.9625
5
1.0331
149
0.9549
10
0.9540
5
0.9563
3
0.9560
3
0.9693
1
0.9649
5
0.9557
10
0.9550
3
0.9646
3
0.9584
3
0.9557
3
  0.9505
2
0.9512
2
  0.9595
1
0.9610
1
0.9552
3
 
CISD 1.0264
5
1.0849
145
1.0863
137
1.0780
137
1.0567
171
0.9592
5
0.9633
5
1.0389
140
0.9555
10
0.9548
4
0.9573
3
0.9569
3
0.9706
1
0.9657
5
0.9565
10
0.9559
3
0.9655
3
0.9593
3
0.9566
3
  0.9511
2
0.9517
2
  0.9603
1
0.9618
1
0.9563
3
 
STO-3G 3-21G 3-21G* 6-31G 6-31G* 6-31G** 6-31+G** 6-311G* 6-311G** 6-31G(2df,p) 6-311+G(3df,2p) 6-311+G(3df,2pd) TZVP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(D+d)Z cc-pV(T+d)Z aug-cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ aug-cc-pCVTZ daug-cc-pVTZ Sadlej_pVTZ
Quadratic configuration interaction QCISD 1.0312
14
1.0913
175
1.0910
142
1.0729
139
1.0750
171
1.0552
149
1.0441
153
1.0368
160
1.0541
147
1.0539
143
0.9688
1
0.9681
1
1.1097
106
1.0863
170
1.0731
146
0.9675
1
1.0789
106
1.0436
103
0.9684
1
0.9713
1
0.9622
6
0.9584
2
0.9742
2
0.9662
3
0.9704
1
0.9614
3
 
QCISD(T) 1.0361
3
0.9989
5
0.9997
5
0.9793
4
1.1343
135
0.9666
9
1.1438
13
1.1259
50
1.1889
10
0.9635
4
0.9632
3
0.9628
3
1.1259
97
1.1132
119
1.1178
101
0.9620
3
1.1045
88
0.9866
73
0.9631
3
0.9734
1
0.9635
4
0.9614
2
0.9764
2
0.9693
3
0.9741
1
0.9642
3
 
QCISD(T)=FULL         1.0484
41
  0.9757
36
            1.0307
43
1.1530
43
1.0117
24
1.1685
41
0.9989
34
0.9709
17
        0.9707
1
0.9734
1
0.9615
3
 
QCISD(TQ) 1.0284
2
1.0017
3
1.0017
3
0.9843
3
1.0536
27
0.9668
3
0.9786
22
0.9636
3
0.9631
3
0.9631
3
0.9632
3
0.9628
3
0.9752
1
1.0697
26
0.9770
20
0.9750
13
1.0167
26
0.9782
13
0.9687
6
               
QCISD(TQ)=FULL         1.0791
28
  1.0170
24
            1.0654
27
0.9788
19
0.9773
10
1.0175
25
0.9758
12
0.9761
2
               
Coupled Cluster CCD 1.0292
14
1.0871
150
1.0891
141
1.0797
144
1.0730
180
1.0533
149
1.0457
147
1.0372
155
1.0483
134
1.0603
132
0.9670
1
0.9665
1
1.1074
106
1.0631
169
1.0550
124
0.9659
1
1.0721
112
1.0551
91
0.9666
1
0.9697
1
0.9596
5
0.9569
2
0.9726
2
0.9630
4
0.9679
1
0.9592
3
 
CCSD 1.0536
1
0.9995
3
1.0010
3
0.9836
3
1.0881
146
0.9668
7
0.9681
10
1.0564
18
0.9608
6
1.0930
62
0.9685
1
0.9678
1
1.1375
80
1.0851
112
1.0552
124
0.9945
38
1.1035
74
1.0642
81
0.9711
22
  0.9618
5
0.9580
2
0.9768
1
0.9678
2
0.9699
1
0.9607
3
 
CCSD=FULL 1.0536
1
1.0143
1
1.0143
1
0.9971
1
1.0973
94
0.9741
1
0.9755
1
0.9708
1
0.9687
1
1.0976
59
0.9674
1
0.9662
1
1.0957
77
1.1128
78
1.0678
92
0.9926
40
1.1081
71
0.9775
79
0.9693
27
  0.9588
4
0.9556
2
  0.9671
1
0.9691
1
0.9580
3
 
CCSD(T) 1.0368
3
1.1292
25
0.9978
4
0.9792
4
1.1692
159
1.1208
53
1.1200
35
1.1292
49
1.1122
16
0.9755
11
0.9631
5
1.0451
12
1.1252
91
1.1057
120
1.1056
109
0.9723
41
1.0871
102
1.0665
84
0.9957
40
0.9733
1
0.9641
4
0.9612
2
0.9724
7
1.3338
10
0.9740
1
0.9639
3
 
CCSD(T)=FULL 1.0368
3
1.0015
3
1.0015
3
0.9838
3
1.1327
112
0.9658
3
0.9673
3
0.9631
3
0.9623
3
0.9619
3
0.9620
3
0.9612
3
1.1279
95
1.0933
106
1.0721
83
0.9909
45
1.0897
98
0.9837
68
0.9949
37
0.9728
1
0.9625
4
0.9589
2
0.9707
6
1.3319
10
0.9732
1
0.9612
3
 
STO-3G 3-21G 3-21G* 6-31G 6-31G* 6-31G** 6-31+G** 6-311G* 6-311G** 6-31G(2df,p) 6-311+G(3df,2p) 6-311+G(3df,2pd) TZVP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(D+d)Z cc-pV(T+d)Z aug-cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ aug-cc-pCVTZ daug-cc-pVTZ Sadlej_pVTZ

average calculated bond lengths (Å)
Methods with effective core potentials (select basis sets)
CEP-31G CEP-31G* CEP-121G CEP-121G* LANL2DZ SDD
hartree fock HF 1.0474
192
1.0435
185
1.0225
193
1.0224
197
1.0426
207
1.0403
193
ROHF 0.9722
1
0.9620
1
0.9697
1
0.9583
1
0.9706
1
0.9706
1
density functional LSDA 1.0051
4
0.9918
4
1.0016
4
0.9882
4
0.9977
4
0.9976
4
SVWN 1.0013
3
0.9891
3
0.9974
3
0.9854
3
0.9929
3
0.9929
3
BLYP 1.0020
3
0.9894
3
0.9970
3
0.9848
3
0.9981
3
0.9982
3
B1B95 1.0360
99
1.0511
105
0.9765
7
0.9665
7
0.9786
7
0.9785
7
B3LYP 1.0603
190
1.0520
185
1.0515
192
1.0451
197
1.0501
200
1.0498
191
B3LYPultrafine 0.9898
3
0.9787
3
0.9849
3
0.9748
5
1.1381
6
0.9853
3
B3PW91 0.9859
3
0.9752
3
0.9814
3
0.9708
3
0.9823
3
0.9823
3
mPW1PW91 0.9828
3
0.9725
3
0.9782
3
0.9681
3
0.9794
3
0.9794
3
M06-2X 0.9795
3
0.9697
3
0.9747
3
0.9657
3
0.9804
3
0.9804
3
PBEPBE 0.9972
3
0.9851
3
0.9925
3
0.9807
3
0.9947
3
0.9947
3
PBEPBEultrafine 0.9972
3
0.9851
3
0.9925
3
0.9807
3
0.9947
3
0.9947
3
PBE1PBE 0.9834
3
0.9730
3
0.9788
3
0.9687
3
0.9803
3
0.9803
3
HSEh1PBE 0.9838
3
0.9734
3
0.9792
3
0.9690
3
0.9805
3
0.9805
3
wB97X-D 1.2382
34
1.2158
34
1.2306
34
1.2114
34
1.2264
34
1.2267
34
Moller Plesset perturbation MP2 1.0529
191
1.0546
187
1.0454
189
1.0470
198
1.0592
202
1.0549
190
MP2=FULL 0.9885
3
0.9780
3
0.9837
3
0.9732
3
0.9849
3
0.9850
3
ROMP2 0.9988
1
0.9846
1
0.9953
1
0.9803
1
0.9974
1
0.9975
1
MP3 0.9880
3
0.9772
3
0.9823
3
0.9718
3
0.9833
3
0.9832
3
MP4 0.9909
3
0.9800
3
0.9864
3
0.9753
3
0.9864
3
0.9865
3
MP4=FULL 0.9909
3
0.9800
3
0.9864
3
0.9753
3
0.9864
3
0.9864
3
B2PLYP 0.9870
3
0.9765
3
0.9824
3
0.9721
3
0.9830
3
0.9831
3
B2PLYP=FULL 0.9993
1
0.9848
1
0.9961
1
0.9808
1
0.9981
1
0.9982
1
Configuration interaction CID 0.9881
3
0.9760
3
0.9826
3
0.9708
3
0.9833
3
0.9833
3
CISD 0.9889
3
0.9766
3
0.9837
3
0.9714
3
0.9843
3
0.9843
3
Quadratic configuration interaction QCISD 1.0052
1
0.9890
1
1.0015
1
0.9845
1
1.0031
1
1.0031
1
QCISD(T) 0.9922
3
0.9810
3
0.9877
3
0.9762
3
0.9879
3
0.9880
3
QCISD(TQ) 0.9927
3
0.9815
3
0.9880
3
0.9766
3
0.9884
3
0.9885
3
Coupled Cluster CCD 1.0033
1
0.9878
1
0.9993
1
0.9832
1
1.0014
1
1.0014
1
CCSD 1.0050
1
0.9889
1
1.0013
1
0.9844
1
1.0033
1
1.0033
1
CCSD=FULL 1.0050
1
0.9889
1
1.0013
1
0.9844
1
1.0032
1
1.0032
1
CCSD(T) 0.9922
3
0.9810
3
0.9876
3
0.9762
3
0.9879
3
0.9880
3
CCSD(T)=FULL 0.9922
3
0.9810
3
0.9876
3
0.9762
3
0.9878
3
0.9878
3
For descriptions of the methods (AM1, HF, MP2, ...) and basis sets (3-21G, 3-21G*, 6-31G, ...) see the glossary in section I.C. Predefined means the basis set used is determined by the method.