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Release 17bSeptember 2015
NIST Standard Reference Database 101
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III.G.1.a.

Comparison of levels of theory for H-O


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 1.0086
101
PM3 1.0256
112
PM6 1.0576
197
composite G2 1.0164
196
G3 0.9783
184
G3B3 1.0357
226
G3MP2 0.9486
8
G4 1.0265
213
CBS-Q 0.9766
167
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 Sadlej_pVTZ
hartree fock HF 1.0328
182
1.0294
221
1.0051
187
0.9935
184
1.0234
237
0.9821
188
1.0038
146
0.9683
190
0.9710
183
0.9803
185
1.0173
107
1.2005
36
1.0082
228
0.9843
187
0.9707
183
0.9625
77
0.9733
177
0.9946
191
0.9638
68
0.9499
1
0.9446
6
0.9401
2
0.9551
3
0.9484
5
0.9469
1
0.9454
5
ROHF 1.0147
6
1.0513
24
1.0488
25
1.0634
21
1.0542
29
1.0552
24
0.9587
25
0.9604
24
0.9666
20
0.9569
7
0.9502
1
0.9505
1
0.9660
11
1.0394
24
0.9604
22
0.9619
15
0.9593
21
0.9572
20
0.9591
15
    0.9395
1
  0.9458
1
0.9464
1
 
density functional LSDA 1.0936
211
1.0592
218
1.0712
219
1.0557
213
1.0342
214
1.0436
215
1.0365
215
1.0351
215
1.0340
215
1.0402
213
0.9740
3
0.9737
3
1.0279
89
1.0455
213
1.0332
215
0.9890
8
1.0361
201
0.9909
96
0.9896
8
0.9837
1
0.9761
5
0.9706
2
0.9869
2
0.9830
3
0.9910
1
 
SVWN 1.0378
3
1.0810
210
1.0112
3
0.9910
3
1.0530
211
1.0428
91
1.0340
210
1.0259
91
1.0247
91
1.0378
91
0.9740
3
0.9737
3
1.0713
168
1.0422
92
1.0236
91
0.9736
3
1.0316
82
0.9903
73
0.9741
3
  0.9761
5
0.9706
2
0.9900
1
0.9862
2
0.9910
1
 
BLYP 1.1009
180
1.0552
188
1.0551
174
1.0368
185
1.0576
249
1.0195
189
1.0086
189
1.0100
173
1.0064
183
1.0165
184
0.9757
3
0.9756
3
1.0316
89
1.0232
184
1.0062
180
0.9752
3
0.9796
67
0.9785
16
0.9755
3
0.9871
1
0.9766
5
0.9717
2
0.9897
2
0.9829
3
0.9890
1
 
B1B95 1.0687
205
1.0437
213
1.0397
207
1.0316
210
1.0257
206
1.0226
213
1.0186
207
1.0055
206
1.0061
203
1.0206
203
0.9608
3
0.9610
3
1.0151
87
1.0238
208
1.0068
205
0.9851
18
1.0132
188
1.0122
122
0.9819
18
0.9697
1
0.9621
5
0.9572
2
0.9727
2
0.9670
3
0.9715
1
 
B3LYP 1.0785
181
1.0772
220
1.0359
186
1.0200
189
1.0343
219
1.0060
189
1.0264
225
0.9940
190
1.0031
142
1.0223
228
0.9631
55
1.1980
34
1.0238
224
1.0084
188
0.9939
184
0.9867
72
1.0146
154
1.0279
214
0.9859
68
0.9751
1
0.9664
6
0.9614
2
0.9780
2
0.9703
5
0.9762
1
0.9684
5
B3LYPultrafine 1.0353
3
1.1302
61
1.0037
3
0.9830
3
1.0391
207
1.0308
28
1.0656
81
0.9736
28
0.9665
3
0.9669
3
0.9653
3
1.1845
36
0.9976
37
1.0358
69
0.9960
99
0.9648
3
1.0160
61
1.0164
208
0.9651
3
  0.9612
2
0.9614
2
  0.9753
1
0.9762
1
 
B3PW91 1.0718
138
1.0348
185
1.0320
186
1.0180
186
1.0073
186
1.0031
188
0.9965
175
0.9926
189
1.0015
141
1.0007
185
0.9634
3
0.9635
3
1.0167
89
1.0065
185
0.9924
183
0.9632
3
0.9672
69
0.9637
32
0.9635
3
0.9730
1
0.9648
5
0.9600
2
0.9760
2
0.9699
3
0.9748
1
 
mPW1PW91 1.0717
145
1.0314
188
1.0380
152
1.0150
185
1.0193
187
1.0002
189
0.9916
189
0.9896
190
0.9898
185
0.9981
184
0.9611
3
0.9612
3
1.0137
90
1.0036
186
0.9938
162
0.9609
3
0.9966
145
0.9778
86
0.9612
3
0.9705
1
0.9613
3
0.9578
2
0.9735
2
0.9675
3
0.9719
1
 
M06-2X 1.0490
95
1.0582
94
1.0541
213
1.0447
94
1.0423
214
1.0282
97
1.0135
96
1.0110
97
1.0107
97
1.0169
111
0.9625
3
0.9626
3
1.0165
89
1.0298
97
1.0041
110
0.9623
3
1.0174
88
0.9774
93
0.9626
3
0.9711
1
0.9646
6
0.9593
2
0.9747
2
0.9691
3
0.9726
1
 
PBEPBE 1.0968
138
1.0933
210
1.0615
143
1.0459
141
1.0474
208
1.0162
185
1.0334
211
1.0050
186
1.0040
184
1.0580
183
0.9723
57
1.3694
32
1.0284
89
1.0185
186
1.0128
185
0.9992
18
1.0249
105
1.0343
135
0.9955
18
0.9849
1
0.9745
4
0.9705
2
0.9873
2
0.9818
3
0.9886
1
0.9771
5
PBEPBEultrafine 1.0453
3
1.1364
61
1.0150
3
0.9929
3
1.0522
158
1.0393
28
1.0927
65
0.9850
28
0.9748
3
0.9753
3
0.9737
3
1.1834
36
1.0068
37
1.0441
69
1.0180
68
0.9736
3
1.0250
61
1.0655
86
0.9739
3
  0.9703
2
0.9705
2
  0.9876
1
0.9886
1
 
PBE1PBE 1.0555
81
1.0429
81
1.0429
81
1.0334
79
1.0389
202
1.0225
81
1.0009
81
0.9990
81
0.9989
81
1.0161
81
0.9619
3
0.9620
3
1.0018
79
1.0195
82
0.9982
81
0.9618
3
1.0047
72
0.9797
68
0.9621
3
  0.9636
5
0.9587
2
0.9770
1
0.9708
2
0.9731
1
 
HSEh1PBE 1.0723
94
1.0887
209
1.0527
94
1.0468
92
1.0425
204
1.0287
94
1.0345
214
1.0109
95
1.0109
95
1.0250
95
0.9619
3
0.9621
3
1.0166
87
1.0298
95
1.0494
213
0.9617
3
1.0178
86
0.9785
77
0.9620
3
0.9712
1
0.9636
6
0.9587
2
0.9743
2
0.9685
3
0.9728
1
 
TPSSh 1.0433
3
1.0634
40
1.0630
40
1.0478
40
1.0464
223
1.0374
40
1.0385
223
1.0292
40
0.9724
3
1.0457
219
    1.0018
36
1.0364
41
1.0351
223
0.9680
2
1.0006
34
0.9988
32
0.9684
2
  0.9637
2
0.9639
2
  0.9777
1
0.9786
1
 
wB97X-D 1.0244
9
0.9892
9
1.0565
250
0.9757
9
1.0394
250
0.9674
9
0.9679
9
0.9644
9
1.0329
250
0.9649
9
    0.9650
9
0.9706
9
1.0326
250
0.9586
4
0.9675
9
1.0322
249
0.9588
4
             
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 Sadlej_pVTZ
Moller Plesset perturbation MP2 1.0598
138
1.0737
225
1.0322
186
1.0231
184
1.0643
243
1.0026
190
1.0218
226
1.0466
241
0.9905
187
1.0305
172
0.9594
4
1.1612
35
1.0290
227
1.0048
189
1.0031
180
0.9895
58
1.0039
153
1.0495
156
0.9894
54
0.9733
1
0.9661
6
0.9620
2
0.9691
9
0.9659
10
0.9735
1
0.9705
5
MP2=FULL 1.0618
135
1.0396
164
1.0433
144
1.0347
143
1.0147
193
1.0051
175
0.9981
172
0.9910
186
0.9991
142
1.0276
151
0.9607
3
0.9598
3
1.0560
92
1.0103
162
0.9995
162
0.9909
53
1.0130
110
1.0067
110
0.9908
50
0.9727
1
0.9645
6
0.9598
2
0.9685
9
0.9648
10
0.9727
1
0.9700
5
ROMP2 1.0381
20
1.0910
20
1.0910
20
1.0772
20
1.0722
20
1.0570
20
0.9851
21
0.9897
20
0.9861
21
1.0534
20
0.9674
1
0.9666
1
0.9908
11
1.0415
22
0.9860
19
0.9825
4
0.9861
20
0.9834
6
0.9753
4
        0.9707
1
0.9732
1
 
MP3 1.0293
3
0.9950
3
0.9950
3
0.9788
3
1.0094
176
0.9632
3
1.0326
222
0.9586
3
0.9586
3
0.9594
3
0.9581
3
0.9578
3
0.9975
31
1.0364
32
0.9937
31
0.9570
3
0.9662
3
0.9603
3
0.9578
3
  0.9580
5
0.9552
2
  0.9639
1
0.9659
1
 
MP3=FULL   0.9919
9
0.9919
9
0.9788
9
1.0449
218
0.9638
11
1.0350
213
0.9605
11
0.9595
11
0.9605
11
    0.9982
30
1.0379
31
0.9929
30
  0.9666
11
0.9594
11
    0.9529
2
0.9529
2
  0.9632
1
0.9652
1
 
MP4 1.0299
6
1.0417
120
1.0001
10
0.9846
10
1.0625
140
0.9681
4
0.9699
4
0.9618
21
1.0121
108
0.9602
5
0.9634
3
0.9630
3
1.0187
58
1.0418
58
1.0084
113
0.9623
3
1.0240
54
0.9932
44
0.9635
3
0.9735
1
0.9655
4
0.9628
2
0.9737
1
1.7041
5
0.9747
1
 
MP4=FULL 1.0333
3
1.0737
58
0.9997
3
0.9825
3
1.0526
59
0.9651
3
0.9669
3
0.9627
3
1.0130
59
0.9614
3
0.9624
3
0.9616
3
0.9741
1
1.0426
57
1.0187
52
0.9607
3
1.0225
55
0.9895
45
0.9622
3
  0.9597
2
0.9605
2
  2.7976
2
0.9739
1
 
B2PLYP 1.0803
43
1.0912
43
1.0886
43
1.0797
43
1.0681
166
1.0655
43
1.0280
44
1.0281
43
1.0280
43
1.0334
60
0.9630
3
0.9629
3
1.0308
43
1.0622
44
1.0501
176
0.9623
3
1.0425
36
0.9843
50
0.9630
3
        0.9726
1
0.9742
1
 
B2PLYP=FULL 1.0803
43
1.0708
44
1.0886
43
1.0797
43
1.0513
44
1.0652
43
1.0277
44
1.0280
43
1.0276
43
1.0616
43
0.9701
1
0.9698
1
1.0307
43
1.0619
44
1.0268
43
0.9694
1
1.0423
36
0.9947
33
0.9702
1
        0.9724
1
0.9740
1
 
B2PLYP=FULLultrafine 1.0222
11
0.9957
11
0.9957
11
0.9798
11
0.9829
86
0.9690
11
0.9698
11
0.9655
11
0.9656
11
0.9660
11
    0.9679
11
0.9720
11
0.9658
11
  0.9701
11
0.9664
11
               
Configuration interaction CID 1.0262
5
1.0397
134
1.0376
132
1.0273
132
1.0222
169
0.9618
5
0.9625
5
0.9885
145
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
 
CISD 1.0264
5
1.0392
141
1.0388
133
1.0281
133
1.0189
167
0.9592
5
0.9633
5
0.9915
136
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
 
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 Sadlej_pVTZ
Quadratic configuration interaction QCISD 1.0308
16
1.0524
173
1.0439
140
1.0210
137
1.0377
167
1.0109
147
0.9992
152
0.9943
158
1.0091
143
1.0091
138
0.9610
3
0.9606
3
1.0547
91
1.0477
168
1.0282
143
0.9596
3
1.0183
92
0.9771
88
0.9605
3
0.9713
1
0.9622
6
0.9584
2
0.9742
2
0.9662
3
0.9704
1
 
QCISD(T) 1.0361
3
0.9994
7
0.9997
5
0.9793
4
1.0897
134
0.9674
11
1.1211
15
0.9632
29
1.1889
10
0.9635
4
0.9632
3
0.9628
3
1.0714
79
1.0591
116
1.0538
98
0.9620
3
1.0291
82
0.9873
69
0.9631
3
0.9734
1
0.9635
4
0.9614
2
0.9764
2
0.9693
3
0.9741
1
 
QCISD(T)=FULL         1.0564
21
  0.9699
20
            1.0312
22
0.9692
20
0.9646
10
0.9713
20
0.9636
17
0.9593
9
        0.9707
1
0.9734
1
 
QCISD(TQ) 1.0284
2
1.0017
3
1.0017
3
0.9843
3
1.0460
12
0.9668
3
0.9689
12
0.9636
3
0.9631
3
0.9631
3
0.9632
3
0.9628
3
0.9752
1
1.0925
11
0.9670
10
0.9598
5
0.9696
11
0.9634
5
0.9629
3
             
QCISD(TQ)=FULL         1.1021
13
  0.9665
9
            1.0819
12
0.9717
9
0.9550
2
0.9680
10
0.9580
4
               
Coupled Cluster CCD 1.0290
16
1.0418
147
1.0419
138
1.0303
142
1.0373
176
1.0088
147
0.9993
145
0.9934
153
0.9987
130
1.0112
128
0.9595
3
0.9592
3
1.0524
91
1.0239
167
1.0011
122
0.9583
3
1.0125
106
0.9803
89
0.9591
3
0.9697
1
0.9596
5
0.9569
2
0.9726
2
0.9630
4
0.9679
1
 
CCSD 1.0367
3
0.9968
7
0.9977
5
0.9805
5
1.0459
135
0.9661
11
0.9676
14
1.0392
22
0.9599
8
0.9607
37
0.9607
3
0.9603
3
1.0731
61
1.0299
96
1.0042
105
0.9951
31
1.0204
54
0.9801
64
1.0111
21
  0.9618
5
0.9580
2
0.9768
1
0.9678
2
0.9699
1
 
CCSD=FULL 1.0367
3
0.9998
3
0.9998
3
0.9829
3
1.0329
75
0.9650
3
0.9661
3
0.9617
3
0.9608
3
0.9603
35
0.9596
3
0.9588
3
1.0133
60
1.0358
61
0.9986
73
0.9930
33
1.0188
55
0.9774
64
0.9645
19
  0.9588
4
0.9556
2
  0.9671
1
0.9691
1
 
CCSD(T) 1.0368
3
1.1197
27
0.9978
4
0.9792
4
1.1347
151
0.9670
32
1.1413
30
0.9635
28
1.1882
10
0.9608
5
0.9631
5
1.0451
12
1.0708
79
1.0532
115
1.0474
104
0.9938
47
1.0216
97
0.9859
81
0.9956
42
0.9733
1
0.9641
4
0.9612
2
0.9724
7
1.3338
10
0.9740
1
 
CCSD(T)=FULL 1.0368
3
1.0015
3
1.0015
3
0.9838
3
1.0791
104
0.9658
3
0.9673
3
0.9631
3
0.9623
3
0.9619
3
0.9620
3
0.9612
3
1.0726
77
1.0373
89
1.0053
71
0.9919
45
1.0260
83
0.9839
58
0.9947
39
0.9728
1
0.9625
4
0.9589
2
0.9707
6
1.3319
10
0.9732
1
 
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 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 1.0118
187
1.0080
178
0.9851
188
0.9881
190
1.0100
202
1.0048
188
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 1.0349
101
1.0511
105
0.9765
7
0.9665
7
0.9786
7
0.9785
7
B3LYP 1.0232
184
1.0164
177
1.0132
187
1.0111
190
1.0153
195
1.0132
186
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 0.9810
9
0.9742
9
0.9768
9
0.9706
9
0.9773
9
0.9773
9
Moller Plesset perturbation MP2 1.0152
186
1.0192
180
1.0074
184
1.0131
191
1.0243
198
1.0172
186
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 0.9918
3
0.9799
3
0.9868
3
0.9750
3
0.9872
3
0.9873
3
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 0.9906
3
0.9790
3
0.9854
3
0.9739
3
0.9861
3
0.9861
3
CCSD 0.9917
3
0.9798
3
0.9867
3
0.9749
3
0.9873
3
0.9873
3
CCSD=FULL 0.9917
3
0.9798
3
0.9867
3
0.9749
3
0.9872
3
0.9872
3
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.