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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 1.1073
73
PM3 1.0538
164
PM6 1.0986
197
composite G2 1.0606
186
G3 1.0196
168
G3B3 1.0751
216
G4 1.0671
193
CBS-Q 1.0229
151
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 Sadlej_pVTZ
hartree fock HF 1.0752
168
1.0612
211
1.0382
172
1.0278
169
1.0393
432
1.0133
173
1.0445
205
1.0077
175
1.0115
170
1.0121
170
1.0158
109
1.2005
36
1.0532
226
1.0172
172
1.0126
168
0.9977
78
1.0159
166
1.0371
188
1.0155
74
0.9499
1
1.4100
6
2.3352
2
0.9551
3
0.9489
4
0.9454
5
ROHF 1.0147
6
0.9840
21
0.9842
22
0.9711
20
0.9661
26
0.9583
22
0.9603
22
0.9530
22
0.9600
17
0.9569
7
0.9502
1
0.9505
1
0.9589
7
0.9641
20
0.9578
20
0.9657
11
0.9627
17
0.9610
16
0.9659
11
    2.3183
1
     
density functional LSDA 1.1265
200
1.0886
208
1.1011
209
1.0881
203
1.0648
204
1.0748
205
1.0729
205
1.0717
205
1.0711
205
1.0717
203
0.9740
3
0.9737
3
1.1461
60
1.0785
203
1.0693
205
0.9890
8
1.0716
194
1.0672
78
0.9896
8
0.9837
1
1.5342
5
2.3617
2
0.9869
2
0.9796
2
 
SVWN 1.0378
3
1.1260
207
1.0112
3
0.9910
3
1.0960
203
1.1376
64
1.0808
207
1.1329
64
1.1325
64
1.1311
64
0.9740
3
0.9737
3
0.9863
1
1.1413
64
1.1312
64
0.9736
3
1.1438
61
1.1032
53
0.9741
3
  1.5342
5
2.3617
2
0.9900
1
0.9826
1
 
BLYP 1.1437
167
1.0878
174
1.0906
160
1.0706
171
1.0711
175
1.0507
175
1.0499
175
1.0546
159
1.0477
171
1.0475
172
0.9757
3
0.9756
3
1.1536
60
1.0676
170
1.0493
166
0.9752
3
0.9791
63
0.9768
3
0.9755
3
0.9871
1
1.5452
5
2.3895
2
0.9897
2
0.9803
2
 
B1B95 1.1074
190
1.0762
203
1.0730
197
1.0663
200
1.0563
191
1.0557
203
1.0735
201
1.0471
196
1.0483
194
1.0515
192
0.9608
3
0.9610
3
1.1389
58
1.0577
200
1.0491
196
0.9851
18
1.0500
175
1.0533
81
0.9819
18
0.9697
1
1.5200
5
2.3497
2
0.9727
2
0.9652
2
 
B3LYP 1.1179
168
1.1100
209
1.0692
171
1.0540
174
1.0799
212
1.0382
174
1.0648
215
1.0340
175
1.0688
116
1.0400
173
0.9631
58
1.1980
34
1.0692
222
1.0416
173
1.0358
169
1.0312
80
1.0656
143
1.0831
163
1.0356
74
0.9751
1
1.4353
6
2.3652
2
0.9780
2
0.9690
4
0.9684
5
B3LYPultrafine 1.0353
3
1.1754
36
1.0037
3
0.9830
3
1.0722
201
0.9702
3
1.0922
63
0.9672
3
0.9665
3
0.9669
3
0.9653
3
1.1845
36
1.4450
8
1.1838
41
1.0789
77
0.9648
3
1.1871
40
1.0569
200
0.9651
3
  2.3682
2
2.3655
2
     
B3PW91 1.1392
115
1.0695
171
1.0655
172
1.0526
172
1.0399
172
1.0356
174
1.0407
161
1.0320
175
1.0665
116
1.0335
171
0.9634
3
0.9635
3
1.1362
60
1.0410
170
1.0338
169
0.9632
3
0.9667
63
0.9646
3
0.9635
3
0.9730
1
1.5263
5
2.3617
2
0.9760
2
0.9680
2
 
mPW1PW91 1.1350
122
1.0660
173
1.0879
128
1.0494
172
1.0535
172
1.0329
174
1.0323
174
1.0291
175
1.0300
172
1.0309
171
0.9611
3
0.9612
3
1.1335
60
1.0384
170
1.0419
147
0.9609
3
1.0432
133
1.0718
65
0.9612
3
0.9705
1
1.8955
3
2.3575
2
0.9735
2
0.9657
2
 
M06-2X 1.1434
68
1.1491
67
1.1376
69
1.1381
67
1.0897
205
1.1121
70
1.1149
69
1.1088
70
1.1092
70
1.1084
70
0.9625
3
0.9626
3
1.1353
60
1.1180
69
1.1109
69
0.9623
3
1.1198
67
1.0831
59
0.9626
3
0.9711
1
1.4279
6
2.3473
2
0.9747
2
0.9678
2
 
PBEPBE 1.1631
115
1.1265
203
1.1127
122
1.1031
117
1.0804
201
1.0483
173
1.0728
204
1.0446
174
1.0445
172
1.0933
171
0.9723
61
1.3694
32
1.1488
60
1.0519
173
1.0538
173
0.9992
18
1.1144
86
1.0931
133
0.9955
18
0.9849
1
1.6833
4
2.3847
2
0.9873
2
0.9788
2
0.9771
5
PBEPBEultrafine 1.0453
3
1.1780
36
1.0150
3
0.9929
3
1.0778
181
0.9782
3
1.1631
40
0.9760
3
0.9748
3
0.9753
3
0.9737
3
1.1834
36
1.4543
8
1.1932
41
1.1856
41
0.9736
3
1.1965
40
1.1798
71
0.9739
3
  2.3881
2
2.3849
2
     
PBE1PBE 1.1764
54
1.1478
54
1.1478
54
1.1485
52
1.0828
196
1.1270
54
1.1251
54
1.1202
54
1.1212
54
1.1208
54
0.9619
3
0.9620
3
1.1370
50
1.1281
54
1.1209
54
0.9618
3
1.1349
51
1.1070
48
0.9621
3
  1.5245
5
2.3592
2
0.9770
1
0.9695
1
 
HSEh1PBE 1.1764
67
1.1517
66
1.1410
67
1.1442
65
1.0923
195
1.1174
67
1.1187
67
1.1121
68
1.1128
68
1.1115
68
0.9619
3
0.9621
3
1.1407
58
1.1214
67
1.1121
68
0.9617
3
1.1242
65
1.0853
57
0.9620
3
0.9712
1
1.4312
6
2.3597
2
0.9743
2
0.9666
2
 
TPSSh   1.3825
10
1.3688
10
1.3737
10
1.0841
205
1.3505
10
1.0799
205
1.3466
10
        1.5117
7
1.3562
10
1.0761
205
  1.3535
10
1.3877
9
    2.3652
2
2.3625
2
     
Moller Plesset perturbation MP2 1.1261
114
1.1058
215
1.0658
171
1.0585
169
1.0687
244
1.0351
175
1.0400
362
1.0309
173
1.0311
172
1.0543
149
0.9594
4
1.1612
35
1.0726
227
1.0387
174
1.0542
183
1.0504
49
1.0543
142
1.0786
131
1.0571
45
0.9733
1
1.4321
6
2.3573
2
0.9691
9
0.9653
9
0.9705
5
MP2=FULL 1.1303
111
1.0797
149
1.0939
123
1.0879
122
1.0391
204
1.0408
160
1.0436
157
1.0315
171
1.0642
116
1.0637
117
0.9607
3
0.9598
3
1.1901
62
1.0517
146
1.0549
151
1.0592
44
1.0825
94
1.0629
68
1.0653
41
0.9727
1
1.4283
6
2.3452
2
0.9685
9
0.9642
9
 
ROMP2 1.0433
15
1.0211
15
1.0211
15
1.0064
15
0.9988
15
0.9895
15
0.9898
16
0.9837
15
0.9834
16
0.9845
15
0.9674
1
0.9666
1
0.9844
6
0.9911
16
0.9863
14
0.9825
4
0.9923
15
0.9834
6
0.9753
4
           
MP3 1.0293
3
0.9950
3
0.9950
3
0.9788
3
1.0406
170
0.9632
3
1.0711
210
0.9586
3
0.9586
3
0.9594
3
0.9581
3
0.9578
3
1.4359
8
1.3491
10
1.3372
10
0.9570
3
0.9662
3
0.9603
3
0.9578
3
  1.5171
5
2.3507
2
     
MP3=FULL         1.0805
206
  1.0737
200
          1.5019
7
1.5118
7
1.4959
7
          2.3445
2
2.3398
2
     
MP4 1.0311
7
1.0867
109
1.0001
10
0.9846
10
1.0966
131
0.9681
4
0.9699
4
0.9618
21
1.0531
89
0.9602
5
0.9634
3
0.9630
3
1.1937
36
1.1919
37
1.0407
101
0.9623
3
1.2207
33
1.1080
28
0.9635
3
0.9735
1
1.6673
4
2.3634
2
0.9737
1
1.8872
4
 
MP4=FULL 1.0480
1
1.2416
36
1.0128
1
0.9951
1
1.1968
37
0.9738
1
0.9755
1
0.9713
1
1.1827
37
0.9695
1
0.9695
1
0.9682
1
0.9741
1
1.2107
34
1.1426
31
0.9678
1
1.2279
32
1.1093
27
0.9692
1
  2.3574
2
2.3518
2
  2.7976
2
 
B2PLYP 1.4362
12
1.4126
12
1.4043
12
1.4137
12
1.0972
156
1.3925
12
1.3956
12
1.3861
12
1.3889
12
1.3879
12
    1.3947
12
1.3942
12
1.1014
155
  1.4386
11
1.3538
9
             
B2PLYP=FULL 1.4362
12
1.4126
12
1.4042
12
1.4137
12
1.3968
12
1.3921
12
1.3952
12
1.3859
12
1.3881
12
1.3873
12
    1.3946
12
1.3936
12
1.3887
12
  1.4382
11
1.3528
9
             
B2PLYP=FULLultrafine         1.0174
82
                                       
Configuration interaction CID 1.0262
5
1.0883
118
1.0865
115
1.0781
115
1.0551
158
0.9618
5
0.9625
5
1.0350
131
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
  2.3438
2
2.3432
2
     
CISD 1.0264
5
1.0833
127
1.0872
116
1.0784
116
1.0542
157
0.9592
5
0.9633
5
1.0495
117
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
  2.3457
2
2.3437
2
     
Quadratic configuration interaction QCISD 1.0782
19
1.0923
157
1.0940
121
1.0754
115
1.0768
153
1.0603
125
1.0530
135
1.0440
142
1.0694
124
1.0721
102
0.9610
3
0.9606
3
1.1882
62
1.0940
157
1.0918
117
0.9596
3
1.1158
71
1.0381
54
0.9605
3
0.9713
1
1.4287
6
2.3549
2
0.9742
2
0.9652
2
 
QCISD(T) 1.0361
3
0.9994
7
0.9997
5
0.9793
4
1.1494
122
0.9674
11
1.1211
15
0.9616
22
1.1685
11
0.9639
5
0.9632
3
0.9628
3
1.2067
56
1.1180
97
1.1022
83
0.9620
3
1.0959
61
1.0481
52
0.9631
3
0.9734
1
1.6649
4
2.3613
2
0.9764
2
0.9682
2
 
QCISD(TQ) 1.0284
2
1.0017
3
1.0017
3
0.9843
3
0.9760
3
0.9668
3
0.9682
3
0.9636
3
0.9631
3
0.9631
3
0.9632
3
0.9628
3
0.9752
1
0.9711
3
0.9635
3
0.9620
3
0.9712
3
0.9657
3
0.9629
3
           
Coupled Cluster CCD 1.0765
19
1.0919
127
1.0973
115
1.0850
120
1.0472
160
1.0583
125
1.0598
123
1.0458
136
1.0697
106
1.0693
103
0.9595
3
0.9592
3
1.1856
62
1.0692
156
1.0628
104
0.9583
3
1.0928
85
1.0270
68
0.9591
3
0.9697
1
1.5187
5
2.3521
2
0.9726
2
0.9621
3
 
CCSD 1.0367
3
0.9968
7
0.9976
5
0.9783
5
1.1111
119
0.9661
11
0.9676
14
1.0392
22
0.9599
8
0.9589
5
0.9607
3
0.9603
3
1.2753
38
1.0950
79
1.0571
76
1.1162
25
1.1400
33
1.0860
32
1.1047
17
  1.5213
5
2.3539
2
0.9768
1
0.9678
1
 
CCSD=FULL 1.0367
3
0.9998
3
0.9998
3
0.9829
3
1.1888
40
0.9650
3
0.9661
3
0.9617
3
0.9608
3
0.9604
3
0.9596
3
0.9588
3
1.1899
36
1.1829
38
1.1140
36
1.1141
25
1.1391
33
1.0909
30
1.1520
15
  1.6550
4
2.3427
2
     
CCSD(T) 1.0368
3
1.1160
28
0.9978
4
0.9792
4
1.1925
147
0.9660
25
1.1413
30
0.9623
19
1.1515
12
0.9616
6
0.9630
8
1.0451
12
1.2030
57
1.1164
98
1.0978
92
1.0653
42
1.0686
80
1.0405
73
1.0760
37
0.9733
1
1.6653
4
2.3608
2
0.9729
5
1.4913
7
 
CCSD(T)=FULL 1.0368
3
1.0015
3
1.0015
3
0.9838
3
1.1431
86
0.9658
3
0.9673
3
0.9631
3
0.9623
3
0.9619
3
0.9620
3
0.9612
3
1.2060
56
1.0802
68
1.0722
52
1.0728
37
1.0907
62
1.0579
42
1.0855
33
0.9728
1
1.6607
4
2.3494
2
0.9708
4
1.4890
7
 

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 1.0329
172
1.0257
162
1.0268
173
1.0335
179
1.0364
192
1.0287
173
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 1.0670
107
1.0810
110
1.0842
9
1.0689
9
1.0855
9
1.0855
9
B3LYP 1.0631
170
1.0518
161
1.0559
172
1.0560
179
1.0499
185
1.0467
171
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
Moller Plesset perturbation MP2 1.0535
171
1.0520
164
1.0498
169
1.0575
180
1.0582
188
1.0501
171
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 1.0036
1
0.9888
1
1.0002
1
0.9845
1
1.0011
1
1.0011
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.