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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 O-S


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 1.4655
26
PM3 1.5026
25
PM6 1.4924
59
composite G2 1.4701
51
G3 1.4677
62
G3B3 1.5077
62
G4 1.4794
62
CBS-Q 1.4630
54

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 1.7026
62
1.5905
62
1.4722
62
1.6371
59
1.4667
60
1.4674
62
1.4767
35
1.4601
62
1.4602
62
1.4428
62
1.4307
28
1.3929
2
1.4796
59
1.4814
62
1.4515
62
1.4276
20
1.4853
62
1.4448
55
1.4244
17
1.4231
3
1.4267
20
1.4175
2
  1.4678
4
1.4262
2
ROHF 1.6373
13
1.5903
17
1.4738
17
1.6368
17
1.4665
17
1.4664
17
1.4663
17
1.4590
17
1.4590
17
1.4187
13
    1.4684
1
1.4800
17
1.4413
17
1.4190
14
1.4846
17
1.4230
14
1.4075
11
1.4600
1
         
density functional LSDA 1.6644
62
1.5911
62
1.5076
62
1.6525
62
1.5063
62
1.5067
62
1.5078
62
1.5005
62
1.5007
62
1.4837
62
1.4384
2
1.4384
2
1.5189
13
1.5229
62
1.4913
59
1.4767
15
1.5244
58
1.4867
25
1.4651
14
1.4679
3
1.4856
5
1.4252
1
     
SVWN 1.6183
2
1.6157
56
1.4712
2
1.6129
2
1.5035
53
1.5129
13
1.5183
52
1.5068
13
1.5070
13
1.4907
13
1.4384
2
1.4384
2
1.5177
53
1.5295
13
1.4988
13
  1.5328
13
1.4915
9
    1.4856
5
1.4252
1
     
BLYP 1.7079
62
1.6513
59
1.5370
54
1.6937
59
1.5242
65
1.5369
62
1.5409
60
1.5286
54
1.5317
62
1.5113
62
1.4610
2
1.4610
2
1.5535
13
1.5543
62
1.5213
62
  1.5482
27
1.5650
5
  1.4886
3
1.5163
5
1.4432
1
     
B1B95 1.6563
58
1.5581
58
1.4989
58
1.6466
58
1.4957
57
1.4962
58
1.4970
58
1.4899
58
1.4899
58
1.4754
57
1.4265
2
1.4265
2
1.5068
13
1.5112
58
1.4813
58
1.4674
17
1.5116
53
1.4896
39
1.4634
17
1.4559
3
1.4681
9
1.4485
2
1.5156
1
1.4823
1
 
B3LYP 1.6809
62
1.6264
62
1.5114
62
1.6663
62
1.5096
59
1.5088
62
1.5113
60
1.5029
62
1.5104
36
1.4853
62
1.4712
27
1.4367
2
1.5218
59
1.5257
62
1.4940
62
1.4793
17
1.5279
43
1.4992
58
1.4755
17
1.4662
3
1.4661
20
1.4565
2
  1.5091
4
1.4746
2
B3LYPultrafine 1.6185
2
1.6571
5
1.4685
2
1.6113
2
1.5097
61
1.5457
5
1.5096
20
1.5413
5
1.4569
2
1.4425
2
1.4367
2
1.4367
2
1.5477
6
1.5476
11
1.4849
33
  1.5512
11
1.4836
55
    1.4231
1
1.4240
1
     
B3PW91 1.6736
33
1.6198
62
1.5058
62
1.6583
62
1.5031
62
1.5030
62
1.5014
54
1.4967
62
1.5039
36
1.4819
62
1.4333
2
1.4333
2
1.5159
13
1.5189
62
1.4890
62
  1.5141
27
1.4469
8
  1.4621
3
1.4861
6
1.4216
1
     
mPW1PW91 1.6643
36
1.6116
62
1.5108
36
1.6487
62
1.4990
62
1.4988
62
1.5000
62
1.4926
62
1.4927
62
1.4778
62
1.4287
2
1.4287
2
1.5102
13
1.5139
62
1.4856
43
  1.5189
40
1.4835
9
  1.4576
3
1.4174
1
1.4183
1
     
M06-2X 1.6447
16
1.6028
16
1.4989
57
1.6332
16
1.5025
59
1.5076
16
1.5088
16
1.5024
16
1.5024
16
1.4839
19
1.4233
2
1.4233
2
1.5031
13
1.5209
16
1.4896
19
  1.5243
16
1.4722
12
    1.4789
5
1.4157
1
     
PBEPBE 1.6993
36
1.6447
62
1.5378
36
1.6905
36
1.5260
62
1.5259
62
1.5271
62
1.5200
62
1.5203
62
1.5031
62
1.4876
27
1.4552
2
1.5410
13
1.5453
59
1.5113
62
1.4977
16
1.5643
16
1.4990
17
1.4871
14
1.4821
3
1.4499
3
1.4394
1
    1.4943
2
PBEPBEultrafine 1.6360
2
1.6827
5
1.4889
2
1.6338
2
1.5222
37
1.5649
5
1.5681
5
1.5614
5
1.4765
2
1.4619
2
1.4551
2
1.4551
2
1.5670
6
1.5663
11
1.5352
11
  1.5703
11
1.5328
7
    1.4385
1
1.4393
1
     
PBE1PBE 1.6750
11
1.5401
11
1.5198
11
1.6615
11
1.4987
54
1.5194
11
1.5203
11
1.5130
11
1.5133
11
1.4995
11
1.4292
2
1.4292
2
1.5250
11
1.5346
11
1.5058
11
  1.5382
11
1.5033
7
    1.4819
5
1.4190
1
     
HSEh1PBE 1.6591
16
1.6092
55
1.5151
16
1.6447
16
1.5080
55
1.5138
16
1.5089
55
1.5083
16
1.5084
16
1.4956
16
1.4298
2
1.4298
2
1.5114
13
1.5281
16
1.4950
55
  1.5313
16
1.4845
9
    1.4825
5
1.4192
1
     
TPSSh   1.6936
4
1.5880
4
1.7249
4
1.5056
58
1.5825
4
1.5063
58
1.5790
4
  1.4917
59
    1.5881
4
1.5990
4
1.4960
58
  1.6018
4
1.5675
4
             
wB97X-D     1.5038
65
  1.5019
65
      1.4980
65
          1.4930
65
    1.4931
65
             
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
Moller Plesset perturbation MP2 1.6710
36
1.6205
62
1.5066
59
1.6589
62
1.5092
63
1.5084
62
1.5094
62
1.5005
62
1.4961
62
1.4816
49
1.4460
2
1.4460
2
1.5191
59
1.5216
62
1.4997
52
1.4828
11
1.5334
43
1.5008
39
1.4792
8
1.4760
3
1.4679
20
1.4596
2
1.5050
3
1.4859
7
1.4954
2
MP2=FULL 1.6684
38
1.6232
43
1.5179
38
1.6604
38
1.5108
62
1.5043
54
1.5083
54
1.4951
62
1.5022
36
1.4821
40
1.4438
2
1.4438
2
1.5230
17
1.5211
43
1.5001
49
1.4878
9
1.5305
22
1.4832
26
1.4820
9
1.4751
3
1.4642
20
1.4552
2
1.5045
3
1.4832
7
1.4950
2
ROMP2 1.6805
12
1.6164
17
1.5339
17
1.6680
12
1.5155
14
1.5155
14
1.5236
17
1.5032
14
1.5071
17
1.4916
17
    1.5474
1
1.5333
17
1.4960
14
1.4842
10
1.5401
14
1.4995
11
1.4809
10
1.5408
1
         
MP3 1.6259
2
1.5669
2
1.4497
2
1.5970
2
1.4937
61
1.4470
2
1.4955
58
1.4330
2
1.4330
2
1.4252
2
1.4182
2
1.4182
2
1.5251
6
1.5386
6
1.5048
6
  1.4699
2
1.4330
2
    1.4735
5
1.4116
1
     
MP3=FULL         1.4941
58
  1.4949
58
          1.5622
4
1.5763
4
1.5385
4
                   
MP4 1.6286
2
1.6532
35
1.5137
2
1.6628
2
1.5207
41
1.4930
2
1.4979
2
1.4944
3
1.5176
34
1.4622
2
1.4568
2
1.4568
2
1.5468
11
1.5565
11
1.4984
29
  1.5688
11
1.4769
4
  1.4935
3
1.4775
2
1.4357
1
  1.5095
4
 
MP4=FULL 1.6284
2
1.6519
11
1.5129
2
1.6625
2
1.5377
11
1.4911
2
1.4958
2
1.4811
2
1.5288
11
1.4586
2
1.4546
2
1.4546
2
1.5022
2
1.5549
11
1.5175
11
  1.5658
11
1.4721
4
    1.4286
1
1.4314
1
  1.5065
4
 
B2PLYP 1.7227
8
1.6640
8
1.5560
8
1.7133
8
1.5135
48
1.5567
8
1.5609
8
1.5500
8
1.5506
8
1.4897
15
    1.5645
8
1.5736
8
1.4975
57
  1.5809
8
1.4889
11
             
B2PLYP=FULL 1.7393
7
1.6673
7
1.5573
7
1.7204
7
1.5615
7
1.5608
7
1.5657
7
1.5547
7
1.5554
7
1.5369
7
    1.5700
7
1.5786
7
1.5455
7
  1.5863
7
1.5835
3
             
B2PLYP=FULLultrafine         1.4920
28
                                       
Configuration interaction CID 1.5820
3
1.6074
38
1.4975
38
1.6471
38
1.4800
54
1.4401
2
1.4417
2
1.4736
37
1.4276
2
1.4169
2
1.4104
2
1.4104
2
1.4430
2
1.4534
2
1.4227
2
  1.4610
2
1.4242
2
    1.4010
1
1.4026
1
     
CISD 1.5957
3
1.6176
35
1.4970
38
1.6542
38
1.4818
54
  1.4439
2
1.4759
37
1.4299
2
1.4185
2
1.4120
2
1.4120
2
1.4453
2
1.4560
2
1.4244
2
  1.4631
2
1.4258
2
    1.4020
1
1.4035
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 Sadlej_pVTZ
Quadratic configuration interaction QCISD 1.6412
3
1.6272
47
1.5149
35
1.6947
29
1.5006
46
1.5103
33
1.5097
36
1.4899
40
1.4870
50
1.4778
37
1.4295
2
1.4295
2
1.5163
17
1.5221
36
1.4809
39
  1.5330
13
1.4768
12
  1.4635
3
1.4709
9
1.4212
1
     
QCISD(T) 1.6684
2
1.6286
2
1.4832
2
1.6645
2
1.5197
37
1.4725
2
1.4752
2
1.4709
4
1.4597
2
1.4470
2
1.4405
2
1.4405
2
1.5255
17
1.5317
34
1.5011
31
  1.5442
27
1.4812
16
    1.4654
2
1.4282
1
     
QCISD(T)=FULL         1.5983
3
  1.6016
3
            1.6160
3
1.5750
3
  1.6259
3
               
QCISD(TQ) 1.6797
2
1.6095
2
1.4734
2
1.6430
2
1.4671
2
1.4671
2
1.4696
2
1.4541
2
1.4541
2
1.4429
2
1.4362
2
1.4362
2
1.4722
2
1.4835
2
1.4497
2
  1.4937
2
1.4525
2
             
Coupled Cluster CCD 1.6136
4
1.6200
37
1.5038
38
1.6586
38
1.5024
57
1.4988
38
1.4995
35
1.4845
35
1.4863
38
1.4705
36
1.4224
2
1.4224
2
1.5087
17
1.5094
35
1.4753
33
  1.5189
32
1.4696
25
  1.4560
3
1.4624
8
1.4449
2
  1.4917
4
 
CCSD 1.6392
2
1.5909
2
1.4628
2
1.6264
2
1.4919
37
1.4570
2
1.4594
2
1.4629
3
1.4439
2
1.4736
11
1.4264
2
1.4264
2
1.5250
15
1.5207
13
1.4811
16
1.4793
1
1.5448
11
1.4439
9
1.4795
1
  1.4804
6
1.4184
1
     
CCSD=FULL 1.6389
2
1.5906
2
1.4622
2
1.6260
2
1.4969
16
1.4557
2
1.4580
2
1.4431
2
1.4431
2
1.4702
11
1.4241
2
1.4241
2
1.5230
11
1.5344
11
1.4780
16
1.4770
1
1.5422
11
1.4402
9
1.4766
1
  1.4745
5
1.4141
1
     
CCSD(T) 1.6936
2
1.6207
2
1.4791
2
1.6555
2
1.5093
39
1.4904
4
1.4729
2
1.4698
4
1.4574
2
1.4451
2
1.4554
3
1.4386
2
1.5239
17
1.5316
37
1.4937
35
1.4966
2
1.5408
32
1.4766
13
1.4967
2
1.4582
2
1.4598
5
1.4597
2
1.4991
3
1.4834
7
 
CCSD(T)=FULL 1.6932
2
1.6200
2
1.4786
2
1.6551
2
1.5348
29
1.4688
2
1.4714
2
1.4566
2
1.4566
2
1.4421
2
1.4365
2
1.4365
2
1.5230
17
1.5337
16
1.4936
13
1.4944
2
1.5432
16
1.4578
4
1.4937
2
1.4758
3
1.4562
5
1.4875
1
1.4983
3
1.4808
7
 
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

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 1.6642
58
1.4799
61
1.6603
61
1.4793
61
1.6303
61
1.6230
61
density functional LSDA 1.6385
2
1.4915
2
1.6319
2
1.4902
2
1.6188
2
1.5959
2
SVWN 1.6385
2
1.4915
2
1.6319
2
1.4902
2
1.6188
2
1.5959
2
BLYP 1.6594
2
1.5012
2
1.6525
2
1.5005
2
1.6446
2
1.6293
2
B1B95 1.6654
29
1.5007
28
1.6312
3
1.4812
3
1.6242
3
1.6079
3
B3LYP 1.6874
58
1.5222
61
1.6780
61
1.5217
60
1.6592
61
1.6489
59
B3LYPultrafine 1.6269
2
1.4760
2
1.6199
2
1.4756
2
1.6104
2
1.5942
2
B3PW91 1.6211
2
1.4734
2
1.6141
2
1.4726
2
1.6056
2
1.5881
2
mPW1PW91 1.6140
2
1.4679
2
1.6071
2
1.4672
2
1.5988
2
1.5813
2
M06-2X 1.5910
2
1.4497
2
1.5849
2
1.4491
2
1.5843
2
1.5668
2
PBEPBE 1.6493
2
1.4964
2
1.6422
2
1.4953
2
1.6361
2
1.6182
2
PBEPBEultrafine 1.6493
2
1.4964
2
1.6422
2
1.4953
2
1.6361
2
1.6182
2
PBE1PBE 1.6136
2
1.4683
2
1.6067
2
1.4676
2
1.5993
2
1.5814
2
HSEh1PBE 1.6158
2
1.4697
2
1.6088
2
1.4690
2
1.6013
2
1.5830
2
Moller Plesset perturbation MP2 1.6792
59
1.5239
61
1.6706
62
1.5233
62
1.6567
59
1.6441
59
MP2=FULL 1.6475
2
1.4940
2
1.6412
2
1.4932
2
1.6358
2
1.6220
2
MP3 1.6193
2
1.4624
2
1.6070
2
1.4602
2
1.5981
2
1.5786
2
MP4 1.6732
2
1.5071
2
1.6702
2
1.5079
2
1.6634
2
1.6499
2
MP4=FULL 1.6732
2
1.5071
2
1.6702
2
1.5079
2
1.6633
2
1.6503
2
Configuration interaction CID 1.6086
2
1.4541
2
1.5986
2
1.4523
2
1.5907
2
1.5732
2
CISD 1.6167
2
1.4562
2
1.6059
2
1.4543
2
1.5977
2
1.5797
2
Quadratic configuration interaction QCISD 1.6682
2
1.4767
2
1.6565
2
1.4751
2
1.6454
2
1.6244
2
QCISD(T) 1.6856
2
1.4877
2
1.6734
2
1.4865
2
1.6620
2
1.6414
2
QCISD(TQ) 1.6641
2
1.4827
2
1.6525
2
1.4810
2
1.6430
2
1.6227
2
Coupled Cluster CCD 1.6236
2
1.4671
2
1.6146
2
1.4656
2
1.6062
2
1.5884
2
CCSD 1.6479
2
1.4723
2
1.6373
2
1.4706
2
1.6275
2
1.6079
2
CCSD=FULL 1.6479
2
1.4723
2
1.6373
2
1.4706
2
1.6274
2
1.6081
2
CCSD(T) 1.6762
2
1.4854
2
1.6651
2
1.4841
2
1.6552
2
1.6343
2
CCSD(T)=FULL 1.6762
2
1.4854
2
1.6651
2
1.4841
2
1.6552
2
1.6349
2
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.