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III.G.1.a.

Comparison of levels of theory for S-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 1.4481
23
PM3 1.4885
51
PM6 1.4862
57
composite G2 1.4650
49
G3 1.4635
60
G3B3 1.5042
60
G4 1.4749
59
CBS-Q 1.4579
52

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 1.7001
60
1.5876
60
1.4686
60
1.6335
57
1.4601
131
1.4632
60
1.4634
60
1.4559
60
1.4560
60
1.4385
60
1.4310
29
1.3929
2
1.4755
57
1.4772
60
1.4473
60
1.4284
21
1.4810
60
1.4398
53
1.4255
18
1.4323
4
1.4274
21
1.4260
3
  1.4678
4
1.4262
2
ROHF 1.6373
13
1.5891
18
1.4742
18
1.6368
17
1.4665
17
1.4664
17
1.4658
18
1.4590
17
1.4590
17
1.4187
13
    1.4684
1
1.4795
18
1.4414
18
1.4190
14
1.4846
17
1.4230
14
1.4075
11
1.4600
2
         
density functional LSDA 1.6595
60
1.5919
60
1.5041
60
1.6479
60
1.5021
60
1.5027
60
1.5036
60
1.4963
60
1.4965
60
1.4796
60
1.4384
2
1.4384
2
1.4947
10
1.5187
60
1.4869
57
1.4767
15
1.5196
56
1.4741
22
1.4651
14
1.4742
4
1.4856
5
1.4252
1
     
SVWN 1.6183
2
1.6111
54
1.4712
2
1.6129
2
1.4985
51
1.4893
10
1.5137
50
1.4823
10
1.4823
10
1.4675
10
1.4384
2
1.4384
2
1.4730
2
1.5055
10
1.4752
10
  1.5083
10
1.4476
6
    1.4856
5
1.4252
1
     
BLYP 1.7025
60
1.6460
57
1.5320
52
1.6879
57
1.5322
60
1.5321
60
1.5357
58
1.5226
52
1.5266
60
1.5065
60
1.4610
2
1.4610
2
1.5252
10
1.5494
60
1.5164
60
  1.5484
28
1.4769
2
  1.4933
4
1.5163
5
1.4432
1
     
B1B95 1.6513
56
1.5579
56
1.4950
56
1.6420
56
1.4910
55
1.4917
56
1.4925
56
1.4853
56
1.4854
56
1.4709
55
1.4265
2
1.4265
2
1.4822
10
1.5066
56
1.4768
56
1.4683
18
1.5064
51
1.4635
23
1.4645
18
1.4635
4
1.4694
10
1.4593
3
1.5156
2
1.4823
2
 
B3LYP 1.6762
60
1.6224
60
1.5075
60
1.6619
60
1.5053
60
1.5044
60
1.5065
58
1.4983
60
1.5024
33
1.4808
60
1.4719
28
1.4367
2
1.5172
57
1.5211
60
1.4894
60
1.4800
18
1.5210
41
1.4780
34
1.4764
18
1.4731
4
1.4672
21
1.4673
3
  1.5091
4
1.4746
2
B3LYPultrafine 1.6185
2
1.5823
2
1.4685
2
1.6113
2
1.5052
59
1.4636
2
1.4929
17
1.4569
2
1.4569
2
1.4425
2
1.4367
2
1.4367
2
1.4863
3
1.5211
8
1.4748
30
  1.5242
8
1.4776
52
    1.4231
1
1.4240
1
     
B3PW91 1.6670
30
1.6158
60
1.5020
60
1.6539
60
1.4987
60
1.4987
60
1.4962
52
1.4922
60
1.4961
33
1.4776
60
1.4333
2
1.4333
2
1.4907
10
1.5144
60
1.4846
60
  1.5143
28
1.4475
2
  1.4690
4
1.4861
6
1.4216
1
     
mPW1PW91 1.6583
33
1.6077
60
1.5042
33
1.6443
60
1.4947
60
1.4945
60
1.4956
60
1.4882
60
1.4883
60
1.4735
60
1.4287
2
1.4287
2
1.4854
10
1.5095
60
1.4793
41
  1.5119
38
1.4385
6
  1.4648
4
1.4174
1
1.4183
1
     
M06-2X 1.6305
13
1.5866
13
1.4938
13
1.6159
13
1.4997
61
1.4913
13
1.4924
13
1.4856
13
1.4856
13
1.4745
13
1.4233
2
1.4233
2
1.4788
10
1.5040
13
1.4807
13
  1.5073
13
1.4345
6
    1.4789
5
1.4157
1
     
PBEPBE 1.6926
33
1.6401
60
1.5304
33
1.6829
33
1.5213
60
1.5213
60
1.5223
60
1.5153
60
1.5155
60
1.4985
60
1.4882
28
1.4552
2
1.5145
10
1.5404
57
1.5066
60
1.4977
16
1.5460
13
1.4782
15
1.4871
14
1.4872
4
1.4636
4
1.4394
1
    1.4943
2
PBEPBEultrafine 1.6360
2
1.6045
2
1.4889
2
1.6338
2
1.5088
58
1.4829
2
1.4846
2
1.4765
2
1.4765
2
1.4619
2
1.4551
2
1.4551
2
1.5044
3
1.5395
8
1.5086
8
  1.5428
8
1.4763
4
    1.4385
1
1.4393
1
     
PBE1PBE 1.6551
8
1.5239
8
1.4960
8
1.6368
8
1.4938
52
1.4941
8
1.4952
8
1.4874
8
1.4874
8
1.4748
8
1.4292
2
1.4292
2
1.4998
8
1.5092
8
1.4810
8
  1.5125
8
1.4508
4
    1.4819
5
1.4190
1
     
HSEh1PBE 1.6427
13
1.5945
13
1.4991
13
1.6252
13
1.5034
53
1.4969
13
1.4980
13
1.4911
13
1.4910
13
1.4794
13
1.4298
2
1.4298
2
1.4867
10
1.5106
13
1.4852
13
  1.5135
13
1.4395
6
    1.4825
5
1.4192
1
     
TPSSh   1.6286
1
1.5425
1
1.6406
1
1.5002
55
1.5201
1
1.5009
55
1.5149
1
        1.5203
1
1.5314
1
1.4910
55
  1.5302
1
1.5015
1
             
Moller Plesset perturbation MP2 1.6665
33
1.6167
60
1.5028
57
1.6542
60
1.5079
71
1.5043
60
1.5044
114
1.4942
57
1.4920
60
1.4779
46
1.4460
2
1.4460
2
1.5165
61
1.5173
60
1.4935
55
1.4835
12
1.5270
41
1.4792
23
1.4805
9
1.4814
4
1.4690
21
1.4703
3
1.5125
4
1.4866
8
1.4954
2
MP2=FULL 1.6639
35
1.6177
41
1.5116
35
1.6535
35
1.5062
71
1.4996
52
1.5034
52
1.4911
60
1.4948
33
1.4772
35
1.4438
2
1.4438
2
1.5069
14
1.5150
41
1.4935
48
1.4879
10
1.5174
20
1.4709
20
1.4820
9
1.4806
4
1.4653
21
1.4658
3
1.5120
4
1.4840
8
 
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
2
         
MP3 1.6259
2
1.5669
2
1.4497
2
1.5970
2
1.4893
59
1.4470
2
1.4906
55
1.4330
2
1.4330
2
1.4252
2
1.4182
2
1.4182
2
1.4673
3
1.4792
3
1.4483
3
  1.4699
2
1.4330
2
    1.4735
5
1.4116
1
     
MP3=FULL         1.4893
55
  1.4901
55
          1.5026
1
1.5157
1
1.4802
1
                   
MP4 1.6286
2
1.6473
32
1.5137
2
1.6628
2
1.5144
39
1.4930
2
1.4979
2
1.5006
4
1.5100
31
1.4622
2
1.4568
2
1.4568
2
1.5230
8
1.5317
8
1.4892
27
  1.5438
8
1.4769
4
  1.5007
4
1.4775
2
1.4357
1
  1.5095
4
 
MP4=FULL 1.6284
2
1.6281
8
1.5129
2
1.6625
2
1.5135
8
1.4911
2
1.4958
2
1.4811
2
1.5040
8
1.4586
2
1.4546
2
1.4546
2
1.5022
2
1.5302
8
1.4937
8
  1.5409
8
1.4721
4
    1.4286
1
1.4314
1
  1.5065
4
 
B2PLYP 1.7372
4
1.6383
4
1.5289
4
1.6976
4
1.5138
43
1.5341
4
1.5397
4
1.5269
4
1.5273
4
1.5109
4
    1.5435
4
1.5516
4
1.4979
49
  1.5597
4
               
B2PLYP=FULL 1.7371
4
1.6382
4
1.5287
4
1.6975
4
1.5338
4
1.5334
4
1.5390
4
1.5267
4
1.5270
4
1.5098
4
    1.5433
4
1.5512
4
1.5185
4
  1.5589
4
               
B2PLYP=FULLultrafine         1.4920
28
                                       
Configuration interaction CID 1.5820
3
1.6022
35
1.4912
35
1.6415
35
1.4750
52
1.4401
2
1.4417
2
1.4668
35
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
1.6125
32
1.4905
35
1.6489
35
1.4770
52
  1.4439
2
1.4685
34
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
     
Quadratic configuration interaction QCISD 1.6412
3
1.6226
45
1.5077
32
1.6870
26
1.4967
44
1.5020
30
1.5022
34
1.4832
38
1.4814
48
1.4750
30
1.4295
2
1.4295
2
1.4996
14
1.5145
34
1.4747
36
  1.5075
10
1.4532
4
  1.4706
4
1.4709
9
1.4212
1
     
QCISD(T) 1.6684
2
1.6286
2
1.4832
2
1.6645
2
1.5128
35
1.4725
2
1.4752
2
1.4792
5
1.4597
2
1.4470
2
1.4405
2
1.4405
2
1.5087
14
1.5234
31
1.4928
28
  1.5336
24
1.4812
16
    1.4654
2
1.4282
1
     
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
1.6142
34
1.4971
35
1.6522
35
1.4877
52
1.4914
35
1.4912
32
1.4768
33
1.4788
35
1.4624
33
1.4224
2
1.4224
2
1.4921
14
1.5014
33
1.4665
30
  1.5096
29
1.4566
22
  1.4640
4
1.4637
9
1.4550
3
  1.4917
4
 
CCSD 1.6392
2
1.5909
2
1.4628
2
1.6264
2
1.4862
33
1.4570
2
1.4594
2
1.4723
4
1.4439
2
1.4331
2
1.4264
2
1.4264
2
1.5084
12
1.4953
10
1.4636
10
1.4793
1
1.5186
8
1.4503
4
1.4795
1
  1.4804
6
1.4184
1
     
CCSD=FULL 1.6389
2
1.5906
2
1.4622
2
1.6260
2
1.4945
8
1.4557
2
1.4580
2
1.4431
2
1.4431
2
1.4304
2
1.4241
2
1.4241
2
1.4979
8
1.5084
8
1.4733
8
1.4770
1
1.5163
8
1.4461
4
1.4766
1
  1.4745
5
1.4141
1
     
CCSD(T) 1.6936
2
1.6283
3
1.4791
2
1.6555
2
1.5023
37
1.4968
5
1.4891
3
1.4780
5
1.4753
3
1.4451
2
1.4638
4
1.4386
2
1.5071
14
1.5245
35
1.4864
33
1.4966
2
1.5322
30
1.4784
14
1.4967
2
1.4582
2
1.4650
6
1.4706
3
1.5073
4
1.4844
8
 
CCSD(T)=FULL 1.6932
2
1.6200
2
1.4786
2
1.6551
2
1.5286
29
1.4688
2
1.4714
2
1.4566
2
1.4566
2
1.4421
2
1.4365
2
1.4365
2
1.5062
14
1.5164
14
1.4722
11
1.4944
2
1.5255
14
1.4657
5
1.4937
2
1.4852
4
1.4615
6
1.4875
2
1.5065
4
1.4819
8
 

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 1.6620
55
1.4756
58
1.6584
58
1.4750
58
1.6281
58
1.6210
58
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 1.6643
30
1.5007
28
1.6312
3
1.4812
3
1.6242
3
1.6079
3
B3LYP 1.6832
55
1.5174
58
1.6739
58
1.5168
57
1.6551
58
1.6445
56
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 1.6750
55
1.5189
57
1.6666
58
1.5185
58
1.6529
55
1.6396
55
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.