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Comparison of levels of theory for Si-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 1.6240
4
PM3 1.5314
4
PM6 1.3089
6
composite G2 1.5581
4
G3 1.5581
4
G3B3 1.5584
6
G3MP2 1.4871
1
G4 1.5431
6
CBS-Q 1.5585
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) TZVP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(T+d)Z aug-cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
hartree fock HF 1.5563
6
1.6053
6
1.5383
6
1.6307
6
1.5329
6
1.5324
6
1.5345
6
1.5263
6
1.5266
6
1.5224
6
1.5135
4
1.5383
6
1.5559
6
1.5283
6
1.5223
6
1.5574
6
1.5266
6
1.5430
4
1.4753
3
1.4785
1
1.5033
1
1.4784
1
1.4795
1
1.5923
2
1.5256
6
density functional LSDA 1.5747
5
1.5751
5
1.5457
5
1.6104
5
1.5368
5
1.5368
5
1.5378
5
1.5310
5
1.5310
5
1.5232
5
    1.5569
5
1.5303
5
1.5376
2
1.5566
5
1.5394
2
1.5105
1
  1.5125
1
    1.5143
1
   
BLYP 1.6167
6
1.6323
6
1.5818
6
1.6522
6
1.5684
6
1.5768
6
1.5796
6
1.5720
6
1.5722
6
1.5627
6
1.6015
2
1.6214
2
1.5977
6
1.5711
6
  1.6023
4
1.6102
2
    1.5306
1
    1.5322
1
1.6414
2
1.6097
2
B1B95 1.5897
6
1.5846
2
1.5582
6
1.6262
6
1.5516
6
1.5524
6
1.5543
6
1.5465
6
1.5469
6
1.5405
6
1.5759
2
1.5944
2
1.5742
6
1.5467
6
1.5391
2
1.5498
4
1.5746
3
1.5319
2
  1.5054
1
    1.5067
1
1.5379
1
1.5833
2
B3LYP 1.5964
6
1.6137
6
1.5638
6
1.6330
6
1.5584
6
1.5582
6
1.5611
6
1.5531
6
1.5731
4
1.5454
6
1.5461
4
1.5640
6
1.5796
6
1.5532
6
1.5643
4
1.5812
6
1.5516
6
1.5613
4
1.5095
3
1.5119
1
1.5378
1
1.5121
1
1.5133
1
1.6222
2
1.5912
2
B3LYPultrafine   1.6401
2
    1.5585
6
1.5944
2
1.6012
2
1.5900
2
  1.5811
2
1.5832
2
1.6022
2
1.6163
2
1.5896
2
  1.6230
2
1.5494
6
    1.5119
1
    1.5133
1
1.6222
2
1.5912
2
B3PW91 1.6059
4
1.6125
6
1.5625
6
1.6307
6
1.5561
6
1.5559
6
1.5579
6
1.5504
6
1.5701
4
1.5439
6
1.5809
2
1.5996
2
1.5777
6
1.5508
6
  1.5805
4
1.5890
2
    1.5099
1
    1.5113
1
1.6199
2
1.5887
2
mPW1PW91 1.6015
4
1.6088
6
1.5766
4
1.6270
6
1.5526
6
1.5523
6
1.5545
6
1.5468
6
1.5472
6
1.5406
6
1.5773
2
1.5961
2
1.5744
6
1.5474
6
  1.5769
4
1.5853
2
    1.5064
1
    1.5077
1
1.6161
2
1.5851
2
M06-2X 1.6094
2
1.6259
2
1.5516
6
1.6509
2
1.5468
6
1.5846
2
1.5903
2
1.5800
2
1.5812
2
1.5737
2
1.5346
6
1.5923
2
1.6061
2
1.5806
2
  1.6120
2
1.5820
2
    1.5027
1
    1.5041
1
1.6113
2
1.5817
2
PBEPBE 1.6239
4
1.6304
6
1.5962
4
1.6689
4
1.5736
6
1.5734
6
1.5756
6
1.5680
6
1.5683
6
1.5604
6
1.5619
4
1.6177
2
1.5952
6
1.5677
6
1.5558
2
1.6390
2
1.5702
4
1.5486
2
1.5270
1
1.5282
1
    1.5296
1
1.6382
2
1.6063
2
PBEPBEultrafine   1.6589
2
    1.5741
4
1.6099
2
1.6162
2
1.6054
2
  1.5966
2
1.5980
2
1.6177
2
1.6326
2
1.6047
2
  1.6390
2
1.6066
2
    1.5282
1
    1.5296
1
1.6382
2
1.6063
2
PBE1PBE 1.6207
2
1.5889
2
1.5889
2
1.6593
2
1.5534
6
1.5907
2
1.5955
2
1.5846
2
1.5858
2
1.5779
2
1.5782
2
1.5969
2
1.6128
2
1.5847
2
  1.6181
2
1.5862
2
    1.5074
1
    1.5087
1
1.6173
2
1.5859
2
HSEh1PBE 1.6213
2
1.6104
6
1.5890
2
1.6597
2
1.5538
6
1.5902
2
1.5558
6
1.5851
2
1.5863
2
1.5777
2
1.5784
2
1.5974
2
1.6130
2
1.5486
6
  1.6185
2
1.5865
2
    1.5075
1
    1.5089
1
1.6177
2
1.5862
2
TPSSh 1.6318
2
1.6456
2
1.5972
2
1.6680
2
1.5565
6
1.5975
2
1.5579
6
1.5932
2
1.5942
2
1.5462
6
1.5862
2
1.6046
2
1.6202
2
1.5516
6
1.5868
2
1.6256
2
1.5939
2
1.5874
2
  1.5158
1
    1.5172
1
1.6249
2
1.5937
2
wB97X-D 1.6195
2
1.6326
2
1.5524
6
1.6546
2
1.5471
6
1.5875
2
1.5494
6
1.5824
2
1.5428
6
1.5747
2
1.5758
2
1.5519
6
1.5549
6
1.5428
6
1.5762
2
1.6158
2
1.5419
6
1.5765
2
  1.5036
1
    1.5050
1
1.6151
2
1.5835
2
B97D3 1.6421
2
1.6177
6
1.6060
2
1.6798
2
1.5659
6
1.6063
2
1.5673
6
1.6016
2
1.5611
6
1.5928
2
1.5510
6
1.5744
6
1.6290
2
1.5597
6
1.5944
2
1.6348
2
1.5617
6
1.5949
2
  1.5230
1
    1.5244
1
1.6341
2
1.5586
6
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) TZVP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(T+d)Z aug-cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Moller Plesset perturbation MP2 1.6103
4
1.6025
6
1.5685
5
1.6314
6
1.5617
6
1.5687
6
1.5735
6
1.5523
6
1.5586
6
1.5571
6
1.5918
2
1.5748
6
1.5961
5
1.5626
6
1.5723
4
1.5997
6
1.5799
4
1.5710
4
1.5238
3
1.5306
1
1.5591
1
1.5275
1
1.5315
1
1.6394
2
1.6013
2
MP2=FULL 1.6107
4
1.6027
6
1.5812
4
1.6459
4
1.5686
6
1.5679
6
1.5728
6
1.5574
6
1.5765
4
1.5700
4
1.5882
2
1.6104
2
1.5910
6
1.5760
4
1.5651
4
1.6001
4
1.5959
2
1.5619
4
1.5193
3
1.5245
1
1.5588
1
1.5243
1
1.5280
1
1.6376
2
1.5940
2
MP3         1.5520
6
  1.5479
6
      1.6455
1
1.6679
1
1.6891
1
1.6514
1
          1.4999
1
    1.5007
1
1.6985
1
1.6545
1
MP3=FULL   1.7010
1
1.6482
1
1.7355
1
1.5468
6
1.6622
1
1.5485
6
1.6489
1
1.6511
1
1.6434
1
1.6417
1
1.6664
1
1.6871
1
1.6468
1
  1.6975
1
1.6488
1
    1.4951
1
    1.4981
1
1.6958
1
1.6457
1
MP4   1.6163
3
    1.5828
6
    1.5574
1
1.6007
3
  1.6572
1
1.6789
1
1.6975
1
1.5728
6
  1.7123
1
1.6672
1
    1.5461
1
    1.5472
1
1.7108
1
1.6669
1
MP4=FULL   1.7101
1
    1.6732
1
      1.6600
1
  1.6533
1
  1.6953
1
1.6572
1
  1.7093
1
1.6612
1
    1.5397
1
    1.5441
1
1.7077
1
1.6576
1
B2PLYP 1.6288
2
1.6482
2
1.5967
2
1.6740
2
1.5618
6
1.5986
2
1.6056
2
1.5919
2
1.5932
2
1.5855
2
1.5865
2
1.6058
2
1.6214
2
1.5511
6
  1.6296
2
1.5953
2
    1.5204
1
    1.5217
1
1.6288
2
1.5950
2
B2PLYP=FULL 1.6289
2
1.6483
2
1.5966
2
1.6741
2
1.5995
2
1.5984
2
1.6053
2
1.5917
2
1.5930
2
1.5841
2
1.5855
2
1.6056
2
1.6211
2
1.5916
2
  1.6291
2
1.5937
2
    1.5187
1
    1.5207
1
1.6282
2
1.5930
2
B2PLYP=FULLultrafine 1.6289
2
1.6483
2
1.5966
2
1.6741
2
1.5616
6
1.5984
2
1.6053
2
1.5917
2
1.5930
2
1.5841
2
1.5855
2
1.6056
2
1.5838
6
1.5548
6
  1.6291
2
1.5536
6
    1.5187
1
    1.5207
1
1.6282
2
1.5930
2
Configuration interaction CID   1.6239
4
1.5748
3
1.6266
3
1.5504
6
    1.5613
4
    1.5694
2
  1.6073
2
1.5755
2
          1.4994
1
    1.5002
1
1.6153
2
1.5778
2
CISD   1.6292
4
1.5776
3
1.6491
4
1.5523
6
    1.5632
4
    1.5713
2
  1.6104
2
1.5775
2
          1.5020
1
    1.5028
1
1.6178
2
1.5796
2
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) TZVP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(T+d)Z aug-cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Quadratic configuration interaction QCISD   1.6288
6
1.5904
4
1.6743
4
1.5635
6
1.5853
4
1.5673
6
1.5524
6
1.5527
6
1.5701
4
1.5825
2
1.6046
2
1.5879
6
1.5527
6
  1.6330
2
1.5916
2
  1.5136
1
1.5160
1
    1.5168
1
1.6320
2
1.5913
2
QCISD(T)         1.5701
6
    1.5927
2
    1.5885
2
1.6095
2
1.6145
4
1.5785
4
  1.6189
4
1.5783
4
    1.5242
1
    1.5252
1
1.6373
2
1.5976
2
QCISD(T)=FULL         1.6048
2
  1.6092
2
      1.5854
2
  1.6267
2
1.5909
2
1.5807
2
1.6366
2
1.5927
2
1.5801
2
  1.5186
1
    1.5222
1
1.6354
2
1.5907
2
Coupled Cluster CCD   1.6232
4
1.5783
3
1.6357
4
1.5562
6
1.5777
4
1.5805
4
1.5660
4
1.5664
4
1.5646
4
1.5764
2
1.5966
2
1.5783
6
1.5682
4
  1.6071
4
1.5680
4
    1.5069
1
1.5338
1
1.5048
1
1.5077
1
1.6233
2
1.5852
2
CCSD         1.5595
6
1.5951
2
1.6021
2
1.5842
2
1.5851
2
1.5820
2
1.5792
2
1.6000
2
1.6179
2
1.5852
2
1.5783
2
1.6277
2
1.5881
2
    1.5104
1
    1.5113
1
1.6267
2
1.5879
2
CCSD=FULL         1.5967
2
        1.5777
2
1.5760
2
1.5989
2
1.6167
2
1.5816
2
1.5714
2
1.6261
2
1.5828
2
1.5706
2
  1.5051
1
    1.5082
1
1.6249
2
1.5126
1
CCSD(T)   1.5966
1
    1.5661
4
1.5651
4
1.6089
2
1.5912
2
1.5923
2
1.5895
2
1.5871
2
1.6078
2
1.6118
4
1.5584
6
1.5863
2
1.6167
4
1.5764
4
1.5875
2
1.5189
1
1.5219
1
1.5532
1
1.5201
1
1.5229
1
1.6356
2
1.5961
2
CCSD(T)=FULL         1.5872
4
          1.5840
2
1.6067
2
1.6249
2
1.5895
2
1.5794
2
1.6349
2
1.5912
2
1.5787
2
  1.5163
1
1.5528
1
1.5173
1
1.5198
1
1.6338
2
1.5893
2
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) TZVP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(T+d)Z aug-cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ

average calculated bond lengths (Å)
Methods with effective core potentials (select basis sets)
CEP-31G CEP-31G* CEP-121G CEP-121G* LANL2DZ SDD cc-pVTZ-PP aug-cc-pVTZ-PP Def2TZVPP
hartree fock HF 1.6258
6
1.5396
6
1.6258
6
1.5402
6
1.5988
6
1.6158
6
    1.5205
6
density functional BLYP                 1.6006
2
B1B95 1.5859
3
1.5252
3
            1.5756
2
B3LYP 1.6300
6
1.5653
6
1.6297
6
1.5663
6
1.6044
6
1.6201
6
    1.5431
6
B3LYPultrafine                 1.5826
2
B3PW91                 1.5805
2
mPW1PW91                 1.5770
2
M06-2X                 1.5743
2
PBEPBE                 1.5549
6
PBEPBEultrafine                 1.5972
2
PBE1PBE                 1.5779
2
HSEh1PBE                 1.5781
2
TPSSh                 1.5856
2
wB97X-D 1.6532
2
1.5987
2
1.6512
2
1.5975
2
1.6280
2
1.6380
2
    1.5755
2
B97D3                 1.5936
2
Moller Plesset perturbation MP2 1.6386
6
1.5773
6
1.6444
5
1.5782
6
1.6144
6
1.6279
6
    1.5510
6
MP2=FULL                 1.5888
2
MP3                 1.6455
1
MP3=FULL                 1.6424
1
MP4                 1.6564
1
MP4=FULL                 1.6532
1
B2PLYP                 1.5862
2
B2PLYP=FULL                 1.5853
2
B2PLYP=FULLultrafine                 1.5853
2
Configuration interaction CID                 1.5700
2
CISD                 1.5719
2
Quadratic configuration interaction QCISD                 1.5831
2
QCISD(T)                 1.5890
2
QCISD(T)=FULL                 1.5863
2
Coupled Cluster CCD                 1.5770
2
CCSD                 1.5797
2
CCSD=FULL                 1.5770
2
CCSD(T)                 1.5874
2
CCSD(T)=FULL                 1.5848
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.