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Comparison of levels of theory for S-N


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 1.4502
5
PM3 1.5334
5
PM6 1.5552
6
composite G2 1.5796
7
G3 1.5840
7
G3B3 1.5903
7
G3MP2 1.5569
1
G4 1.5541
5
CBS-Q 1.5835
7

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-pCVTZ
hartree fock HF 1.6022
7
1.6913
7
1.5992
7
1.6925
7
1.5769
6
1.5794
7
1.5731
7
1.5781
7
1.5825
7
1.5665
7
1.5389
1
1.5843
5
1.5884
7
1.5685
7
1.5602
7
1.5820
7
1.5550
7
1.5573
7
1.5887
2
1.6364
1
1.5164
1
ROHF 1.6753
1
1.7420
3
1.6430
3
1.7329
3
1.6228
4
1.6119
3
1.6033
3
1.6114
3
1.6114
3
1.6383
1
  1.5623
2
1.6200
3
1.5918
3
1.5814
3
1.6098
3
1.5858
3
1.5782
3
    1.4625
1
density functional LSDA 1.6366
7
1.6045
7
1.5957
7
1.6741
7
1.5777
7
1.5789
7
1.5686
7
1.5724
7
1.5741
7
1.5634
7
  1.5661
3
1.5874
7
1.5632
7
1.5005
2
1.5759
7
1.5533
7
1.4330
1
1.5569
1
1.5561
1
1.4923
1
SVWN   1.6521
5
    1.5554
5
1.5689
3
1.5337
6
1.5643
3
1.5643
3
1.5529
3
  1.5745
6
1.5784
3
1.5532
3
  1.5683
3
1.5467
3
  1.5569
1
1.5561
1
1.4923
1
BLYP 1.6623
7
1.7056
7
1.6275
7
1.7039
7
1.5960
7
1.6085
7
1.5972
7
1.6056
7
1.6081
7
1.5931
7
  1.5986
3
1.6165
7
1.5931
7
  1.5434
1
1.5190
1
  1.5903
1
1.5894
1
1.5142
1
B1B95 1.6242
7
1.5996
7
1.5912
7
1.6662
7
1.5730
7
1.5733
7
1.5643
7
1.5705
7
1.5707
7
1.5594
7
  1.5697
3
1.5817
7
1.5599
7
1.5262
3
1.5725
7
1.5548
7
1.5181
3
1.5353
2
1.5725
1
1.4905
1
B3LYP 1.6375
7
1.6827
7
1.6042
7
1.6802
7
1.5873
7
1.5867
7
1.5775
7
1.5837
7
1.5856
7
1.5718
7
1.5044
1
1.5635
5
1.5956
7
1.5721
7
1.5630
7
1.5846
7
1.5645
7
1.5591
7
1.5449
2
1.5826
1
1.4976
1
B3LYPultrafine   1.6073
1
    1.5874
7
1.5147
1
1.5114
1
1.5088
1
      1.5127
1
1.5923
3
1.5683
3
  1.5838
3
1.5369
5
      1.4938
1
B3PW91 1.6318
7
1.6756
7
1.5972
7
1.6720
7
1.5794
7
1.5793
7
1.5704
7
1.5761
7
1.5778
7
1.5670
7
  1.5746
3
1.5876
7
1.5656
7
  1.5216
1
1.5073
1
  1.5740
1
1.5733
1
1.4948
1
mPW1PW91 1.6184
7
1.6466
6
1.5957
7
1.6702
7
1.5753
7
1.5752
7
1.5665
7
1.5722
7
1.5738
7
1.5630
7
  1.5718
3
1.5834
7
1.5618
7
  1.6005
5
1.5789
5
  1.5731
1
1.5725
1
1.4868
1
M06-2X 1.6332
4
1.7061
4
1.5699
7
1.7031
4
1.5782
6
1.6047
4
1.5973
4
1.6043
4
1.6045
4
1.5899
4
  1.5750
3
1.6135
4
1.5914
4
  1.6058
4
1.5860
4
  1.5893
1
1.5888
1
1.4872
1
PBEPBE 1.6511
7
1.6983
7
1.6169
7
1.6964
7
1.5972
7
1.5980
7
1.5873
7
1.5952
7
1.5954
7
1.5822
7
1.5006
1
1.5866
3
1.6050
7
1.5821
7
1.5479
3
1.6169
5
1.5969
5
1.5370
3
1.5776
1
1.5769
1
1.5089
1
PBEPBEultrafine   1.6233
1
    1.5901
3
1.5291
1
1.5252
1
1.5234
1
      1.5269
1
1.5971
3
1.5736
3
  1.5871
3
1.5669
3
      1.5085
1
PBE1PBE 1.6124
3
1.5884
3
1.5884
3
1.6685
3
1.5551
5
1.5717
3
1.5644
3
1.5692
3
1.5692
3
1.5575
3
  1.5716
3
1.5807
3
1.5584
3
  1.5731
3
1.5533
3
  1.5728
1
1.5723
1
1.4874
1
HSEh1PBE 1.6420
4
1.6783
6
1.6249
4
1.7056
4
1.5806
6
1.6055
4
1.5714
6
1.6039
4
1.6039
4
1.5903
4
  1.5723
3
1.6140
4
1.5623
6
  1.6046
4
1.5839
4
  1.5732
1
1.5726
1
1.4878
1
TPSSh 1.5869
1
1.6136
1
1.5333
1
1.6110
1
1.5604
6
1.5181
1
1.5550
6
1.5131
1
1.5131
1
1.5734
7
  1.5170
1
1.5256
1
1.5513
6
1.4983
1
1.5225
1
1.5034
1
1.4976
1
    1.4984
1
wB97X-D 1.5733
1
1.5917
1
1.5837
7
1.5896
1
1.5716
7
1.5026
1
1.5649
7
1.4970
1
1.5686
7
1.4907
1
  1.5693
7
1.5664
7
1.5621
7
1.4838
1
1.5072
1
1.5584
7
1.4832
1
    1.4836
1
B97D3   1.6561
7
    1.5889
7
      1.5856
7
              1.5739
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) 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-pCVTZ
Moller Plesset perturbation MP2 1.6503
7
1.6963
7
1.5975
7
1.6952
7
1.5818
7
1.5703
7
1.5613
7
1.5781
7
1.5697
7
1.5655
7
  1.5406
5
1.5832
7
1.5530
7
1.5509
6
1.5781
7
1.5600
7
1.5466
6
1.5177
2
1.5578
1
1.4526
1
MP2=FULL 1.6503
7
1.6963
7
1.5939
7
1.7070
7
1.5646
7
1.5685
7
1.5594
7
1.5734
7
1.5687
7
1.5606
7
  1.5679
3
1.5860
7
1.5490
7
1.5525
7
1.6029
5
1.5755
5
1.5482
7
1.5140
2
1.5524
1
1.4508
1
ROMP2 1.6525
3
1.6319
3
1.6319
3
1.7297
3
1.5892
3
1.5887
3
1.5689
3
1.5855
3
1.5854
3
1.5662
3
  1.5419
2
1.5999
3
1.5609
3
  1.5778
3
        1.4805
1
MP3         1.5751
7
  1.5495
6
        1.5136
1
1.5245
1
1.5026
1
          1.5910
1
1.4977
1
MP3=FULL         1.5484
6
1.5135
1
1.5433
6
1.5108
1
1.5108
1
1.5013
1
  1.5133
1
1.5238
1
1.5001
1
  1.5220
1
1.4978
1
      1.4962
1
MP4   1.7739
7
    1.5866
7
    1.4530
1
1.5932
7
    1.5860
3
1.5995
3
1.5815
6
  1.5964
3
1.5678
3
  1.5767
1
1.5766
1
1.5227
1
MP4=FULL   1.6881
3
    1.5834
3
      1.5803
3
      1.5978
3
1.5683
3
  1.5937
3
1.5624
3
  1.5724
1
1.5711
1
1.5208
1
B2PLYP 1.5430
1
1.5703
1
1.5165
1
1.5663
1
1.5370
5
1.5052
1
1.5029
1
1.5014
1
1.5013
1
1.4954
1
  1.5042
1
1.5123
1
1.5076
3
  1.5107
1
1.4944
1
      1.4891
1
B2PLYP=FULL 1.5429
1
1.5715
1
1.5164
1
1.5663
1
1.4896
1
1.5049
1
1.4864
1
1.5012
1
1.5012
1
1.4947
1
  1.5041
1
1.5121
1
1.4950
1
  1.5103
1
1.4933
1
      1.4897
1
B2PLYP=FULLultrafine 1.5429
1
1.5703
1
1.5164
1
1.5663
1
1.5049
1
1.5049
1
1.5028
1
1.5011
1
1.5011
1
1.4947
1
  1.5040
1
1.5121
1
1.4950
1
  1.5103
1
1.4933
1
      1.4897
1
Configuration interaction CID   1.6997
7
1.6119
6
1.7065
6
1.5717
7
    1.5667
7
                    1.5966
1
1.5967
1
1.4922
1
CISD   1.7177
6
1.6177
6
1.7173
6
1.5769
7
    1.5741
7
                    1.5975
1
1.5976
1
1.4922
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) 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-pCVTZ
Quadratic configuration interaction QCISD   1.7218
7
1.6206
7
1.7339
7
1.5964
7
1.5948
7
1.5868
7
1.5878
7
1.5886
7
1.5785
7
  1.5963
3
1.6044
7
1.5793
7
  1.6291
5
1.5978
5
  1.6013
1
1.6018
1
1.4997
1
QCISD(T)         1.5985
7
    1.5184
1
      1.5958
3
1.6130
7
1.5848
7
  1.5837
5
1.5545
5
  1.5928
1
1.5933
1
1.5048
1
QCISD(T)=FULL         1.5284
1
  1.5256
1
          1.5404
1
1.5123
1
1.5028
1
1.5399
1
1.5097
1
1.5022
1
    1.5061
1
QCISD(TQ)         1.5251
1
  1.5223
1
          1.5369
1
1.5126
1
1.5016
1
1.5381
1
1.5119
1
1.5018
1
     
QCISD(TQ)=FULL         1.5235
1
  1.5209
1
          1.5356
1
1.5084
1
1.4994
1
1.5360
1
1.5061
1
       
Coupled Cluster CCD   1.7029
7
1.6172
6
1.7120
6
1.5799
7
1.5797
7
1.5712
7
1.5699
7
1.5751
7
1.5652
7
  1.5848
3
1.5926
7
1.5655
7
  1.5881
7
1.5601
7
  1.5459
2
1.5975
1
1.4679
1
CCSD         1.5905
7
    1.5084
1
  1.5020
1
  1.5912
3
1.6266
5
1.5983
5
1.5621
3
1.6006
3
1.5701
3
1.5601
3
1.6009
1
1.6013
1
1.4950
1
CCSD=FULL         1.5856
3
        1.5096
1
  1.5904
3
1.6008
3
1.5696
3
1.5591
3
1.5976
3
1.5641
3
1.5564
3
1.5960
1
1.5949
1
1.4942
1
CCSD(T)         1.6181
5
1.5233
1
  1.5147
1
    1.4966
1
1.5932
3
1.6109
7
1.5821
7
1.5923
5
1.6075
7
1.5779
7
1.5898
5
1.5463
2
1.5923
1
1.5007
1
CCSD(T)=FULL         1.5900
6
            1.5926
3
1.6304
5
1.5995
5
1.5621
3
1.6274
5
1.5935
5
1.5593
3
1.5438
2
1.5862
1
1.4979
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) 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-pCVTZ

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 1.6915
7
1.5862
7
1.6904
7
1.5865
7
1.6958
6
1.6704
7
density functional B1B95 1.5849
1
1.5201
1
       
B3LYP 1.6892
7
1.5974
7
1.6849
7
1.5959
7
1.6946
6
1.6644
7
wB97X-D 1.6038
1
1.5142
1
1.5981
1
1.5114
1
1.5943
1
1.5776
1
Moller Plesset perturbation MP2 1.6991
7
1.5834
7
1.6942
7
1.5804
7
1.7101
6
1.6736
7
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.