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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 1.5269
24
PM3 1.6553
25
PM6 1.6376
25
composite G2 1.6110
27
G3 1.6121
27
G3B3 1.6329
27
G3MP2 1.5569
1
G4 1.6177
25
CBS-Q 1.6115
27

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(D+d)Z 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 1.6946
27
1.7109
27
1.6145
27
1.7183
27
1.6110
26
1.6100
27
1.6080
27
1.6076
27
1.6086
27
1.5977
27
1.6027
19
1.6197
25
1.6218
27
1.6012
27
1.5711
16
1.6224
27
1.5978
27
1.5699
16
1.5659
8
1.5685
10
1.5940
6
1.5876
9
1.5590
9
1.5859
5
1.6635
3
1.5970
23
ROHF 1.6753
1
1.7069
5
1.6029
5
1.7031
5
1.5978
6
1.5863
5
1.5805
5
1.5852
5
1.5853
5
1.6383
1
1.5326
2
1.5599
4
1.5963
5
1.5723
5
1.5635
5
1.5912
5
1.5687
5
1.5615
5
1.5286
3
1.5291
3
1.4602
1
1.5339
4
1.5130
4
1.4607
1
1.5627
2
1.5431
2
density functional LSDA 1.7185
22
1.6250
14
1.6201
22
1.7322
22
1.6121
22
1.6124
22
1.6043
21
1.6060
22
1.6066
22
1.5966
22
1.6052
13
1.6193
18
1.6239
22
1.5986
22
1.5005
2
1.6209
22
1.5955
22
1.4330
1
1.5884
8
1.5701
9
1.5986
6
1.5938
9
1.5645
9
1.6083
5
   
BLYP 1.7607
27
1.7801
27
1.6657
27
1.7835
26
1.6585
27
1.6618
27
1.6578
27
1.6563
27
1.6574
27
1.6439
27
1.6553
18
1.6721
23
1.6729
27
1.6470
27
  1.6852
21
1.6585
21
  1.6214
8
1.6029
9
1.6347
6
1.6274
9
1.5958
9
1.6448
5
1.6633
3
1.6372
3
B1B95 1.7143
27
1.6394
13
1.6205
27
1.7321
27
1.6170
27
1.6171
27
1.6138
27
1.6131
27
1.6133
27
1.6038
27
1.6152
18
1.6277
23
1.6280
27
1.6067
27
1.5262
3
1.6273
27
1.6054
27
1.5181
3
1.5788
8
1.5619
10
1.5953
6
1.5851
9
1.5607
9
1.6005
5
1.7347
1
1.6000
3
B3LYP 1.7321
27
1.7482
27
1.6376
27
1.7532
27
1.6351
27
1.6348
27
1.6317
27
1.6301
27
1.6308
27
1.6191
27
1.6238
19
1.6370
25
1.6461
27
1.6270
27
1.5841
16
1.6439
27
1.6200
27
1.5823
16
1.5943
8
1.5747
10
1.6098
6
1.6019
9
1.5739
9
1.6161
5
1.6418
3
1.6173
3
B3LYPultrafine   1.7633
21
    1.6351
27
1.6452
21
1.6440
21
1.6398
21
  1.6394
6
1.6304
18
1.6486
21
1.6545
23
1.6304
23
  1.6541
23
1.6190
25
  1.5942
8
1.5821
8
1.6151
5
1.6019
9
1.5735
9
1.6160
5
1.6418
3
1.6173
3
B3PW91 1.7235
27
1.7399
27
1.6294
27
1.7418
27
1.6259
27
1.6257
27
1.6226
27
1.6213
27
1.6220
27
1.6122
27
1.6229
18
1.6366
23
1.6369
27
1.6146
27
  1.6495
21
1.6258
21
  1.5875
8
1.5763
9
1.6027
6
1.5948
9
1.5686
9
1.6094
5
1.6332
3
1.6092
3
mPW1PW91 1.7150
27
1.7302
26
1.6250
27
1.7364
27
1.6209
27
1.6207
27
1.6176
27
1.6166
27
1.6173
27
1.6077
27
1.6186
18
1.6319
23
1.6317
27
1.6101
27
  1.6407
25
1.6174
25
  1.5823
8
1.5727
9
1.5983
6
1.5899
9
1.5642
9
1.6042
5
1.6288
3
1.6053
3
M06-2X 1.7179
24
1.7389
24
1.6205
27
1.7412
24
1.6204
26
1.6281
24
1.6263
24
1.6252
24
1.6254
24
1.6153
24
1.5977
27
1.6287
23
1.6391
24
1.6191
24
  1.6399
24
1.6182
24
  1.5762
8
1.5712
9
1.5965
6
1.5831
9
1.5606
9
1.5987
5
1.6270
3
1.6047
3
PBEPBE 1.7442
27
1.7620
27
1.6503
27
1.7547
19
1.6457
27
1.6458
27
1.6420
27
1.6411
27
1.6416
27
1.6304
27
1.6340
19
1.6553
23
1.6565
27
1.6331
27
1.5479
3
1.6639
25
1.6400
25
1.5370
3
1.6085
7
1.5917
8
1.6221
6
1.6125
8
1.5843
8
1.6320
5
1.6458
3
1.6216
3
PBEPBEultrafine   1.7767
21
    1.6532
23
1.6562
21
1.6547
21
1.6509
21
  1.6440
6
1.6414
18
1.6590
21
1.6645
23
1.6409
23
  1.6640
23
1.6399
23
  1.6090
8
1.5941
8
1.6310
5
1.6141
9
1.5859
9
1.6319
5
1.6458
3
1.6216
3
PBE1PBE 1.7291
23
1.6429
13
1.6287
23
1.7470
23
1.6200
25
1.6279
23
1.6258
23
1.6236
23
1.6238
23
1.6146
23
1.6185
18
1.6315
23
1.6392
23
1.6179
23
  1.6403
23
1.6173
23
  1.5824
8
1.5728
9
1.5984
6
1.5897
9
1.5644
9
1.6042
5
1.6282
3
1.6050
3
HSEh1PBE 1.7307
24
1.7382
26
1.6336
24
1.7515
24
1.6242
26
1.6318
24
1.6211
26
1.6279
24
1.6282
24
1.6182
24
1.6191
18
1.6325
23
1.6434
24
1.6125
26
  1.6435
24
1.6203
24
  1.5832
8
1.5733
9
1.5988
6
1.5907
9
1.5648
9
1.6048
5
1.6296
3
1.6059
3
TPSSh 1.7593
21
1.7704
21
1.6475
21
1.7746
21
1.6309
26
1.6455
21
1.6285
26
1.6410
21
1.6414
21
1.6206
27
1.6321
18
1.6494
21
1.6580
21
1.6201
26
1.5929
10
1.6593
21
1.6341
21
1.5926
10
1.5968
8
1.5849
8
1.6181
5
1.6036
9
1.5763
9
1.6188
5
1.6440
3
1.6186
3
wB97X-D 1.7379
21
1.7389
21
1.6199
27
1.7436
21
1.6185
27
1.6284
21
1.6159
27
1.6239
21
1.6144
27
1.6157
21
1.6170
18
1.6207
27
1.6255
27
1.6091
27
1.5776
10
1.6416
21
1.6082
27
1.5774
10
1.5792
8
1.5704
8
1.6011
5
1.5867
9
1.5620
9
1.6021
5
1.6265
3
1.6038
3
B97D3 1.7855
20
1.7559
27
1.6625
20
1.7998
20
1.6443
27
1.6636
20
1.6416
27
1.6576
20
1.6392
27
1.6465
20
1.6219
26
1.6485
27
1.6760
20
1.6316
27
1.6114
9
1.6770
20
1.6303
27
1.6110
9
1.6081
8
1.5925
8
1.6287
5
1.6145
9
1.5938
8
1.6297
5
1.6527
3
1.6254
26
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(D+d)Z 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 1.7463
27
1.7861
27
1.6533
27
1.7911
27
1.6349
27
1.6317
27
1.6292
27
1.6269
27
1.6251
27
1.6179
27
1.6308
18
1.6355
25
1.6493
27
1.6176
27
1.5776
15
1.6519
27
1.6199
27
1.5760
15
1.6099
8
1.5688
10
1.6235
6
1.6077
9
1.5674
9
1.6366
5
1.6162
3
1.5785
3
MP2=FULL 1.7459
27
1.7860
27
1.6516
27
1.7943
26
1.6283
27
1.6291
27
1.6267
27
1.6246
27
1.6238
27
1.6112
27
1.6252
18
1.6463
23
1.6483
27
1.6125
27
1.5745
16
1.6598
25
1.6223
25
1.5724
16
1.6078
8
1.5797
9
1.6171
6
1.6064
9
1.5644
9
1.6328
5
1.6122
3
1.5716
3
ROMP2 1.6709
5
1.5849
2
1.6131
5
1.7365
5
1.5826
5
1.5823
5
1.5699
5
1.5779
5
1.5778
5
1.5600
4
1.5480
2
1.5609
4
1.5956
5
1.5613
5
  1.5839
5
    1.5535
3
1.5548
3
1.4780
1
1.5674
4
1.5362
4
1.4780
1
1.5919
2
1.5621
2
MP3         1.6174
19
  1.6166
26
      1.6155
18
1.6368
21
1.6489
21
1.6199
21
        1.5879
8
1.5676
8
1.6040
6
1.5950
9
1.5599
9
1.6063
5
1.5810
2
1.5304
2
MP3=FULL   1.7588
20
1.6427
20
1.7687
20
1.6152
26
1.6291
21
1.6134
26
1.6220
21
1.6224
21
1.6114
21
1.6121
18
1.6360
21
1.6470
21
1.6152
21
  1.6507
21
1.6123
20
  1.5861
8
1.5630
8
1.6012
5
1.5938
9
1.5575
9
1.6034
5
1.5765
2
1.5228
2
MP4   1.9292
16
    1.6097
16
    1.4530
1
1.6081
16
  1.6345
7
1.6233
12
1.6370
12
1.6042
15
  1.6396
12
1.6223
10
  1.6212
8
1.5924
9
1.6345
6
1.6214
9
1.5865
9
1.6463
5
1.5653
2
1.5943
1
MP4=FULL   1.7026
8
    1.6146
12
      1.6089
12
  1.6307
7
  1.6348
12
1.6026
12
  1.6362
12
1.6001
12
  1.6189
8
1.5871
9
1.6279
6
1.6198
9
1.5838
9
1.6433
5
1.5625
2
1.4506
1
B2PLYP 1.7576
21
1.7807
21
1.6478
21
1.7889
21
1.6360
24
1.6454
21
1.6446
21
1.6393
21
1.6397
21
1.6307
21
1.6325
18
1.6500
21
1.6592
21
1.6240
23
  1.6619
21
1.6317
13
  1.5992
8
1.5854
8
1.6220
5
1.6025
9
1.5755
9
1.6225
5
1.6289
3
1.6069
3
B2PLYP=FULL 1.7572
21
1.7807
21
1.6477
21
1.7888
21
1.6441
21
1.6446
21
1.6430
21
1.6390
21
1.6393
21
1.6237
12
1.6314
18
1.6496
21
1.6586
21
1.6331
21
  1.6610
21
1.6300
13
  1.5987
8
1.5840
8
1.6201
5
1.6021
9
1.5748
9
1.6215
5
1.6279
3
1.6050
3
B2PLYP=FULLultrafine 1.7572
21
1.7806
21
1.6476
21
1.7888
21
1.6346
27
1.6445
21
1.6438
21
1.6390
21
1.6393
21
1.6286
21
1.6314
18
1.6497
21
1.6478
27
1.6224
27
  1.6610
21
1.6204
27
  1.5986
8
1.5839
8
1.6201
5
1.6021
9
1.5747
9
1.6215
5
1.6279
3
1.6050
3
Configuration interaction CID   1.7300
27
1.6270
26
1.7389
26
1.6120
27
    1.6051
27
    1.6029
18
  1.6607
6
1.6249
6
        1.5760
8
1.5621
9
1.5921
6
1.5864
9
1.5507
9
1.5910
5
1.6411
3
1.5964
3
CISD   1.7376
26
1.6292
26
1.7440
26
1.6142
27
    1.6080
27
    1.6042
18
  1.6623
6
1.6274
6
        1.5779
8
1.5642
9
1.5928
6
1.5878
9
1.5527
9
1.5917
5
1.6422
3
1.5981
3
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(D+d)Z 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   1.7727
26
1.6457
27
1.7845
26
1.6342
27
1.6335
27
1.6311
27
1.6256
27
1.6261
27
1.6183
27
1.6252
18
1.6456
23
1.6492
27
1.6206
27
  1.6617
25
1.6263
24
  1.5992
8
1.5833
9
1.6103
6
1.6059
9
1.5721
9
1.6118
5
1.6507
3
1.6149
3
QCISD(T)         1.6195
17
    1.6156
11
    1.6306
6
1.6296
13
1.6366
17
1.6073
17
  1.6332
15
1.5948
14
  1.6114
8
1.5927
9
1.6215
6
1.6169
9
1.5830
9
1.6271
5
1.6567
3
1.6216
3
QCISD(T)=FULL         1.6222
11
  1.6206
11
      1.6215
7
  1.6390
11
1.6018
9
1.5759
8
1.6442
11
1.6008
10
1.5871
8
1.6078
7
1.5998
7
1.6205
5
1.6154
9
1.5804
9
1.6237
5
1.5938
2
1.5139
1
QCISD(TQ)         1.4966
2
  1.4953
2
      1.4492
1
  1.5085
2
1.4860
2
1.5016
1
1.5109
2
1.5119
1
1.5018
1
               
QCISD(TQ)=FULL         1.4952
2
  1.4939
2
          1.5074
2
1.5084
1
1.4994
1
1.5091
2
1.5061
1
                 
Coupled Cluster CCD   1.7483
27
1.6403
26
1.7591
26
1.6242
27
1.6239
27
1.6214
27
1.6151
27
1.6168
27
1.6087
27
1.6228
10
1.6371
23
1.6368
19
1.6110
27
  1.6424
27
1.6078
26
  1.5904
8
1.5649
10
1.6068
6
1.5975
9
1.5584
9
1.6084
5
1.5822
2
1.5329
2
CCSD         1.6346
26
1.6921
5
1.6919
5
1.6551
6
1.6856
5
1.6244
21
1.6314
10
1.6428
23
1.6553
25
1.6262
25
1.5852
12
1.6587
23
1.6235
22
1.5590
8
1.5959
8
1.5821
9
1.6086
6
1.6034
9
1.5704
9
1.6099
5
1.6495
3
1.6146
3
CCSD=FULL         1.6353
23
        1.6185
21
1.6274
10
1.6416
23
1.6526
23
1.6205
23
1.5702
11
1.6556
23
1.6151
14
1.5334
7
1.5938
8
1.5769
9
1.6022
6
1.6017
9
1.5672
9
1.6062
5
1.5888
2
1.5513
2
CCSD(T)         1.6281
15
1.6228
11
1.6316
10
1.6143
11
1.6249
10
1.6185
10
1.5966
9
1.6283
13
1.6350
17
1.6008
16
1.6000
14
1.6366
17
1.5995
16
1.5994
14
1.6101
8
1.5824
10
1.6205
6
1.6158
9
1.5815
9
1.6260
5
1.6559
3
1.6208
3
CCSD(T)=FULL         1.6154
16
          1.6053
8
1.6273
13
1.6433
15
1.6068
14
1.5912
12
1.6450
15
1.6049
13
1.5903
12
1.6073
8
1.5776
10
1.6141
6
1.6142
9
1.5783
9
1.6226
5
1.5933
2
1.5555
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(D+d)Z 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 1.7235
27
1.6228
27
1.7224
27
1.6217
27
1.7104
26
1.6985
27
    1.5937
26
ROHF                 1.5344
2
density functional LSDA                 1.4412
1
BLYP                 1.6539
6
B1B95 1.5849
1
1.5201
1
            1.6164
6
B3LYP 1.7651
27
1.6487
27
1.7603
27
1.6468
27
1.7520
26
1.7362
27
    1.6139
26
B3LYPultrafine                 1.6332
6
B3PW91                 1.6236
6
mPW1PW91                 1.6199
6
M06-2X                 1.6212
6
PBEPBE                 1.6209
26
PBEPBEultrafine                 1.6378
6
PBE1PBE                 1.6195
6
HSEh1PBE                 1.6204
6
TPSSh                 1.6332
6
wB97X-D 1.7567
21
1.6439
21
1.7529
21
1.6419
21
1.7382
21
1.7278
21
    1.6194
6
B97D3                 1.6405
6
Moller Plesset perturbation MP2 1.8007
27
1.6523
27
1.7938
27
1.6473
27
1.7930
26
1.7777
27
    1.6097
26
MP2=FULL                 1.6065
6
ROMP2                 1.5519
2
MP3                 1.6184
6
MP3=FULL                 1.6158
6
MP4                 1.5889
3
MP4=FULL                 1.5503
4
B2PLYP                 1.6291
6
B2PLYP=FULL                 1.6282
6
B2PLYP=FULLultrafine                 1.6282
6
Configuration interaction CID                 1.6139
6
CISD                 1.6168
6
Quadratic configuration interaction QCISD                 1.6329
6
QCISD(T)                 1.5717
4
QCISD(T)=FULL                 1.5684
4
QCISD(TQ)                 1.4510
1
Coupled Cluster CCD                 1.6197
6
CCSD                 1.6322
6
CCSD=FULL                 1.6287
6
CCSD(T)                 1.5701
4
CCSD(T)=FULL                 1.5669
4
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.