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Comparison of levels of theory for S-P


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 1.7600
4
PM3 1.8313
4
PM6 1.7899
4
composite G2 1.9398
4
G3 1.9398
4
G3B3 1.9593
4
G3MP2 1.9603
1
G4 1.9432
4
CBS-Q 1.9398
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 Def2TZVPP 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 1.9082
4
2.1214
4
1.9272
4
2.0872
4
1.9398
4
1.9398
4
1.9390
4
1.9894
3
1.9384
4
1.9271
4
1.9135
1
1.9461
4
1.9123
4
1.9499
4
1.9303
4
1.9224
4
1.9492
4
1.9282
4
1.9210
4
1.9255
1
1.9253
1
1.9262
1
ROHF   1.9958
1
1.8738
1
1.9921
1
1.9475
2
1.8828
1
1.8828
1
1.8779
1
1.8779
1
    1.8870
1
  1.8925
1
1.8789
1
1.8736
1
1.8959
1
1.8790
1
1.8736
1
1.8834
1
1.8838
1
1.8839
1
density functional LSDA 1.9504
4
1.9682
4
1.9377
4
2.0617
4
1.9516
4
1.9516
4
1.9479
4
1.9457
4
1.9457
4
1.9377
4
  1.9174
1
  1.9599
4
1.9385
4
1.9145
2
1.9554
4
1.9340
4
1.9123
2
1.9065
1
1.9061
1
1.9081
1
BLYP 1.9767
4
2.1082
4
1.9700
4
2.1000
4
1.9638
4
1.9860
4
1.9823
4
1.9835
4
1.9836
4
1.9720
4
  1.9482
1
  1.9936
4
1.9729
4
  1.9548
1
1.9345
1
  1.9273
1
1.9269
1
1.9289
1
B1B95 1.9382
4
  1.9286
4
2.0502
4
1.9388
4
1.9395
4
1.9360
4
1.9362
4
1.9362
4
1.9301
4
  1.9045
1
  1.9490
4
1.9308
4
1.9354
3
1.9812
3
1.9622
3
1.9315
3
1.8985
1
1.8983
1
1.8997
1
B3LYP 1.9525
4
2.0778
4
1.9448
4
2.0710
4
1.9587
4
1.9587
4
1.9557
4
1.9554
4
1.9554
4
1.9466
4
1.9018
1
1.9606
4
1.9344
4
1.9671
4
1.9477
4
1.9404
4
1.9635
4
1.9435
4
1.9372
4
1.9107
1
1.9105
1
1.9121
1
B3LYPultrafine   2.0345
1
    1.9589
4
1.9229
1
1.9226
1
1.9171
1
      1.9232
1
  1.9300
1
1.9114
1
  1.9300
1
1.9820
3
  1.9107
1
1.9105
1
1.9121
1
B3PW91 1.9457
4
2.0677
4
1.9368
4
2.0592
4
1.9479
4
1.9479
4
1.9449
4
1.9439
4
1.9439
4
1.9372
4
  1.9143
1
  1.9571
4
1.9383
4
  1.9222
1
    1.9049
1
1.9047
1
1.9063
1
mPW1PW91 1.9401
4
2.0614
4
1.9314
4
2.0532
4
1.9422
4
1.9422
4
1.9394
4
1.9384
4
1.9385
4
1.9319
4
  1.9093
1
  1.9515
4
1.9334
4
  1.9172
1
1.8987
1
  1.9012
1
1.9011
1
1.9025
1
M06-2X 1.8952
1
2.0068
1
1.9244
4
2.0049
1
1.9357
4
1.9006
1
1.9001
1
1.8949
1
1.8949
1
1.8927
1
  1.9022
1
  1.9085
1
1.8933
1
  1.9101
1
1.8927
1
  1.8975
1
1.8972
1
1.8983
1
PBEPBE 1.9638
4
2.0907
4
1.9561
4
2.0816
4
1.9688
4
1.9688
4
1.9651
4
1.9658
4
1.9658
4
1.9565
4
1.9135
1
1.9343
1
1.9410
4
1.9769
4
1.9578
4
1.9621
3
1.9894
2
1.9693
2
1.9573
3
1.9191
1
1.9188
1
1.9207
1
PBEPBEultrafine         1.9339
1
1.9339
1
1.9335
1
1.9292
1
      1.9343
1
  1.9408
1
1.9231
1
  1.9413
1
1.9225
1
  1.9191
1
1.9188
1
1.9207
1
PBE1PBE 1.9082
1
  1.8975
1
2.0157
1
1.9419
4
1.9079
1
1.9076
1
1.9025
1
1.9025
1
1.8982
1
  1.9094
1
  1.9158
1
1.8994
1
  1.9171
1
1.8991
1
  1.9013
1
1.9012
1
1.9026
1
HSEh1PBE 1.9093
1
2.0331
3
1.8987
1
2.0176
1
1.9194
3
1.9094
1
1.9184
3
1.9039
1
1.9039
1
1.8994
1
  1.9107
1
  1.9172
1
1.9099
3
  1.9185
1
1.9002
1
  1.9022
1
1.9021
1
1.9036
1
TPSSh   2.0362
1
1.9080
1
2.0286
1
1.9442
4
1.9177
1
1.9421
4
1.9126
1
  1.9372
4
  1.9195
1
  1.9264
1
1.9379
4
  1.9274
1
1.9080
1
  1.9087
1
1.9085
1
1.9100
1
wB97X-D     1.9266
4
  1.9344
4
  1.9326
4
  1.9317
4
    1.9361
4
  1.9326
4
1.9285
4
    1.9265
4
       
B97D3   2.0205
4
    1.9541
4
  1.9519
4
  1.9516
4
  1.9377
4
      1.9463
4
    1.9528
4
       
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 Def2TZVPP 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 1.9625
4
2.1208
4
1.9167
4
2.1071
4
1.9461
4
1.9276
4
1.9248
4
1.9429
4
1.9240
4
1.9520
4
  1.9343
4
1.9343
4
1.9444
4
1.9259
4
1.9246
3
1.9776
4
1.9236
4
1.9241
3
1.9340
1
1.9328
1
1.9336
1
MP2=FULL 1.9621
4
2.1217
4
1.9465
4
2.1058
4
1.9257
4
1.9257
4
1.9231
4
1.9239
4
1.9238
4
1.9454
4
  1.9499
1
  1.9430
4
1.9487
4
1.9220
3
1.9941
2
1.9631
2
1.9210
3
1.9300
1
1.9264
1
1.9304
1
ROMP2                                       1.9032
1
1.9038
1
1.9033
1
MP3         1.9206
4
  1.9381
4
        1.9398
1
  1.9456
1
1.9270
1
        1.9194
1
1.9186
1
1.9190
1
MP3=FULL         1.9371
4
            1.9401
1
  1.9449
1
1.9258
1
        1.9158
1
1.9128
1
1.9164
1
MP4   2.2817
3
    1.9439
4
    1.8308
1
1.9719
4
    1.9583
1
  1.9648
1
1.9457
2
  1.9683
1
1.9412
1
  1.9367
1
1.9361
1
1.9366
1
MP4=FULL         1.9532
1
      1.9518
1
        1.9637
1
    1.9672
1
1.9368
1
  1.9340
1
1.9314
1
1.9349
1
B2PLYP 1.8787
1
1.9985
1
1.9086
1
1.9943
1
1.9581
4
1.9210
1
1.9207
1
1.9161
1
1.9158
1
1.9136
1
  1.9245
1
  1.9314
1
1.9408
4
  1.9351
1
1.9143
1
  1.9127
1
1.9128
1
1.9135
1
B2PLYP=FULL 1.8786
1
2.0082
1
1.9081
1
1.9943
1
1.9220
1
1.9205
1
1.9224
1
1.9161
1
1.9161
1
1.9115
1
  1.9246
1
  1.9310
1
1.9132
1
  1.9346
1
1.9123
1
  1.9115
1
1.9110
1
1.9127
1
Configuration interaction CID   2.0999
4
1.9333
4
2.0723
4
1.9212
4
    1.9163
4
                      1.8716
1
1.8705
1
1.8721
1
CISD   2.1037
4
1.9362
4
2.0866
4
1.9314
4
    1.9426
4
                      1.8790
1
1.8782
1
1.8794
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 Def2TZVPP 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   2.1412
4
1.9398
4
2.1270
4
1.9540
4
1.9568
4
1.9519
4
1.9505
4
1.9541
4
1.9485
4
  1.9308
1
  1.9710
4
1.9451
4
  1.9435
1
1.9160
1
  1.9130
1
1.9129
1
1.9130
1
QCISD(T)         1.9624
4
    1.9186
1
      1.9391
1
  1.9835
4
1.9590
4
  1.9867
4
1.9569
4
  1.9086
1
1.9088
1
1.9085
1
QCISD(T)=FULL         1.9300
1
  1.9300
1
            1.9473
1
1.9210
1
  1.9520
1
1.9179
1
       
QCISD(TQ)                           1.9432
1
1.9180
1
    1.9186
1
       
QCISD(TQ)=FULL                           1.9413
1
               
Coupled Cluster CCD   2.1022
3
1.9384
4
2.0819
4
1.9241
4
1.9485
4
1.9464
4
1.9201
4
1.9456
4
1.9425
4
  1.9395
1
  1.9641
4
1.9425
4
  1.9669
4
1.9401
4
  1.9170
1
1.9160
1
1.9167
1
CCSD         1.9496
4
        1.9155
1
  1.9267
1
  1.9348
1
1.9142
1
  1.9386
1
1.9136
1
1.8907
1
1.9019
1
1.9093
1
1.9011
1
CCSD=FULL         1.9221
1
            1.9270
1
  1.9336
1
1.9130
1
  1.9374
1
1.9112
1
  1.9053
1
1.9031
1
1.9062
1
CCSD(T)         1.9230
1
1.9230
1
  1.9156
1
    1.9016
1
1.9388
1
  1.9812
4
1.9538
4
1.9559
2
1.9816
4
1.9550
4
1.9010
1
1.9041
1
1.9044
1
1.9039
1
CCSD(T)=FULL         1.8919
2
            1.9392
1
  1.9462
1
1.9215
1
1.9607
2
1.9506
1
1.9189
1
    1.9133
1
1.9165
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 Def2TZVPP 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)
daug-cc-pVDZ daug-cc-pVTZ daug-cc-pVQZ Sadlej_pVTZ CEP-31G CEP-31G* CEP-121G CEP-121G* LANL2DZ SDD
hartree fock HF         2.0999
4
1.9629
4
2.0974
4
1.9579
4
2.1200
4
2.1057
4
density functional B1B95           1.9388
1
       
B3LYP         2.0939
4
1.9803
4
2.0908
4
1.9777
4
2.0978
4
2.0762
4
Moller Plesset perturbation MP2         2.1305
4
1.9545
4
2.1242
4
1.9484
4
2.1288
4
2.1111
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.