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Comparison of levels of theory for S-Si


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 1.8577
4
PM3 1.7960
4
PM6 1.9004
5
composite G2 1.9412
5
G3 1.9412
5
G3B3 1.9709
5
G4 1.9588
5
CBS-Q 1.9412
5

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 cc-pCVTZ aug-cc-pCVTZ
hartree fock HF 1.9029
5
2.0326
5
1.9251
5
2.0423
5
1.9344
5
1.9344
5
1.9337
5
1.9310
5
1.9310
5
1.9310
5
1.9102
1
1.9392
5
1.9482
5
1.9352
5
1.9459
3
1.9514
5
1.9344
5
1.9449
3
1.9051
3
1.9029
2
1.9032
2
ROHF                                     1.9023
2
1.9029
2
 
density functional LSDA 1.9314
5
1.9620
5
1.9454
5
2.0431
5
1.9577
5
1.9577
5
1.9559
5
1.9513
5
1.9513
5
1.9477
5
  1.9321
2
1.9692
5
1.9502
5
1.9698
2
1.9677
5
1.9498
4
1.9115
1
1.9195
2
1.9218
2
 
SVWN   2.0306
5
    1.9348
4
1.9337
2
1.9559
5
1.9267
2
1.9267
2
1.9242
2
  1.9730
3
1.9452
2
1.9272
2
  1.9455
2
1.9269
2
  1.9195
2
1.9218
2
 
BLYP 1.9556
5
2.0637
5
1.9729
5
2.0773
5
1.9659
5
1.9876
5
1.9860
5
1.9831
5
1.9831
5
1.9771
5
  1.9594
2
1.9979
5
1.9796
5
  1.9842
1
    1.9456
2
1.9479
2
 
B1B95 1.9229
5
1.9544
5
1.9381
5
2.0374
5
1.9478
5
1.9484
5
1.9469
5
1.9446
5
1.9446
5
1.9432
5
  1.9246
2
1.9612
5
1.9455
5
1.9684
2
1.9606
5
1.9489
4
1.9643
2
1.9147
2
1.9162
2
 
B3LYP 1.9360
5
2.0435
5
1.9521
5
2.0562
5
1.9649
5
1.9649
5
1.9636
5
1.9604
5
1.9637
4
1.9562
5
1.9384
1
1.9653
5
1.9761
5
1.9590
5
1.9687
3
1.9757
5
1.9571
5
1.9660
3
1.9301
3
1.9280
2
 
B3LYPultrafine   2.0108
2
    1.9649
5
1.9391
2
1.9390
2
1.9337
2
      1.9386
2
1.9501
2
1.9335
2
  1.9512
2
1.9529
5
  1.9261
2
1.9280
2
 
B3PW91 1.9370
4
2.0360
5
1.9461
5
2.0461
5
1.9563
5
1.9563
5
1.9548
5
1.9519
5
1.9548
4
1.9492
5
  1.9324
2
1.9684
5
1.9521
5
  1.9571
1
1.9336
1
  1.9210
2
1.9228
2
 
mPW1PW91 1.9324
4
2.0317
5
1.9445
4
2.0416
5
1.9515
5
1.9515
5
1.9502
5
1.9474
5
1.9474
5
1.9449
5
  1.9283
2
1.9638
5
1.9481
5
  1.9449
3
1.9244
2
  1.9173
2
1.9190
2
 
M06-2X 1.9042
2
1.9910
2
1.9309
5
2.0107
2
1.9454
5
1.9221
2
1.9219
2
1.9172
2
1.9172
2
1.9202
3
  1.9229
2
1.9332
2
1.9223
3
  1.9348
2
1.9222
3
  1.9141
2
1.9153
2
 
PBEPBE 1.9511
4
2.0516
5
1.9655
4
2.0661
4
1.9747
5
1.9747
5
1.9730
5
1.9707
5
1.9707
5
1.9664
5
1.9516
1
1.9496
2
1.9859
5
1.9691
5
1.9913
2
1.9618
2
1.9492
3
1.9864
2
1.9420
3
1.9396
2
 
PBEPBEultrafine   2.0188
2
    1.9547
3
1.9498
2
1.9497
2
1.9448
2
      1.9495
2
1.9608
2
1.9447
2
  1.9618
2
1.9448
2
  1.9375
2
1.9396
2
 
PBE1PBE 1.9115
2
1.9183
2
1.9183
2
2.0142
2
1.9518
5
1.9279
2
1.9277
2
1.9231
2
1.9231
2
1.9218
2
  1.9288
2
1.9396
2
1.9250
2
  1.9413
2
1.9251
2
  1.9181
2
1.9197
2
 
HSEh1PBE 1.9125
2
2.0336
5
1.9191
2
2.0159
2
1.9533
5
1.9290
2
1.9519
5
1.9240
2
1.9240
2
1.9224
2
  1.9297
2
1.9407
2
1.9497
5
  1.9423
2
1.9257
2
  1.9186
2
1.9203
2
 
TPSSh   2.0104
2
1.9265
2
2.0227
2
1.9461
5
1.9351
2
1.9450
5
1.9306
2
  1.9490
3
  1.9363
2
1.9473
2
1.9431
5
  1.9488
2
1.9317
2
  1.9248
2
1.9264
2
 
wB97X-D     1.9359
5
  1.9435
5
  1.9426
5
  1.9402
5
    1.9446
5
1.9426
5
1.9415
5
    1.9407
5
       
B97D3   2.0113
5
    1.9614
5
      1.9582
5
              1.9556
5
       
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 cc-pCVTZ aug-cc-pCVTZ
Moller Plesset perturbation MP2 1.9153
4
2.0473
5
1.9379
5
2.0576
5
1.9384
5
1.9484
5
1.9474
5
1.9390
3
1.9438
5
1.9480
5
  1.9544
5
1.9691
5
1.9511
5
1.9552
3
1.9751
5
1.9508
5
1.9839
2
1.9327
3
1.9283
2
1.9297
2
MP2=FULL 1.9149
4
2.0478
5
1.9371
4
2.0564
4
1.9450
5
1.9463
5
1.9454
5
1.9435
5
1.9447
4
1.9402
5
  1.9352
2
1.9673
5
1.9459
5
1.9506
3
1.9603
3
1.9283
3
1.9556
2
1.9241
3
1.9229
2
1.9240
2
ROMP2                                     1.9282
2
1.9282
2
 
MP3         1.9429
5
  1.9346
5
        1.9273
2
1.9431
2
1.9265
2
        1.9202
2
1.9203
2
 
MP3=FULL         1.9332
5
  1.9320
5
        1.9275
2
1.9413
2
1.9202
2
        1.9120
2
1.9161
2
 
MP4   2.0688
4
    1.9647
5
    1.9573
1
1.9606
4
    1.9477
2
1.9634
2
1.9655
5
  1.9689
2
1.9453
2
  1.9376
2
1.9376
2
1.9387
2
MP4=FULL   2.0497
2
    1.9416
2
      1.9376
2
      1.9613
2
1.9372
2
  1.9663
2
1.9339
2
  1.9288
2
1.9335
2
1.9343
2
B2PLYP 1.9248
2
2.0210
2
1.9244
2
2.0374
2
1.9595
5
1.9369
2
1.9369
2
1.9313
2
1.9313
2
1.9330
3
  1.9381
2
1.9508
2
1.9457
5
  1.9539
2
1.9364
3
  1.9272
2
1.9284
2
 
B2PLYP=FULL 1.9247
2
2.0211
2
1.9238
2
2.0374
2
1.9361
2
1.9361
2
1.9362
2
1.9312
2
1.9312
2
1.9279
2
  1.9381
2
1.9501
2
1.9322
2
  1.9531
2
1.9315
2
  1.9244
2
1.9269
2
 
B2PLYP=FULLultrafine   2.0211
2
1.9238
2
2.0374
2
1.9361
2
1.9361
2
1.9362
2
1.9312
2
1.9312
2
1.9279
2
    1.9502
2
1.9322
2
  1.9531
2
1.9315
2
  1.9244
2
1.9269
2
1.9275
2
Configuration interaction CID   2.0469
4
1.9327
4
2.0586
4
1.9401
5
    1.9349
5
                    1.9103
2
1.9105
2
 
CISD   2.0570
4
1.9369
4
2.0687
4
1.9447
5
    1.9423
4
                    1.9115
2
1.9117
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 cc-pCVTZ aug-cc-pCVTZ
Quadratic configuration interaction QCISD   2.0783
5
1.9500
4
2.0948
4
1.9581
5
1.9629
4
1.9583
5
1.9536
5
1.9536
5
1.9548
5
  1.9361
2
1.9804
5
1.9571
5
  1.9565
2
1.9337
3
  1.9293
3
1.9250
2
1.9257
2
QCISD(T)         1.9667
5
    1.9495
1
      1.9444
2
1.9921
4
1.9700
4
  1.9965
4
1.9694
4
  1.9338
2
1.9337
2
 
QCISD(T)=FULL         1.9379
2
  1.9385
2
          1.9579
2
1.9331
2
  1.9628
2
1.9296
2
  1.9245
2
1.9292
2
 
QCISD(TQ)         1.9362
2
  1.9364
2
          1.9563
2
1.9374
2
  1.9622
2
1.9380
2
       
QCISD(TQ)=FULL         1.9338
2
  1.9343
2
          1.9542
2
    1.9595
2
         
Coupled Cluster CCD   2.0504
4
1.9371
4
2.0622
4
1.9443
5
1.9481
4
1.9467
4
1.9396
5
1.9429
4
1.9488
4
  1.9281
2
1.9663
5
1.9518
4
  1.9749
4
1.9510
4
  1.9197
2
1.9198
2
1.9206
2
CCSD         1.9522
5
    1.9332
1
  1.9328
1
  1.9326
2
1.9481
2
1.9308
3
  1.9534
2
1.9313
3
  1.9226
2
1.9227
2
1.9234
2
CCSD=FULL         1.9285
3
        1.9274
1
  1.9324
2
1.9461
2
1.9254
3
  1.9509
2
1.9224
3
  1.9137
2
1.9177
2
1.9182
2
CCSD(T)   2.0570
1
    1.9426
3
1.9515
1
1.9515
1
1.9458
1
1.9458
1
  1.9423
1
1.9423
2
1.9848
5
1.9643
5
  1.9900
5
1.9640
5
  1.9370
3
1.9322
2
1.9331
2
CCSD(T)=FULL 1.9165
1
      1.9402
3
1.9491
1
  1.9453
1
1.9453
1
    1.9423
2
1.9604
3
1.9372
3
  1.9663
3
1.9342
3
  1.9231
2
1.9277
2
1.9286
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 cc-pCVTZ aug-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 2.0539
5
1.9474
5
2.0525
5
1.9454
5
2.0172
5
2.0345
5
density functional B1B95 2.0507
1
1.9655
1
       
B3LYP 2.0763
5
1.9800
5
2.0740
5
1.9793
5
2.0463
5
2.0494
5
Moller Plesset perturbation MP2 2.0691
5
1.9696
5
2.0687
5
1.9637
5
2.0385
5
2.0483
5
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.