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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 1.8451
5
PM3 1.7950
5
PM6 1.9004
5
composite G2 1.9412
5
G3 1.9412
5
G3B3 1.9709
5
G3MP2 1.9171
1
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 aug-cc-pV(T+d)Z cc-pCVTZ aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
hartree fock HF 1.9029
5
2.0326
5
1.9250
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
1.9116
1
1.9029
2
1.9032
2
1.9331
1
1.9343
5
ROHF                                     1.9023
2
  1.9029
2
     
density functional LSDA 1.9314
5
1.9890
3
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
1.9327
1
1.9218
2
     
BLYP 1.9556
5
2.0638
5
1.9729
5
2.0774
5
1.9697
5
1.9876
5
1.9860
5
1.9831
5
1.9831
5
1.9771
5
1.9595
1
1.9642
3
1.9979
5
1.9796
5
  1.9842
1
1.9661
1
  1.9456
2
1.9591
1
1.9479
2
  1.9838
1
1.9661
1
B1B95 1.9224
5
1.9265
1
1.9375
5
2.0369
5
1.9478
5
1.9478
5
1.9463
5
1.9440
5
1.9440
5
1.9427
5
1.9259
1
1.9289
3
1.9608
5
1.9454
5
1.9684
2
1.9605
5
1.9498
4
1.9643
2
1.9147
2
1.9261
1
1.9162
2
  1.9482
1
1.9322
1
B3LYP 1.9361
5
2.0436
5
1.9521
5
2.0563
5
1.9649
5
1.9649
5
1.9636
5
1.9605
5
1.9605
5
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
1.9384
1
1.9280
2
  1.9622
1
1.9451
1
B3LYPultrafine   2.0156
3
    1.9649
5
1.9433
3
1.9433
3
1.9382
3
  1.9427
1
1.9384
1
1.9431
3
1.9535
3
1.9373
3
  1.9550
3
1.9545
5
  1.9261
2
1.9384
1
1.9280
2
  1.9622
1
1.9451
1
B3PW91 1.9303
5
2.0360
5
1.9461
5
2.0461
5
1.9563
5
1.9563
5
1.9548
5
1.9519
5
1.9519
5
1.9492
5
1.9332
1
1.9369
3
1.9684
5
1.9521
5
  1.9571
1
1.9398
1
  1.9210
2
1.9332
1
1.9228
2
  1.9568
1
1.9397
1
mPW1PW91 1.9256
5
2.0318
5
1.9419
5
2.0416
5
1.9515
5
1.9515
5
1.9502
5
1.9474
5
1.9474
5
1.9449
5
1.9291
1
1.9328
3
1.9637
5
1.9481
5
  1.9449
3
1.9282
3
  1.9173
2
1.9292
1
1.9190
2
  1.9526
1
1.9357
1
M06-2X 1.8979
3
1.9948
3
1.9335
5
2.0119
3
1.9454
5
1.9257
3
1.9255
3
1.9210
3
1.9210
3
1.9211
3
1.9362
5
1.9269
3
1.9363
3
1.9234
3
  1.9384
3
1.9233
3
  1.9141
2
1.9244
1
1.9153
2
  1.9454
1
1.9301
1
PBEPBE 1.9451
5
2.0517
5
1.9633
5
2.0625
5
1.9747
5
1.9747
5
1.9730
5
1.9707
5
1.9707
5
1.9664
5
1.9516
1
1.9547
3
1.9860
5
1.9691
5
1.9913
2
1.9664
3
1.9492
3
1.9864
2
1.9420
3
1.9512
1
1.9396
2
  1.9752
1
1.9579
1
PBEPBEultrafine   2.0258
3
    1.9547
3
1.9547
3
1.9545
3
1.9500
3
  1.9556
1
1.9516
1
1.9547
3
1.9651
3
1.9490
3
  1.9663
3
1.9492
3
  1.9375
2
1.9512
1
1.9396
2
  1.9752
1
1.9579
1
PBE1PBE 1.9069
3
1.9320
1
1.9229
3
2.0176
3
1.9518
5
1.9321
3
1.9319
3
1.9275
3
1.9275
3
1.9257
3
1.9299
1
1.9333
3
1.9434
3
1.9287
3
  1.9453
3
1.9289
3
  1.9181
2
1.9301
1
1.9197
2
  1.9531
1
1.9365
1
HSEh1PBE 1.9080
3
2.0336
5
1.9238
3
2.0193
3
1.9533
5
1.9333
3
1.9519
5
1.9286
3
1.9286
3
1.9265
3
1.9308
1
1.9343
3
1.9445
3
1.9497
5
  1.9464
3
1.9296
3
  1.9186
2
1.9310
1
1.9203
2
  1.9543
1
1.9374
1
TPSSh 1.9071
1
2.0161
3
1.9311
3
2.0262
3
1.9478
5
1.9395
3
1.9468
5
1.9351
3
1.9442
1
1.9512
3
1.9371
1
1.9407
3
1.9513
3
1.9445
5
1.9381
1
1.9530
3
1.9356
3
1.9381
1
1.9248
2
1.9370
1
1.9264
2
  1.9611
1
1.9434
1
wB97X-D 1.8907
1
2.0034
1
1.9361
5
2.0115
1
1.9441
5
1.9325
1
1.9433
5
1.9277
1
1.9406
5
1.9265
1
1.9226
1
1.9453
5
1.9455
5
1.9419
5
1.9236
1
1.9468
1
1.9411
5
1.9237
1
  1.9230
1
    1.9466
1
1.9294
1
B97D3 1.9237
1
2.0540
5
1.9530
1
2.0502
1
1.9800
5
1.9630
1
1.9790
5
1.9586
1
1.9771
5
1.9533
1
1.9661
5
1.9747
5
1.9716
1
1.9739
5
1.9491
1
1.9733
1
1.9655
5
1.9491
1
  1.9482
1
    1.9730
1
1.9597
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 aug-cc-pV(T+d)Z cc-pCVTZ aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Moller Plesset perturbation MP2 1.9146
5
2.0475
5
1.9379
5
2.0577
5
1.9399
5
1.9484
5
1.9474
5
1.9410
3
1.9438
5
1.9495
5
1.9410
1
1.9544
5
1.9691
5
1.9527
5
1.9552
3
1.9751
5
1.9525
5
1.9839
2
1.9327
3
1.9439
1
1.9283
2
1.9297
2
1.9731
1
1.9496
1
MP2=FULL 1.9143
5
2.0479
5
1.9361
5
2.0578
5
1.9463
5
1.9463
5
1.9454
5
1.9435
5
1.9435
5
1.9414
5
1.9371
1
1.9406
3
1.9673
5
1.9473
5
1.9506
3
1.9603
3
1.9305
3
1.9485
3
1.9241
3
1.9335
1
1.9229
2
1.9240
2
1.9706
1
1.9417
1
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
1.9315
1
1.9203
2
     
MP3=FULL         1.9332
5
  1.9320
5
        1.9275
2
1.9413
2
1.9202
2
        1.9120
2
1.9231
1
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
1.9554
1
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
1.9457
1
1.9335
2
1.9343
2
   
B2PLYP 1.9212
3
2.0280
3
1.9296
3
2.0423
3
1.9614
5
1.9417
3
1.9417
3
1.9366
3
1.9366
3
1.9357
3
1.9409
1
1.9434
3
1.9551
3
1.9476
5
  1.9587
3
1.9393
3
  1.9272
2
1.9421
1
1.9284
2
  1.9680
1
1.9482
1
B2PLYP=FULL 1.9212
3
2.0281
3
1.9290
3
2.0423
3
1.9410
3
1.9410
3
1.9411
3
1.9364
3
1.9364
3
1.9329
3
1.9398
1
1.9434
3
1.9545
3
1.9371
3
  1.9580
3
1.9366
3
  1.9244
2
1.9390
1
1.9269
2
  1.9672
1
1.9462
1
B2PLYP=FULLultrafine 1.9141
1
2.0281
3
1.9290
3
2.0423
3
1.9607
5
1.9410
3
1.9411
3
1.9364
3
1.9364
3
1.9329
3
1.9398
1
1.9540
1
1.9754
5
1.9573
5
  1.9580
3
1.9552
5
  1.9244
2
1.9390
1
1.9269
2
1.9275
2
1.9672
1
1.9462
1
Configuration interaction CID   2.0422
5
1.9297
5
2.0537
5
1.9401
5
    1.9349
5
    1.9218
1
  1.9460
1
1.9288
1
        1.9103
2
1.9239
1
1.9105
2
  1.9524
1
1.9296
1
CISD   2.0523
5
1.9340
5
2.0638
5
1.9447
5
    1.9392
5
    1.9246
1
  1.9497
1
1.9316
1
        1.9115
2
1.9264
1
1.9117
2
  1.9560
1
1.9323
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 aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Quadratic configuration interaction QCISD   2.0783
5
1.9470
5
2.0905
5
1.9581
5
1.9597
5
1.9583
5
1.9536
5
1.9536
5
1.9562
5
1.9372
1
1.9415
3
1.9804
5
1.9571
5
  1.9616
3
1.9363
3
  1.9293
3
1.9390
1
1.9250
2
1.9257
2
1.9713
1
1.9452
1
QCISD(T)         1.9667
5
    1.9495
1
    1.9482
1
1.9503
3
1.9888
5
1.9671
5
  1.9937
5
1.9668
5
  1.9338
2
1.9498
1
1.9337
2
  1.9825
1
1.9564
1
QCISD(T)=FULL         1.9429
3
  1.9433
3
      1.9448
1
  1.9631
3
1.9391
3
1.9393
1
1.9687
3
1.9358
3
1.9390
1
1.9245
2
1.9404
1
1.9292
2
  1.9797
1
1.9482
1
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   2.0465
5
1.9340
5
2.0582
5
1.9443
5
1.9449
5
1.9438
5
1.9396
5
1.9396
5
1.9456
5
1.9284
1
1.9317
3
1.9663
5
1.9485
5
  1.9720
5
1.9481
5
  1.9197
2
1.9307
1
1.9198
2
1.9206
2
1.9599
1
1.9365
1
CCSD         1.9522
5
1.9390
1
1.9389
1
1.9332
1
1.9329
1
1.9379
1
1.9328
1
1.9368
3
1.9514
3
1.9327
3
1.9299
1
1.9574
3
1.9332
3
1.9304
1
1.9226
2
1.9349
1
1.9227
2
1.9234
2
1.9650
1
1.9408
1
CCSD=FULL         1.9301
3
        1.9308
1
1.9294
1
1.9368
3
1.9495
3
1.9269
3
1.9251
1
1.9551
3
1.9237
3
1.9247
1
1.9137
2
1.9255
1
1.9177
2
1.9182
2
1.9626
1
1.9331
1
CCSD(T)   2.0570
1
    1.9426
3
1.9515
1
1.9511
1
1.9458
1
1.9455
1
1.9504
1
1.9423
1
1.9476
3
1.9848
5
1.9643
5
1.9419
1
1.9900
5
1.9640
5
1.9426
1
1.9370
3
1.9477
1
1.9322
2
1.9331
2
1.9789
1
1.9536
1
CCSD(T)=FULL 1.9165
1
      1.9605
5
1.9491
1
  1.9453
1
1.9453
1
  1.9420
1
1.9477
3
1.9604
3
1.9372
3
1.9370
1
1.9663
3
1.9342
3
1.9368
1
1.9231
2
1.9379
1
1.9277
2
1.9286
2
1.9762
1
1.9456
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 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 2.0540
5
1.9474
5
2.0525
5
1.9454
5
2.0172
5
2.0345
5
    1.9284
5
density functional BLYP                 1.9587
1
B1B95 2.0507
1
1.9655
1
            1.9256
1
B3LYP 2.0764
5
1.9800
5
2.0741
5
1.9793
5
2.0463
5
2.0494
5
    1.9477
5
B3LYPultrafine                 1.9379
1
B3PW91                 1.9331
1
mPW1PW91                 1.9291
1
M06-2X                 1.9238
1
PBEPBE                 1.9555
5
PBEPBEultrafine                 1.9512
1
PBE1PBE                 1.9298
1
HSEh1PBE                 1.9307
1
TPSSh                 1.9368
1
wB97X-D 2.0317
1
1.9560
1
2.0298
1
1.9536
1
2.0055
1
2.0041
1
    1.9225
1
B97D3                 1.9482
1
Moller Plesset perturbation MP2 2.0691
5
1.9696
5
2.0689
5
1.9637
5
2.0386
5
2.0484
5
    1.9423
5
MP2=FULL                 1.9361
1
B2PLYP                 1.9403
1
B2PLYP=FULL                 1.9392
1
B2PLYP=FULLultrafine                 1.9392
1
Configuration interaction CID                 1.9213
1
CISD                 1.9241
1
Quadratic configuration interaction QCISD                 1.9363
1
QCISD(T)                 1.9467
1
QCISD(T)=FULL                 1.9439
1
Coupled Cluster CCD                 1.9276
1
CCSD                 1.9321
1
CCSD=FULL                 1.9289
1
CCSD(T)                 1.9442
1
CCSD(T)=FULL                 1.9412
1
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.