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Comparison of levels of theory for B-B


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 1.5743
11
PM3 1.7265
11
PM6 1.6370
15
composite G2 1.7486
14
G3 1.7485
14
G3B3 1.7368
14
G3MP2 1.5913
4
G4 1.7129
15
CBS-Q 1.7542
13

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 cc-pCVDZ cc-pCVTZ aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
hartree fock HF 1.7161
14
1.7660
14
1.7672
14
1.7648
14
1.7432
14
1.7558
14
1.7570
14
1.7555
14
1.7561
14
1.7587
14
1.6817
5
1.7438
16
1.6286
18
1.7634
14
1.7570
14
1.7707
11
1.7664
13
1.7570
14
1.7706
11
1.7054
1
1.6492
1
1.6709
2
1.7480
4
1.6797
1
1.6718
1
ROHF   2.0560
2
2.0560
2
2.0061
2
1.9226
2
1.9226
2
1.9197
2
1.9189
2
1.9189
2
    1.9211
2
  1.9273
2
1.9254
2
1.9244
2
1.9298
2
1.9266
2
1.9243
2
      1.9267
2
   
density functional LSDA 1.6898
14
1.7123
14
1.7135
14
1.7126
14
1.7087
14
1.7084
14
1.7091
14
1.7005
14
1.7006
14
1.7067
14
1.5890
1
1.7077
12
1.5910
1
1.7148
14
1.7005
14
  1.7124
14
1.7101
11
        1.6947
4
1.6030
1
1.5907
1
BLYP 1.7278
14
1.7487
14
1.7500
14
1.7494
14
1.6846
17
1.7435
14
1.7439
14
1.7375
14
1.7377
14
1.7420
14
1.6217
1
1.7470
12
1.6230
1
1.7499
14
1.7354
14
  1.6318
5
1.8089
8
  1.6862
1
    1.7258
4
1.6324
1
1.6225
1
B1B95 1.6949
14
1.7411
13
1.7364
14
1.7336
14
1.7170
14
1.7170
14
1.7300
14
1.7230
14
1.7232
14
1.7273
14
1.6233
1
1.7305
12
1.6239
1
1.7214
14
1.7222
14
1.5170
2
1.6979
13
1.7352
11
1.6403
1
  1.6288
1
1.6155
1
1.7214
4
  1.6239
1
B3LYP 1.7067
14
1.7401
14
1.7413
14
1.7405
14
1.7530
13
1.7346
14
1.7349
14
1.7298
14
1.7395
12
1.7339
14
1.6657
4
1.7192
16
1.6365
18
1.7411
14
1.7279
14
1.7406
11
1.7405
13
1.7183
13
1.7405
11
1.6840
1
1.6280
1
1.6479
2
1.7168
4
1.6364
1
1.6267
1
B3LYPultrafine   1.7560
12
    1.7350
14
1.7437
12
1.7439
12
1.7395
12
  1.6349
1
1.6261
1
1.7378
12
1.6271
1
1.7516
12
1.7366
12
  1.7488
12
1.7071
15
  1.6841
1
    1.7168
4
1.6364
1
1.6267
1
B3PW91 1.7180
12
1.7366
14
1.7378
14
1.7358
14
1.7311
14
1.7303
14
1.7307
14
1.7260
14
1.7350
12
1.7308
14
1.6263
1
1.7339
12
1.6271
1
1.7360
14
1.7252
14
  1.6312
5
1.5431
2
  1.6864
1
    1.7196
4
1.6362
1
1.6271
1
mPW1PW91 1.7028
12
1.7346
14
1.7508
12
1.7343
14
1.7287
14
1.7284
14
1.7294
14
1.7246
14
1.7248
14
1.7291
14
1.6273
1
1.7324
12
1.6281
1
1.7340
14
1.7246
13
  1.7328
14
1.7360
11
  1.6857
1
    1.7188
4
1.6369
1
1.6281
1
M06-2X 1.7184
12
1.7529
12
1.6578
18
1.7513
12
1.7269
15
1.7419
12
1.7421
12
1.7380
12
1.7383
12
1.7409
12
1.6358
1
1.7365
12
1.6371
1
1.7473
12
1.7363
12
  1.7454
12
1.7413
11
        1.7266
4
1.6444
1
1.6366
1
PBEPBE 1.7217
12
1.7389
14
1.7555
12
1.7518
12
1.7339
14
1.7334
14
1.7335
14
1.7285
13
1.7278
14
1.7327
14
1.6646
4
1.7361
12
1.6376
18
1.7384
14
1.7270
14
1.5908
2
1.7460
12
1.7311
12
1.5907
2
    1.6857
1
1.7234
4
1.6274
1
1.6182
1
PBEPBEultrafine   1.7540
12
    1.7339
14
1.7419
12
1.7421
12
1.7369
12
  1.6265
1
1.6173
1
1.7360
12
1.6184
1
1.7485
12
1.7351
12
  1.7459
12
1.7397
11
        1.7234
4
1.6274
1
1.6182
1
PBE1PBE 1.7124
12
1.7564
11
1.7499
12
1.7460
12
1.7217
15
1.7359
12
1.7357
12
1.7321
12
1.7324
12
1.7362
12
1.6267
1
1.7313
12
1.6275
1
1.7423
12
1.7308
12
  1.7403
12
1.7350
11
        1.7189
4
1.6361
1
1.6275
1
HSEh1PBE 1.7133
12
1.7046
15
1.7500
12
1.7463
12
1.7219
15
1.7358
12
1.7217
15
1.7323
12
1.7324
12
1.7364
12
1.6264
1
1.7314
12
1.6272
1
1.7428
12
1.6913
15
  1.7407
12
1.7349
11
        1.7185
4
1.6360
1
1.6272
1
TPSSh 1.5322
2
1.7624
12
1.7639
12
1.7556
12
1.6885
15
1.7478
12
1.6880
15
1.7446
12
1.5514
2
1.5258
9
1.6338
1
1.7440
12
1.6343
1
1.7548
12
1.6851
15
1.5480
2
1.7528
12
1.7483
11
1.5480
2
      1.7280
4
1.6433
1
1.6344
1
wB97X-D 1.5307
2
1.5517
2
1.5486
13
1.5559
2
1.5505
13
1.5563
2
1.5514
13
1.5505
2
1.5452
13
1.5537
2
1.6368
1
1.5464
13
1.6372
1
1.5514
13
1.5457
13
1.5471
2
1.5610
2
1.5457
13
1.5471
2
      1.5474
2
1.6465
1
1.6372
1
B97D3 1.5375
2
1.5690
13
1.5581
2
1.5623
2
1.5736
13
1.5607
2
1.5740
13
1.5548
2
1.5702
13
1.5573
2
1.6419
18
1.5532
2
  1.5678
2
1.5708
13
1.5506
2
1.5647
2
1.6923
13
1.5506
2
        1.6419
1
1.6320
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 cc-pCVDZ cc-pCVTZ aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Moller Plesset perturbation MP2 1.7299
12
1.7497
14
1.7508
14
1.7506
14
1.6306
18
1.7237
14
1.7252
14
1.6321
18
1.7318
14
1.7267
13
1.6499
1
1.7176
16
1.6277
18
1.7455
14
1.7257
14
1.7315
11
1.7466
13
1.7367
11
1.7319
11
1.6901
1
1.6187
1
1.6437
2
1.7142
4
1.6701
1
1.6509
1
MP2=FULL 1.7292
12
1.7536
13
1.7666
12
1.7638
12
1.7197
14
1.7209
13
1.7219
13
1.7246
14
1.7373
12
1.7234
12
1.6446
1
1.7315
12
1.6461
1
1.7447
13
1.7097
12
1.7223
11
1.7436
13
1.7234
11
1.7223
11
1.6757
1
1.6169
1
1.6353
2
1.7095
4
1.6678
1
1.6392
1
ROMP2 1.7993
2
1.9745
2
1.9745
2
1.9381
2
1.8630
2
1.8630
2
1.8628
2
1.8741
2
1.8741
2
1.8712
2
  1.8694
2
  1.8880
2
1.8693
2
  1.8898
2
          1.8695
2
   
MP3         1.7249
14
  1.6706
14
      1.6530
1
1.7433
11
1.6534
1
1.7622
12
1.7420
11
              1.7155
4
1.6748
1
1.6533
1
MP3=FULL   1.5683
2
1.5683
2
1.5748
2
1.6697
15
1.5579
2
1.6722
15
1.5607
2
1.5648
2
1.5537
2
1.6479
1
1.7366
12
1.6487
1
1.7597
12
1.7247
12
  1.5813
2
1.5477
2
        1.7110
4
1.6725
1
1.6411
1
MP4   1.7826
11
    1.7263
14
      1.7547
11
  1.6517
1
1.7462
11
1.6520
1
1.7654
12
1.7275
14
  1.7705
11
1.7447
11
        1.7190
4
1.6746
1
1.6518
1
MP4=FULL   1.7820
11
    1.7312
12
      1.7512
11
  1.6465
1
  1.6473
1
1.7627
12
1.7309
11
  1.7674
11
1.7308
11
        1.7145
4
1.6723
1
1.6396
1
B2PLYP 1.7270
12
1.7583
12
1.7597
12
1.7569
12
1.7236
14
1.7388
12
1.7393
12
1.7383
12
1.7398
12
1.7401
12
1.6355
1
1.7364
12
1.6364
1
1.7523
12
1.6570
15
  1.7502
12
1.7397
11
      1.6849
1
1.7153
4
1.6487
1
1.6361
1
B2PLYP=FULL 1.7268
12
1.7584
12
1.7595
12
1.7567
12
1.7377
12
1.7377
12
1.7383
12
1.7373
12
1.7388
12
1.7367
12
1.6339
1
1.7355
12
1.6349
1
1.7514
12
1.7316
12
  1.7492
12
1.7362
11
      1.6809
1
1.7139
4
1.6480
1
1.6328
1
B2PLYP=FULLultrafine 1.5350
2
1.5539
2
1.5539
2
1.5591
2
1.5984
3
1.5538
2
1.5546
2
1.5501
2
1.5508
2
1.5501
2
1.6339
1
1.5485
2
1.6349
1
1.5660
2
1.5443
2
  1.5632
2
1.5444
2
        1.5459
2
1.6480
1
1.6328
1
Configuration interaction CID   1.7704
12
1.7715
12
1.7694
12
1.7283
14
    1.7419
13
    1.6548
1
  1.6550
1
1.6775
1
1.6553
1
              1.7195
4
1.6758
1
1.6549
1
CISD   1.7723
12
1.7734
12
1.7715
12
1.7364
13
    1.7456
12
    1.6537
1
  1.6538
1
1.6763
1
1.6542
1
              1.7227
4
1.6742
1
1.6539
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 cc-pCVDZ cc-pCVTZ aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Quadratic configuration interaction QCISD   1.7592
14
1.7768
12
1.7752
12
1.7299
14
1.7400
12
1.7410
12
1.7379
14
1.7443
13
1.7453
12
1.6525
1
1.7448
12
1.6529
1
1.7679
12
1.7431
12
  1.7045
7
1.7480
11
  1.6930
1
  1.6931
1
1.7258
4
1.6744
1
1.6527
1
QCISD(T)         1.7355
13
    1.6170
3
    1.6507
1
1.7440
12
1.6512
1
1.7678
12
1.7423
12
  1.7677
12
1.7426
12
      1.6922
1
1.7234
4
1.6737
1
1.6509
1
QCISD(T)=FULL         1.7461
11
  1.7488
11
      1.6455
1
  1.6464
1
1.7774
11
1.7411
11
1.6762
5
1.7767
11
1.7475
10
1.6759
5
    1.6789
1
1.5560
2
1.6714
1
1.6386
1
QCISD(TQ)         1.7218
4
  1.7250
4
      1.6508
1
  1.6513
1
1.7557
4
1.7301
4
1.8922
2
1.7574
4
1.8174
3
1.8930
2
        1.6739
1
 
QCISD(TQ)=FULL         1.6810
5
  1.6838
5
      1.6456
1
    1.7137
5
1.8312
2
1.7598
3
1.7150
5
1.7541
3
1.7594
3
        1.6716
1
 
Coupled Cluster CCD   1.7717
12
1.7729
12
1.7712
12
1.7330
13
1.7364
12
1.7376
12
1.7422
13
1.7496
12
1.7424
12
1.6550
1
1.7416
12
1.6551
1
1.7648
12
1.7404
12
  1.7646
12
1.7451
11
  1.6943
1
1.6278
1
1.6479
2
1.7205
4
1.6768
1
1.6552
1
CCSD         1.7300
13
        1.8102
8
1.6528
1
1.7441
12
1.6532
1
1.7672
12
1.7426
12
1.6713
6
1.7669
12
1.6792
7
1.7297
4
      1.7253
4
1.6747
1
1.6530
1
CCSD=FULL         1.7339
12
        1.7966
8
1.6477
1
1.7414
12
1.6485
1
1.7646
12
1.6647
7
1.6629
6
1.7638
12
1.6597
6
1.7201
4
      1.7207
4
1.6724
1
1.6408
1
CCSD(T)         1.7283
14
1.6152
3
1.6552
1
1.6169
3
1.6609
1
1.6566
1
1.5694
2
1.7433
12
1.6513
1
1.7671
12
1.7416
12
1.6691
6
1.7670
12
1.7466
11
1.6694
6
1.6929
1
1.6255
1
1.6451
2
1.7226
4
1.6738
1
1.6510
1
CCSD(T)=FULL         1.7329
12
          1.6456
1
1.7405
12
1.6465
1
1.7644
12
1.7278
12
1.6605
6
1.7693
11
1.7323
11
1.6603
6
1.6777
1
1.6236
1
1.6364
2
1.7179
4
1.6715
1
1.6387
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 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)
daug-cc-pVDZ daug-cc-pVTZ daug-cc-pVQZ Sadlej_pVTZ CEP-31G CEP-31G* CEP-121G CEP-121G* LANL2DZ SDD
hartree fock HF 1.6797
1
1.6718
1
    1.7930
14
1.7796
14
1.7809
14
1.7634
14
1.7772
14
1.7767
14
density functional LSDA 1.6030
1
1.5907
1
               
BLYP 1.6324
1
1.6225
1
               
B1B95   1.6239
1
    1.7023
4
1.7087
4
       
B3LYP 1.6364
1
1.6267
1
    1.7926
13
1.7741
14
1.7664
14
1.7532
14
1.7567
14
1.7573
14
B3LYPultrafine 1.6364
1
1.6267
1
               
B3PW91 1.6362
1
1.6271
1
               
mPW1PW91 1.6369
1
1.6281
1
               
M06-2X 1.6444
1
1.6366
1
               
PBEPBE 1.6274
1
1.6182
1
               
PBEPBEultrafine 1.6274
1
1.6182
1
               
PBE1PBE 1.6361
1
1.6275
1
               
HSEh1PBE 1.6360
1
1.6272
1
               
TPSSh 1.6433
1
1.6344
1
               
wB97X-D 1.6465
1
1.6372
1
    1.6029
2
1.6007
2
1.5666
2
1.5613
2
1.5657
2
1.5655
2
B97D3 1.6419
1
1.6320
1
               
Moller Plesset perturbation MP2 1.6701
1
1.6509
1
    1.7933
14
1.7585
14
1.7703
14
1.7333
14
1.7725
14
1.7717
14
MP2=FULL 1.6678
1
1.6392
1
               
MP3 1.6748
1
1.6533
1
               
MP3=FULL 1.6725
1
1.6411
1
               
MP4 1.6746
1
1.6518
1
               
MP4=FULL 1.6723
1
1.6396
1
               
B2PLYP 1.6487
1
1.6361
1
               
B2PLYP=FULL 1.6480
1
1.6328
1
               
B2PLYP=FULLultrafine 1.6480
1
1.6328
1
               
Configuration interaction CID 1.6758
1
1.6549
1
               
CISD 1.6742
1
1.6539
1
               
Quadratic configuration interaction QCISD 1.6744
1
1.6527
1
               
QCISD(T) 1.6737
1
1.6509
1
               
QCISD(T)=FULL 1.6714
1
1.6386
1
               
QCISD(TQ) 1.6739
1
                 
QCISD(TQ)=FULL 1.6716
1
                 
Coupled Cluster CCD 1.6768
1
1.6552
1
               
CCSD 1.6747
1
1.6530
1
               
CCSD=FULL 1.6724
1
1.6408
1
               
CCSD(T) 1.6738
1
1.6510
1
               
CCSD(T)=FULL 1.6715
1
1.6387
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.