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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 1.5680
22
PM3 1.6945
13
PM6 1.6233
17
composite G2 1.7205
24
G3 1.7619
54
G3B3 1.7039
25
G3MP2 1.5913
4
G4 1.6911
26
CBS-Q 1.7669
53

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-pCVDZ cc-pCVTZ aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
hartree fock HF 1.6954
25
1.7324
25
1.7331
25
1.7323
25
1.7056
25
1.7226
25
1.7235
25
1.7240
25
1.7245
25
1.7251
25
1.6807
16
1.7182
27
1.7319
25
1.7235
25
1.7252
22
1.7315
24
1.7220
24
1.7252
22
1.7054
1
1.6492
1
1.6709
2
1.7480
4
1.6539
3
1.6647
20
ROHF   1.8450
4
1.8450
4
1.8241
4
1.7732
4
1.7743
4
1.7729
4
1.7756
4
1.7754
4
  1.6281
2
1.7747
4
1.7852
4
1.7770
4
1.7759
4
1.7860
4
1.7775
4
1.7757
4
      1.9267
2
1.6414
2
1.6283
2
density functional LSDA 1.6805
23
1.6982
23
1.6989
23
1.6976
23
1.6921
23
1.6918
23
1.6923
23
1.6859
23
1.6859
23
1.6904
23
1.6516
10
1.6878
21
1.6996
23
1.6847
23
  1.6967
23
1.6875
20
        1.6947
4
1.6030
1
1.5907
1
BLYP 1.7043
25
1.7190
25
1.7197
25
1.7193
25
1.6799
28
1.7122
25
1.7127
25
1.7077
25
1.7077
25
1.7108
25
1.6617
12
1.7090
23
1.7196
25
1.7047
25
  1.6638
16
1.7261
19
  1.6862
1
    1.7258
4
1.5987
3
1.5855
3
B1B95 1.6752
25
1.7051
24
1.7039
25
1.7025
25
1.6885
25
1.6885
25
1.6959
25
1.6915
25
1.6916
25
1.6942
25
1.6457
12
1.6915
23
1.6945
25
1.6898
25
1.5170
2
1.6793
15
1.6970
21
1.6403
1
  1.6288
1
1.6155
1
1.7214
4
  1.6239
1
B3LYP 1.6875
25
1.7096
25
1.7102
25
1.7103
25
1.7112
24
1.7026
25
1.7030
25
1.6993
25
1.7017
23
1.7020
25
1.6587
15
1.6943
27
1.7105
25
1.6966
25
1.6983
22
1.7076
24
1.6901
24
1.6983
22
1.6840
1
1.6280
1
1.6479
2
1.7168
4
1.5925
3
1.5790
3
B3LYPultrafine   1.7152
23
    1.7028
25
1.7046
23
1.7050
23
1.7017
23
  1.6591
12
1.6536
12
1.6997
23
1.7133
23
1.6984
23
  1.7105
23
1.6857
26
  1.6841
1
    1.7168
4
1.5925
3
1.5790
3
B3PW91 1.6884
23
1.7065
25
1.7072
25
1.7062
25
1.6991
25
1.6986
25
1.6990
25
1.6957
25
1.6977
23
1.6988
25
1.6508
12
1.6960
23
1.7058
25
1.6938
25
  1.6542
16
1.6367
13
  1.6864
1
    1.7196
4
1.5873
3
1.5752
3
mPW1PW91 1.6793
23
1.7046
25
1.7105
23
1.7047
25
1.6967
25
1.6965
25
1.6973
25
1.6941
25
1.6942
25
1.6969
25
1.6493
12
1.6943
23
1.7036
25
1.6913
24
  1.7018
25
1.6940
22
  1.6857
1
    1.7188
4
1.5850
3
1.5733
3
M06-2X 1.6920
23
1.7103
23
1.6601
29
1.7135
23
1.6962
26
1.7000
23
1.7004
23
1.6975
23
1.6978
23
1.6991
23
1.6790
26
1.6956
23
1.7064
23
1.6951
23
  1.7042
23
1.6957
22
        1.7266
4
1.5874
3
1.5756
3
PBEPBE 1.6932
23
1.7109
25
1.7172
23
1.7145
23
1.7036
25
1.7033
25
1.7035
25
1.6983
24
1.6991
25
1.7026
25
1.6641
16
1.7000
23
1.7096
25
1.6974
25
1.5908
2
1.7099
23
1.6970
23
1.5907
2
    1.6857
1
1.7234
4
1.5913
3
1.5798
3
PBEPBEultrafine   1.7164
23
    1.7036
25
1.7050
23
1.7053
23
1.7014
23
  1.6611
12
1.6554
12
1.7000
23
1.7124
23
1.6990
23
  1.7098
23
1.6997
22
        1.7234
4
1.5913
3
1.5798
3
PBE1PBE 1.6833
23
1.7113
22
1.7099
23
1.7078
23
1.6937
26
1.6974
23
1.6974
23
1.6951
23
1.6952
23
1.6975
23
1.6488
12
1.6935
23
1.7049
23
1.6929
23
  1.7028
23
1.6933
22
        1.7189
4
1.5837
3
1.5724
3
HSEh1PBE 1.6842
23
1.6882
26
1.7098
23
1.7081
23
1.6938
26
1.6974
23
1.6939
26
1.6953
23
1.6953
23
1.6976
23
1.6489
12
1.6935
23
1.7053
23
1.6745
26
  1.7030
23
1.6932
22
        1.7185
4
1.5842
3
1.5727
3
TPSSh 1.6417
13
1.7206
23
1.7214
23
1.7170
23
1.6780
26
1.7077
23
1.6780
26
1.7057
23
1.6462
13
1.6019
20
1.6575
12
1.7043
23
1.7159
23
1.6746
26
1.5541
4
1.7136
23
1.7043
22
1.6423
13
      1.7280
4
1.5985
3
1.5856
3
wB97X-D 1.6386
13
1.6494
13
1.6029
24
1.6527
13
1.5997
24
1.6424
13
1.6004
24
1.6415
13
1.5969
24
1.6422
13
1.6524
12
1.5964
24
1.6049
24
1.5954
24
1.6371
13
1.6495
13
1.5954
24
1.6371
13
      1.5474
2
1.5906
3
1.5780
3
B97D3 1.6476
13
1.6194
24
1.6603
13
1.6602
13
1.6169
24
1.6514
13
1.6172
24
1.6496
13
1.6143
24
1.6508
13
1.6498
29
1.6793
24
1.6599
13
1.6131
24
1.6453
13
1.6573
13
1.6789
24
1.6454
13
        1.6025
3
1.7023
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(T+d)Z cc-pCVDZ cc-pCVTZ aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Moller Plesset perturbation MP2 1.7057
23
1.7228
25
1.7234
25
1.7245
25
1.6385
29
1.6922
25
1.6934
25
1.6423
29
1.7012
25
1.6941
24
1.6525
12
1.6922
27
1.7157
25
1.6945
25
1.6912
22
1.7141
24
1.6959
22
1.6915
22
1.6901
1
1.6187
1
1.6437
2
1.7142
4
1.6000
3
1.5775
3
MP2=FULL 1.7050
23
1.7233
24
1.7288
23
1.7287
23
1.6882
25
1.6877
24
1.6886
24
1.6946
25
1.6999
23
1.6853
23
1.6453
12
1.6936
23
1.7129
24
1.6788
23
1.6824
22
1.7110
24
1.6851
22
1.6825
22
1.6757
1
1.6169
1
1.6353
2
1.7095
4
1.5976
3
1.5669
3
ROMP2 1.7161
4
1.7965
4
1.7963
4
1.7839
4
1.6998
4
1.7008
4
1.7018
4
1.7092
4
1.7099
4
1.7047
4
1.5377
2
1.7046
4
1.7270
4
1.7045
4
  1.7272
4
          1.8695
2
1.5638
2
1.5396
2
MP3         1.6941
25
  1.6644
25
      1.5794
3
1.7015
22
1.7300
23
1.7007
22
              1.7155
4
1.6497
3
1.5820
2
MP3=FULL   1.6714
13
1.6714
13
1.6750
13
1.6620
26
1.6377
13
1.6641
26
1.6452
13
1.6490
13
1.6333
13
1.6501
12
1.6985
23
1.7276
23
1.6886
23
  1.6735
13
1.5316
3
        1.7110
4
1.6024
2
1.5707
2
MP4   1.7577
13
    1.7037
16
      1.7240
13
  1.5815
3
1.7158
13
1.7476
14
1.7051
16
  1.7408
13
1.7145
13
        1.7190
4
1.6090
3
1.5826
3
MP4=FULL   1.7572
13
    1.7042
14
      1.7207
13
  1.5762
3
  1.7449
14
1.7013
13
  1.7377
13
1.7009
13
        1.7145
4
1.6062
3
1.5715
3
B2PLYP 1.7014
23
1.7178
23
1.7185
23
1.7204
23
1.6948
25
1.7006
23
1.7017
23
1.7010
23
1.7028
23
1.7015
23
1.6538
12
1.6986
23
1.7175
23
1.6569
26
  1.7161
23
1.6983
22
      1.6849
1
1.7153
4
1.6265
3
1.5811
3
B2PLYP=FULL 1.7011
23
1.7177
23
1.7183
23
1.7201
23
1.6991
23
1.6995
23
1.7004
23
1.7000
23
1.7015
23
1.6980
23
1.6516
12
1.6977
23
1.7165
23
1.6943
23
  1.7150
23
1.6952
22
      1.6809
1
1.7139
4
1.6257
3
1.5778
3
B2PLYP=FULLultrafine 1.6518
13
1.6550
13
1.6550
13
1.6616
13
1.7374
56
1.6417
13
1.6429
13
1.6426
13
1.6441
13
1.6395
13
1.6516
12
1.6398
13
1.7517
56
1.7340
56
  1.6599
13
1.7344
56
        1.5459
2
1.6257
3
1.5777
3
Configuration interaction CID   1.7306
23
1.7312
23
1.7314
23
1.6999
25
    1.7095
24
    1.6641
12
  1.6881
12
1.6656
12
              1.7195
4
1.6495
3
1.5805
2
CISD   1.7318
23
1.7324
23
1.7327
23
1.7034
24
    1.7263
14
    1.6642
12
  1.6881
12
1.6657
12
              1.7227
4
1.6488
3
1.5805
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-pCVDZ cc-pCVTZ aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Quadratic configuration interaction QCISD   1.7296
25
1.7362
23
1.7369
23
1.7007
25
1.7056
23
1.7065
23
1.7101
25
1.7148
24
1.7102
23
1.6681
12
1.7102
23
1.7494
14
1.7087
23
  1.6977
18
1.7283
12
  1.6930
1
  1.6931
1
1.7258
4
1.6491
3
1.5818
2
QCISD(T)         1.7114
15
    1.5953
5
    1.5860
3
1.7171
14
1.7496
14
1.7233
14
  1.7493
14
1.7235
14
      1.6922
1
1.7234
4
1.6499
3
1.6229
3
QCISD(T)=FULL         1.7161
13
  1.7267
13
      1.5796
3
  1.7559
13
1.7124
13
1.6479
6
1.7550
13
1.7132
12
1.6477
6
    1.6789
1
1.5560
2
1.6472
3
1.5713
2
QCISD(TQ)         1.6660
6
  1.6838
5
      1.5864
3
  1.7122
5
1.6870
5
1.7651
3
1.7180
6
1.7418
4
1.8930
2
        1.6063
2
1.5151
1
QCISD(TQ)=FULL         1.6439
7
  1.6615
7
      1.5780
2
  1.6918
7
1.7231
3
1.6965
4
1.6854
6
1.6914
4
1.7594
3
        1.6044
2
1.5044
1
Coupled Cluster CCD   1.7331
23
1.7338
23
1.7344
23
1.6973
24
1.7034
23
1.7044
23
1.7060
24
1.7160
23
1.7084
23
1.6678
12
1.7082
23
1.7312
23
1.7071
23
  1.7303
23
1.7254
12
  1.6943
1
1.6278
1
1.6479
2
1.7205
4
1.6511
3
1.5822
2
CCSD         1.6998
24
1.6070
2
1.6091
2
1.6083
2
1.6196
2
1.7301
19
1.6225
3
1.7097
23
1.7327
23
1.7084
22
1.6478
7
1.7317
23
1.6581
8
1.6852
5
      1.7253
4
1.6494
3
1.5817
2
CCSD=FULL         1.6971
23
        1.7173
19
1.6608
12
1.7069
23
1.7301
23
1.6495
9
1.6400
7
1.7286
23
1.6367
7
1.7201
4
      1.7207
4
1.6023
2
1.5705
2
CCSD(T)         1.7066
16
1.6120
5
1.6244
3
1.5947
5
1.6331
3
1.5876
3
1.5609
4
1.7163
14
1.7490
14
1.7228
14
1.6465
7
1.7487
14
1.7175
13
1.6468
7
1.6929
1
1.6255
1
1.6451
2
1.7226
4
1.6498
3
1.5873
3
CCSD(T)=FULL         1.7068
14
          1.5791
3
1.7134
14
1.7463
14
1.7016
14
1.6385
7
1.7487
13
1.7028
13
1.6383
7
1.6777
1
1.6236
1
1.6364
2
1.7179
4
1.6470
3
1.5713
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-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 1.7632
25
1.7484
25
1.7504
25
1.7319
25
1.7486
25
1.7480
25
    1.6482
29
ROHF                 1.6281
2
density functional LSDA                 1.6526
10
BLYP                 1.6624
12
B1B95 1.7023
4
1.7087
4
            1.6462
12
B3LYP 1.7586
24
1.7425
25
1.7366
25
1.7200
25
1.7277
25
1.7279
25
    1.6442
29
B3LYPultrafine                 1.6542
12
B3PW91                 1.6513
12
mPW1PW91                 1.6498
12
M06-2X                 1.6489
12
PBEPBE                 1.6459
29
PBEPBEultrafine                 1.6561
12
PBE1PBE                 1.6493
12
HSEh1PBE                 1.6493
12
TPSSh                 1.6578
12
wB97X-D 1.6948
13
1.6805
13
1.6697
13
1.6531
13
1.6686
13
1.6682
13
    1.6529
12
B97D3                 1.6628
11
Moller Plesset perturbation MP2 1.7688
25
1.7320
25
1.7457
25
1.7014
25
1.7495
25
1.7484
25
    1.6378
29
MP2=FULL                 1.6487
12
ROMP2                 1.5396
2
MP3                 1.6585
12
MP3=FULL                 1.5778
3
MP4                 1.5832
3
MP4=FULL                 1.5786
3
B2PLYP                 1.6550
12
B2PLYP=FULL                 1.6534
12
B2PLYP=FULLultrafine                 1.6535
12
Configuration interaction CID                 1.6246
3
CISD                 1.6239
3
Quadratic configuration interaction QCISD                 1.6692
12
QCISD(T)                 1.6227
3
QCISD(T)=FULL                 1.6168
3
QCISD(TQ)                 1.5832
2
QCISD(TQ)=FULL                 1.5112
1
Coupled Cluster CCD                 1.6689
12
CCSD                 1.6691
12
CCSD=FULL                 1.6179
3
CCSD(T)                 1.6227
3
CCSD(T)=FULL                 1.6170
3
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.