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III.G.1.a.

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 1.2660
7
PM3 1.6035
4
PM6 1.4699
12
composite G2 1.5757
13
G3 1.5757
13
G3B3 1.6271
13
G4 1.5830
10
CBS-Q 1.5542
11

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
hartree fock HF 1.5140
12
1.5811
13
1.5823
13
1.5836
13
1.5901
17
1.5796
13
1.5819
13
1.5781
13
1.5729
12
1.5744
12
1.6746
5
1.5733
14
1.5877
13
1.5789
13
1.5393
10
1.5765
12
1.5782
13
1.5392
10
1.7046
1
1.6492
2
1.6364
2
ROHF 1.4469
1
1.5897
2
1.5897
2
1.5888
2
1.5918
3
1.5701
2
1.5724
2
1.5715
2
1.5715
2
1.5034
1
  1.6321
1
1.5826
2
1.5703
2
1.6353
1
1.5829
2
1.5699
2
1.6353
1
     
density functional LSDA 1.5377
11
1.5733
11
1.5748
11
1.5782
11
1.5787
11
1.5787
11
1.5808
11
1.5701
11
1.5700
11
1.5759
11
  1.5839
3
1.5853
11
1.5709
11
  1.5845
11
1.5254
7
       
SVWN   1.5516
11
    1.5854
9
1.5901
3
1.5526
11
1.5843
3
1.5843
3
1.5888
3
    1.6005
3
1.5828
3
  1.6000
3
1.5826
3
       
BLYP 1.5753
12
1.6130
13
1.6088
12
1.6500
13
1.6139
13
1.6143
13
1.6156
13
1.6011
12
1.6064
12
1.6103
12
  1.5980
3
1.6200
13
1.6055
13
  1.6817
3
         
B1B95 1.5070
13
1.6314
13
1.6327
13
1.5990
13
1.5733
13
1.5734
13
1.6025
13
1.6251
13
1.6250
13
1.6282
13
  1.5903
3
1.5793
13
1.5910
13
1.5418
4
1.5801
13
1.5789
8
1.5911
3
  1.6288
2
1.6155
2
B3LYP 1.5626
13
1.6295
13
1.6308
13
1.6333
13
1.6377
12
1.6289
13
1.6302
13
1.6239
13
1.6072
9
1.6276
12
1.6789
3
1.6523
14
1.6352
13
1.6220
13
1.6039
10
1.6221
11
1.6079
11
1.6038
10
1.6838
1
1.6280
2
1.6121
2
B3LYPultrafine   1.6047
3
    1.6299
12
1.5941
3
1.6211
4
1.5914
3
      1.5895
3
1.6042
3
1.6123
4
  1.6040
3
1.5836
10
       
B3PW91 1.5152
9
1.6315
13
1.6328
13
1.6339
13
1.6306
13
1.6301
13
1.6019
12
1.6256
13
1.6091
9
1.6300
12
  1.5915
3
1.6359
13
1.6245
13
  1.6815
3
         
mPW1PW91 1.4869
10
1.6308
13
1.6248
10
1.6336
13
1.5966
13
1.5966
13
1.5985
13
1.5921
13
1.5901
12
1.6291
12
  1.5903
3
1.6025
13
1.5711
11
  1.6217
8
1.5712
5
       
M06-2X 1.5289
5
1.5852
5
1.5852
5
1.5885
5
1.5536
13
1.5804
5
1.5824
5
1.5774
5
1.5774
5
1.5782
5
  1.6036
4
1.5896
5
1.5750
5
  1.5885
5
1.5746
5
       
PBEPBE 1.5388
9
1.6129
13
1.6009
10
1.6018
10
1.6140
13
1.6140
13
1.6147
13
1.5983
12
1.6062
12
1.6108
12
1.6803
3
1.5984
3
1.6187
13
1.6064
13
1.5855
4
1.5542
7
1.5592
9
1.5853
4
     
PBEPBEultrafine   1.6122
3
    1.6485
8
1.6031
3
1.6055
3
1.5994
3
      1.5984
3
1.6115
3
1.5971
3
  1.6114
3
1.5970
3
       
PBE1PBE 1.5279
3
1.6067
3
1.6067
3
1.6076
3
1.5948
12
1.5948
3
1.5973
3
1.5929
3
1.5929
3
1.5944
3
  1.5910
3
1.6043
3
1.5910
3
  1.6044
3
1.5909
3
       
HSEh1PBE 1.5276
5
1.5832
5
1.5832
5
1.5853
5
1.6426
12
1.5773
5
1.5791
5
1.5740
5
1.5738
5
1.5760
5
  1.6003
4
1.5860
5
1.5717
5
  1.5849
5
1.5716
5
       
TPSSh   1.6156
3
1.6156
3
1.6148
3
1.5506
10
1.6023
3
1.5508
10
1.6002
3
      1.5980
3
1.6114
3
1.5475
10
  1.6114
3
1.5975
3
       
Moller Plesset perturbation MP2 1.4920
9
1.5811
13
1.5822
13
1.5867
13
1.5740
13
1.5739
13
1.5921
15
1.5777
13
1.5759
12
1.5577
11
  1.5728
14
1.5934
13
1.5644
12
1.5282
11
1.6063
11
1.5403
10
1.5287
11
1.6901
1
1.6187
2
1.5972
2
MP2=FULL 1.4917
9
1.5624
11
1.5575
10
1.5604
10
1.5714
13
1.5478
11
1.5504
11
1.5756
13
1.5388
9
1.5284
9
  1.5799
3
1.5702
11
1.5303
10
1.5215
11
1.5773
9
1.5346
8
1.5153
10
1.6756
1
1.6169
2
1.5934
2
ROMP2 1.5082
2
1.5802
2
1.5802
2
1.5820
2
1.5594
2
1.5594
2
1.5628
2
1.5671
2
1.5671
2
1.5595
2
  1.5975
1
1.5828
2
1.5609
2
  1.5836
2
         
MP3         1.5720
12
  1.5060
10
        1.5835
3
1.6100
3
1.5849
3
             
MP3=FULL         1.5251
10
  1.5273
10
        1.5817
3
1.6083
3
1.5730
3
             
MP4   1.6284
10
    1.5702
12
      1.5516
9
    1.5888
3
1.6161
3
1.5798
10
  1.6180
3
1.5897
3
       
MP4=FULL   1.6091
3
    1.5830
3
      1.5974
3
      1.6143
3
1.5774
3
  1.6161
3
1.5751
3
       
B2PLYP 1.5305
3
1.6033
3
1.6033
3
1.6051
3
1.5522
11
1.5889
3
1.5923
3
1.5904
3
1.5904
3
1.5884
3
  1.5865
3
1.6039
3
1.4867
8
  1.6042
3
1.5862
3
       
B2PLYP=FULL 1.5304
3
1.6032
3
1.6032
3
1.6049
3
1.5881
3
1.5881
3
1.5915
3
1.5899
3
1.5899
3
1.5867
3
  1.5859
3
1.6033
3
1.5831
3
  1.6036
3
1.5823
3
       
B2PLYP=FULLultrafine         1.6893
1
                               
Configuration interaction CID   1.6815
9
1.6815
9
1.5817
9
1.5975
10
    1.6007
9
                         
CISD   1.5982
8
1.5982
8
1.6014
8
1.5938
9
    1.5874
8
                         
Quadratic configuration interaction QCISD   1.6832
12
1.6888
9
1.5720
10
1.5797
13
1.5484
10
1.5661
9
1.5927
11
1.5888
10
1.5595
8
  1.5892
3
1.5907
9
1.5642
9
  1.6044
5
1.5899
6
       
QCISD(T)         1.5832
11
    1.7219
1
      1.5879
3
1.5954
9
1.5862
8
  1.6493
7
1.5942
6
       
QCISD(T)=FULL         1.5761
2
  1.5803
2
          1.6067
2
1.5691
2
1.5667
2
1.6083
2
1.5667
2
1.5667
2
     
QCISD(TQ)         1.6380
2
  1.6301
1
          1.6679
2
1.6413
2
1.6235
1
1.6633
1
1.6412
2
1.6239
1
     
QCISD(TQ)=FULL         1.5748
2
  1.5791
2
          1.6060
2
1.5206
1
1.5658
2
1.6079
2
1.5659
2
1.5658
2
     
Coupled Cluster CCD   1.6074
10
1.6074
10
1.5671
10
1.5705
12
1.5438
10
1.5469
10
1.5677
11
1.5463
9
1.5386
9
  1.5859
3
1.5705
10
1.5562
8
  1.6469
9
1.5675
9
    1.6278
2
1.6015
2
CCSD         1.5675
10
            1.5868
3
1.6026
5
1.5762
5
1.5814
3
1.6156
3
1.5874
3
1.5816
3
     
CCSD=FULL         1.5818
3
            1.5851
3
1.6123
3
1.5754
3
1.5736
3
1.6137
3
1.5729
3
1.5736
3
     
CCSD(T)         1.5825
11
1.7188
1
  1.7220
1
    1.4883
2
1.5855
3
1.5972
10
1.5864
9
1.6037
10
1.6338
9
1.6089
11
1.5990
9
  1.6255
2
1.5979
2
CCSD(T)=FULL         1.5921
8
            1.5835
3
1.6053
6
1.5607
7
1.5953
10
1.6016
5
1.5752
6
1.5772
10
  1.6236
2
1.5939
2

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 1.6277
13
1.6179
13
1.6005
13
1.5871
13
1.5965
13
1.5956
13
density functional B1B95 1.6984
5
1.7087
4
       
B3LYP 1.7164
12
1.6607
12
1.6874
13
1.6477
13
1.6500
13
1.6508
13
Moller Plesset perturbation MP2 1.7191
13
1.6215
13
1.6672
13
1.5832
13
1.6067
13
1.6055
13
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.