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Comparison of levels of theory for C-Al


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 1.7511
5
PM3 1.9342
5
PM6 1.9420
5
composite G2 1.9896
5
G3 1.9896
5
G3B3 1.9874
5
G4 1.9774
5
CBS-Q 1.9893
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 daug-cc-pVDZ daug-cc-pVTZ
hartree fock HF 1.9215
5
2.0112
5
1.9844
5
2.0113
5
1.9886
5
1.9876
5
1.9921
5
1.9863
5
1.9850
5
1.9785
5
2.0325
1
1.9936
5
2.0001
5
1.9869
5
2.0015
2
2.0008
5
1.9865
5
2.0018
2
1.9702
1
1.9706
1
2.0621
1
1.9865
5
ROHF   2.0268
1
1.9776
1
2.0269
1
1.9705
1
1.9705
1
1.9797
1
1.9718
1
1.9718
1
    1.9829
1
1.9973
1
1.9754
1
1.9693
1
2.0012
1
1.9756
1
1.9694
1
1.9701
1
1.9704
1
   
density functional LSDA 1.8985
1
1.9654
1
1.9654
1
2.0134
1
1.9561
1
1.9561
1
1.9616
1
1.9542
1
1.9542
1
1.9440
1
  1.9609
1
1.9742
1
1.9548
1
  1.9768
1
1.9538
1
  1.9484
1
1.9476
1
   
BLYP 1.9486
5
2.0219
5
1.9956
5
2.0224
5
1.9987
5
1.9980
5
2.0036
5
1.9984
5
1.9975
5
1.9864
5
2.0455
1
2.0272
2
2.0076
5
1.9974
5
  2.0407
2
2.0192
2
  1.9824
1
1.9820
1
2.0721
1
2.0491
1
B1B95 1.9277
5
1.9979
1
1.9779
5
2.0025
5
1.9789
5
1.9781
5
1.9822
5
1.9771
5
1.9762
5
1.9857
2
2.0262
1
2.0089
2
1.9888
5
2.0004
2
  2.0235
2
2.0011
2
  1.9665
1
1.9665
1
2.0539
1
2.0301
1
B3LYP 1.9355
5
2.0100
5
1.9832
5
2.0095
5
1.9857
5
1.9849
5
1.9900
5
1.9849
5
1.9839
5
1.9744
5
2.0321
1
1.9910
5
1.9950
5
1.9843
5
2.0004
2
2.0288
2
1.9838
5
2.0011
2
1.9704
1
1.9703
1
2.0593
1
2.0371
1
B3LYPultrafine 1.9163
3
2.0349
2
    1.9857
5
2.0022
2
2.0129
2
2.0038
2
  2.0148
1
2.0321
1
2.0150
2
2.0218
2
2.0054
2
  2.0288
2
1.9842
5
  1.9704
1
1.9703
1
2.0593
1
2.0371
1
B3PW91 1.9322
5
2.0094
5
1.9830
5
2.0075
5
1.9999
2
1.9828
5
1.9868
5
1.9818
5
1.9807
5
1.9729
5
2.0280
1
2.0114
2
1.9934
5
1.9812
5
  2.0259
2
2.0028
2
  1.9683
1
1.9681
1
2.0559
1
2.0317
1
mPW1PW91 1.9288
5
2.0067
5
1.9802
5
2.0044
5
1.9808
5
1.9799
5
1.9839
5
1.9787
5
1.9776
5
1.9702
5
2.0251
1
2.0082
2
1.9905
5
1.9784
5
  2.0234
2
2.0003
2
  1.9659
1
1.9659
1
2.0530
1
2.0288
1
M06-2X 1.9551
2
2.0291
2
1.9728
5
2.0366
2
1.9768
5
1.9965
2
2.0062
2
1.9990
2
1.9990
2
1.9867
2
1.9718
5
2.0088
2
2.0180
2
2.0021
2
  2.0244
2
2.0028
2
  1.9654
1
1.9651
1
2.0582
1
2.0349
1
PBEPBE 1.9407
5
2.0174
5
1.9913
5
2.0160
5
1.9921
5
1.9912
5
1.9958
5
1.9904
5
1.9894
5
1.9807
5
2.0375
1
2.0198
2
2.0018
5
1.9898
5
  2.0342
2
2.0114
2
  1.9760
1
1.9757
1
2.0655
1
2.0412
1
PBEPBEultrafine   2.0437
2
    2.0087
2
2.0087
2
2.0183
2
2.0095
2
  2.0204
1
2.0375
1
2.0198
2
2.0286
2
2.0107
2
  2.0341
2
2.0114
2
  1.9760
1
1.9757
1
2.0655
1
2.0412
1
PBE1PBE 1.9570
2
1.9993
1
1.9894
2
2.0388
2
1.9808
5
1.9972
2
2.0063
2
1.9980
2
1.9980
2
1.9856
2
2.0256
1
2.0088
2
2.0180
2
2.0000
2
  2.0239
2
2.0008
2
  1.9662
1
1.9663
1
2.0539
1
2.0296
1
HSEh1PBE 1.9582
2
2.0070
5
1.9899
2
2.0397
2
1.9811
5
1.9979
2
1.9843
5
1.9990
2
1.9990
2
1.9859
2
2.0261
1
2.0097
2
2.0187
2
1.9790
5
  2.0246
2
2.0014
2
  1.9668
1
1.9668
1
2.0544
1
2.0301
1
TPSSh 2.0095
1
2.0358
2
1.9931
2
2.0402
2
1.9876
5
1.9992
2
1.9904
5
2.0003
2
2.0273
1
1.9816
4
2.0259
1
2.0100
2
2.0196
2
1.9846
5
2.0252
1
2.0248
2
2.0022
2
2.0261
1
1.9695
1
1.9694
1
2.0526
1
2.0295
1
wB97X-D 2.0036
1
2.0322
1
1.9794
5
2.0460
1
1.9808
5
2.0227
1
1.9838
5
2.0249
1
1.9780
5
2.0082
1
2.0236
1
1.9844
5
1.9856
5
1.9786
5
2.0221
1
2.0518
1
1.9778
5
2.0228
1
    2.0517
1
2.0273
1
B97D3 2.0253
1
2.0197
5
2.0159
1
2.0662
1
1.9970
5
2.0424
1
1.9997
5
2.0446
1
1.9945
5
2.0272
1
1.9900
5
1.9998
5
2.0624
1
1.9944
5
2.0403
1
2.0704
1
1.9929
5
2.0417
1
    2.0702
1
1.9925
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 daug-cc-pVDZ daug-cc-pVTZ
Moller Plesset perturbation MP2 1.9301
5
2.0232
5
1.9838
5
2.0250
5
1.9816
5
1.9807
5
1.9860
5
1.9799
5
1.9787
5
1.9724
5
2.0209
1
1.9878
5
1.9992
5
2.0035
2
1.9979
2
2.0055
5
2.0076
2
1.9996
2
1.9770
1
1.9797
1
2.0613
1
2.0301
1
MP2=FULL 1.9297
5
2.0227
5
1.9815
5
2.0245
5
1.9779
5
1.9770
5
1.9820
5
1.9770
5
1.9762
5
1.9612
5
2.0152
1
2.0098
2
1.9963
5
1.9950
2
1.9513
2
2.0332
2
1.9916
2
1.9393
2
1.9679
1
1.9636
1
2.0506
1
2.0096
1
ROMP2 1.9149
1
  1.9741
1
2.0412
1
1.9707
1
1.9707
1
1.9816
1
1.9754
1
1.9754
1
1.9671
1
  1.9855
1
2.0062
1
1.9839
1
  2.0201
1
    1.9785
1
1.9814
1
   
MP3         1.9707
4
  1.9730
4
        1.9836
1
2.0070
1
1.9838
1
        1.9785
1
1.9817
1
   
MP3=FULL         1.9679
4
  1.9695
4
        1.9840
1
2.0052
1
1.9762
1
        1.9702
1
1.9664
1
   
MP4   2.0226
4
    1.9747
4
      1.9761
1
    1.9858
1
2.0093
1
1.9856
1
  2.0266
1
1.9889
1
  1.9805
1
1.9838
1
   
MP4=FULL   2.0438
1
    1.9685
1
      1.9748
1
      2.0067
1
1.9779
1
  2.0214
1
1.9745
1
  1.9719
1
1.9678
1
   
B2PLYP 1.9585
2
2.0359
2
1.9870
2
2.0454
2
1.9820
5
1.9960
2
2.0076
2
1.9981
2
1.9981
2
1.9850
2
2.0253
1
2.0101
2
2.0198
2
1.9817
5
  2.0290
2
2.0037
2
  1.9695
1
1.9705
1
2.0570
1
2.0311
1
B2PLYP=FULL 1.9585
2
2.0359
2
1.9864
2
2.0454
2
1.9951
2
1.9951
2
2.0063
2
1.9975
2
1.9975
2
1.9812
2
2.0235
1
2.0099
2
2.0189
2
1.9990
2
  2.0272
2
1.9989
2
  1.9665
1
1.9655
1
2.0535
1
2.0251
1
B2PLYP=FULLultrafine 2.0038
1
2.0381
1
1.9957
1
2.0560
1
1.9809
5
2.0212
1
2.0355
1
2.0244
1
2.0244
1
2.0041
1
2.0235
1
2.0394
1
1.9931
5
1.9788
5
  2.0544
1
1.9776
5
      2.0535
1
2.0251
1
Configuration interaction CID   2.0208
5
1.9826
5
2.0236
5
1.9803
5
    1.9782
5
    2.0214
1
  2.0492
1
2.0258
1
        1.9759
1
1.9785
1
2.0622
1
2.0296
1
CISD   2.0215
5
1.9834
5
2.0240
5
1.9804
5
    1.9781
5
    2.0215
1
  2.0498
1
2.0259
1
        1.9727
1
1.9751
1
2.0626
1
2.0296
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 daug-cc-pVDZ daug-cc-pVTZ
Quadratic configuration interaction QCISD   2.0283
5
1.9902
2
2.0622
2
1.9827
5
1.9944
2
2.0049
2
1.9963
2
1.9963
2
1.9863
2
2.0215
1
2.0082
2
2.0270
2
2.0014
2
  2.0412
2
2.0047
2
  1.9715
1
1.9738
1
2.0656
1
2.0305
1
QCISD(T)         1.9841
5
    1.9963
2
    2.0217
1
2.0094
2
2.0279
2
2.0020
2
  2.0430
2
2.0059
2
  1.9729
1
1.9758
1
2.0671
1
2.0316
1
QCISD(T)=FULL         1.9922
2
  2.0017
2
      2.0166
1
  2.0252
2
1.9937
2
1.9484
2
2.0357
2
1.9907
2
1.9366
2
1.9630
1
1.9592
1
2.0561
1
2.0111
1
QCISD(TQ)         1.9673
1
  1.9756
1
          2.0036
1
1.9778
1
1.9687
1
2.0174
1
1.9799
1
1.9697
1
       
QCISD(TQ)=FULL         1.9651
1
  1.9726
1
          2.0016
1
1.9693
1
1.9288
1
2.0123
1
1.9656
1
1.9187
1
       
Coupled Cluster CCD   2.0265
5
1.9873
2
2.0603
2
1.9822
5
1.9952
2
2.0062
2
1.9980
2
1.9980
2
1.9882
2
2.0210
1
2.0099
2
2.0284
2
2.0042
2
  2.0437
2
2.0080
2
  1.9777
1
1.9807
1
2.0639
1
2.0300
1
CCSD         1.9823
5
2.0226
1
2.0348
1
2.0226
1
2.0226
1
1.9859
2
2.0213
1
2.0078
2
2.0264
2
2.0011
2
1.9948
2
2.0404
2
2.0045
2
1.9961
2
1.9713
1
1.9735
1
2.0650
1
2.0302
1
CCSD=FULL         1.9914
2
        1.9744
2
2.0160
1
2.0077
2
2.0240
2
1.9931
2
1.9485
2
2.0336
2
1.9892
2
1.9367
2
1.9619
1
1.9572
1
2.0545
1
2.0107
1
CCSD(T)         1.9837
5
1.9947
2
2.0347
1
1.9959
2
2.0220
1
2.0087
1
2.0216
1
2.0090
2
2.0273
2
2.0017
2
1.9954
2
2.0424
2
2.0055
2
1.9966
2
1.9723
1
1.9752
1
2.0668
1
2.0315
1
CCSD(T)=FULL         1.9917
2
          2.0165
1
2.0087
2
2.0246
2
1.9934
2
1.9483
2
2.0352
2
1.9904
2
1.9365
2
1.9626
1
1.9588
1
2.0558
1
2.0110
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 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 2.0100
5
1.9993
5
2.0119
5
1.9949
5
2.0100
5
1.9976
5
    1.9831
5
density functional BLYP                 2.0431
1
B1B95 1.9829
3
1.9810
3
1.9824
3
1.9761
3
1.9821
3
1.9678
3
    2.0256
1
B3LYP 2.0127
5
2.0000
5
2.0127
5
1.9961
5
2.0089
5
1.9967
5
    1.9815
5
B3LYPultrafine                 2.0306
1
B3PW91                 2.0270
1
mPW1PW91                 2.0242
1
M06-2X                 2.0300
1
PBEPBE                 1.9870
5
PBEPBEultrafine                 2.0359
1
PBE1PBE                 2.0247
1
HSEh1PBE                 2.0252
1
TPSSh                 2.0251
1
wB97X-D 2.0570
1
2.0542
1
2.0616
1
2.0467
1
2.0463
1
2.0244
1
    2.0222
1
B97D3                 2.0416
1
Moller Plesset perturbation MP2 2.0316
5
1.9959
5
2.0294
5
1.9883
5
2.0310
5
2.0134
5
    1.9793
5
MP2=FULL                 2.0180
1
B2PLYP                 2.0246
1
B2PLYP=FULL                 2.0234
1
B2PLYP=FULLultrafine                 2.0234
1
Configuration interaction CID                 2.0228
1
CISD                 2.0230
1
Quadratic configuration interaction QCISD                 2.0233
1
QCISD(T)                 2.0233
1
QCISD(T)=FULL                 2.0200
1
Coupled Cluster CCD                 2.0227
1
CCSD                 2.0231
1
CCSD=FULL                 2.0200
1
CCSD(T)                 2.0232
1
CCSD(T)=FULL                 2.0199
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.