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Comparison of levels of theory for Al-O


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 1.6354
6
PM3 1.7295
3
PM6 1.6367
6
composite G2 1.6903
4
G3 1.6903
4
G3B3 1.6897
4
G3MP2 1.6972
1
G4 1.6605
6
CBS-Q 1.6911
4

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-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
hartree fock HF 1.6549
6
1.6807
6
1.6598
6
1.7543
3
1.6668
6
1.6653
6
1.6701
6
1.6629
6
1.6633
6
1.6530
6
1.6762
4
1.6656
6
1.6936
6
1.6591
6
1.6530
6
1.6842
6
1.6587
6
1.6528
6
1.6739
4
1.6729
3
1.6966
3
1.6582
6
ROHF   1.7195
1
1.6917
1
  1.7044
1
1.7044
1
1.7165
1
1.7048
1
        1.7375
1
1.7006
1
               
density functional LSDA 1.6016
3
1.6416
3
1.6317
3
1.6813
3
1.6267
3
1.6267
3
1.6333
3
1.6279
3
1.6279
3
1.6134
3
    1.6479
3
1.6207
3
1.6145
2
1.6433
3
1.6213
2
1.6147
2
1.6803
3
1.6831
3
   
BLYP 1.6772
6
1.7009
6
1.6804
6
1.7184
6
1.6913
6
1.6862
6
1.6924
6
1.6864
6
1.6871
6
1.6729
6
1.7117
3
1.7222
3
1.7054
6
1.6821
6
  1.7218
4
1.7177
3
  1.7083
3
1.7105
3
1.7377
3
1.7171
3
B1B95 1.6520
6
1.6850
3
1.6596
6
1.6926
6
1.6652
6
1.6654
6
1.6692
6
1.6628
6
1.6635
6
1.6531
6
1.6877
3
1.6974
3
1.6857
6
1.6599
6
1.6180
2
1.6471
2
1.6658
5
1.6183
2
1.6854
3
1.6875
3
   
B3LYP 1.6591
6
1.6821
6
1.6648
6
1.6995
6
1.6708
6
1.6697
6
1.6755
6
1.6693
6
1.6700
6
1.6575
6
1.6774
4
1.6716
6
1.6903
6
1.6656
6
1.6660
5
1.6868
6
1.6659
6
1.6601
6
1.6743
4
1.6933
3
1.7195
3
1.6992
3
B3LYPultrafine   1.6962
3
    1.6707
6
1.7047
3
1.7082
3
1.7016
3
  1.6929
3
1.6940
3
1.7043
3
1.7232
3
1.7003
3
  1.7205
3
1.6677
6
  1.6909
3
1.6932
3
1.7195
3
1.6992
3
B3PW91 1.6569
6
1.6813
6
1.6643
6
1.6970
6
1.6686
6
1.6676
6
1.6724
6
1.6661
6
1.6669
6
1.6558
6
1.6926
3
1.7027
3
1.6893
6
1.6630
6
  1.7025
4
1.6985
3
  1.6900
3
1.6922
3
1.7183
3
1.6978
3
mPW1PW91 1.6530
6
1.6775
6
1.6611
6
1.6938
6
1.6653
6
1.6643
6
1.6690
6
1.6627
6
1.6634
6
1.6528
6
1.6891
3
1.6990
3
1.6863
6
1.6597
6
  1.6991
4
1.6951
3
  1.6866
3
1.6887
3
1.7148
3
1.6944
3
M06-2X 1.6952
3
1.6774
3
1.6521
6
1.6921
3
1.6600
6
1.6962
3
1.6985
3
1.6918
3
1.6931
3
1.6868
3
1.6493
6
1.6934
3
1.7155
3
1.6902
3
  1.7115
3
1.6893
3
  1.6823
3
1.6846
3
1.7103
3
1.6888
3
PBEPBE 1.6724
6
1.6996
6
1.6846
5
1.7183
5
1.6840
6
1.6831
6
1.6882
6
1.6819
6
1.6827
6
1.6703
6
1.6902
4
1.7188
3
1.7038
6
1.6781
6
1.6348
2
1.7371
3
1.7145
3
1.6353
2
1.6866
4
1.7073
3
1.7354
3
1.7137
3
PBEPBEultrafine   1.7186
3
    1.7030
4
1.7200
3
1.7232
3
1.7158
3
  1.7072
3
1.7086
3
1.7185
3
1.7397
3
1.7150
3
  1.7372
3
1.7145
3
  1.7049
3
1.7073
3
1.7354
3
1.7137
3
PBE1PBE 1.7036
3
1.6889
3
1.6889
3
1.7013
3
1.6662
6
1.7035
3
1.7043
3
1.6970
3
1.6985
3
1.6903
3
1.6898
3
1.6997
3
1.7215
3
1.6964
3
  1.7170
3
1.6956
3
  1.6872
3
1.6893
3
1.7153
3
1.6950
3
HSEh1PBE 1.7041
3
1.6786
6
1.6885
3
1.7009
3
1.6664
6
1.7011
3
1.6703
6
1.6971
3
1.6986
3
1.6902
3
1.6897
3
1.6997
3
1.7210
3
1.6607
6
  1.7165
3
1.6957
3
  1.6871
3
1.6893
3
1.7154
3
1.6950
3
TPSSh 1.7164
3
1.7045
3
1.6976
3
1.7123
3
1.6781
6
1.7091
3
1.6817
6
1.7050
3
1.7066
3
1.6670
6
1.6978
3
1.7079
3
1.7292
3
1.6737
6
1.6985
3
1.7257
3
1.7040
3
1.6986
3
1.6952
3
1.6973
3
1.7241
3
1.7032
3
wB97X-D 1.7034
3
1.6865
3
1.6603
6
1.6943
3
1.6696
6
1.7004
3
1.6743
6
1.6958
3
1.6684
6
1.6884
3
1.6883
3
1.6701
6
1.6821
6
1.6658
6
1.6896
3
1.7154
3
1.6660
6
1.6894
3
1.6856
3
1.6878
3
1.7141
3
1.6940
3
B97D3 1.7267
3
1.6997
6
1.7077
3
1.7270
3
1.6871
6
1.7186
3
1.6908
6
1.7149
3
1.6986
6
1.7068
3
1.6772
6
1.6827
6
1.7387
3
1.6827
6
1.7083
3
1.7358
3
1.6772
6
1.7088
3
1.7049
3
1.7069
3
1.7343
3
1.6767
6
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-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Moller Plesset perturbation MP2 1.6351
6
1.6813
6
1.6673
6
1.7010
6
1.6712
6
1.6717
6
1.6730
6
1.6628
6
1.6666
6
1.6596
6
1.6985
3
1.6715
6
1.6931
6
1.6238
3
1.6584
6
1.6913
6
1.6671
6
1.6794
4
1.6748
4
1.6989
3
1.7308
3
1.7068
3
MP2=FULL 1.6371
6
1.6820
6
1.6673
5
1.6930
5
1.6727
6
1.6717
6
1.6722
6
1.6637
6
1.6661
6
1.6628
5
1.6926
3
1.7088
3
1.6932
6
1.6676
5
1.6373
6
1.7126
4
1.6970
3
1.6739
3
1.6648
4
1.6927
3
1.7274
3
1.6934
3
MP3         1.6739
6
  1.6758
6
      1.6872
3
1.6987
3
1.7230
3
1.6939
3
        1.6859
3
1.6875
3
1.7195
3
1.6943
3
MP3=FULL   1.6865
3
1.6856
3
1.7013
3
1.6726
6
1.7022
3
1.6792
6
1.6894
3
1.6935
3
1.6871
3
  1.6977
3
1.7228
3
1.6898
3
  1.7206
3
1.6853
3
  1.6792
3
1.6822
3
1.7164
3
1.6822
3
MP4   1.9208
2
    1.6842
6
      1.6822
5
    1.7108
3
1.7341
3
1.6353
3
  1.7343
3
1.7074
3
    1.6991
3
   
MP4=FULL   1.6977
3
    1.7132
3
      1.7040
3
  1.6937
3
  1.7338
3
    1.7331
3
1.6976
3
  1.6906
3
1.6938
3
   
B2PLYP 1.7008
3
1.6921
3
1.6892
3
1.7048
3
1.6674
6
1.7049
3
1.6872
4
1.6991
3
1.7015
3
1.6937
3
1.6942
3
1.7046
3
1.7246
3
1.6674
6
  1.7227
3
1.7010
3
  1.6915
3
1.6936
3
1.7206
3
1.7011
3
B2PLYP=FULL 1.7010
3
1.6853
4
1.6892
3
1.7049
3
1.6885
4
1.7047
3
1.6911
4
1.6987
3
1.7012
3
1.6926
3
1.6925
3
1.7042
3
1.7245
3
1.6990
3
  1.7223
3
1.6982
3
  1.6894
3
1.6919
3
1.7197
3
1.6974
3
B2PLYP=FULLultrafine 1.7010
3
1.6922
3
1.6892
3
1.7048
3
1.6674
6
1.7046
3
1.7085
3
1.6986
3
1.7011
3
1.6926
3
1.6924
3
1.7040
3
1.6871
6
1.6608
6
  1.7225
3
1.6607
6
  1.6894
3
1.6918
3
1.7205
3
 
Configuration interaction CID   1.6700
5
1.6610
5
1.6874
5
1.6694
6
    1.6608
6
    1.6796
3
  1.7164
3
1.6864
3
        1.6785
3
1.6801
3
   
CISD   1.6783
5
1.6664
5
1.6963
5
1.6708
6
    1.6634
5
        1.7171
3
              1.7113
3
 
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-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Quadratic configuration interaction QCISD   1.6987
6
1.6822
5
1.7192
5
1.6830
6
1.6875
5
1.6872
6
1.6732
6
1.6752
6
1.6725
5
1.6923
3
1.7048
3
1.7056
6
1.6708
6
  1.7276
3
1.6997
3
  1.6764
4
1.6924
3
1.7253
3
1.6994
3
QCISD(T)         1.6900
5
    1.6987
3
    1.6963
3
1.7082
3
1.7125
5
1.6791
5
  1.7100
5
1.6810
5
  1.6947
3
1.6963
3
1.7294
3
1.7037
3
QCISD(T)=FULL             1.7128
3
          1.7320
3
                 
Coupled Cluster CCD   1.6745
5
1.6656
5
1.6930
5
1.6750
6
1.6748
5
1.6808
5
1.6660
6
1.6685
5
1.6627
5
  1.7017
3
1.6945
5
1.6666
5
  1.6944
5
1.6252
2
  1.6883
3
1.6898
3
1.7222
3
 
CCSD         1.6780
6
1.7069
3
1.7109
3
1.6951
3
1.6991
3
1.6944
3
1.6913
3
1.7036
3
1.7276
3
1.6980
3
1.6913
3
1.7262
3
1.6987
3
  1.6899
3
1.6915
3
1.7241
3
1.6983
3
CCSD=FULL         1.7085
3
            1.7026
3
1.7273
3
    1.7251
3
           
CCSD(T)         1.6975
4
1.6958
4
  1.6982
3
1.7026
3
1.6977
3
1.6958
3
1.7077
3
1.6768
2
1.6395
3
1.6754
4
1.7079
5
1.6789
5
1.6968
3
1.6942
3
1.6958
3
   
CCSD(T)=FULL         1.6875
5
                  1.6181
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-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 1.7131
6
1.6676
6
1.7134
6
1.6703
6
1.7040
6
1.7021
6
    1.6593
6
density functional BLYP                 1.7094
3
B1B95 1.6909
1
1.6357
1
            1.6861
3
B3LYP 1.6936
6
1.6733
6
1.6959
6
1.6751
6
1.6855
6
1.6865
6
    1.6649
6
B3LYPultrafine                 1.6920
3
B3PW91                 1.6907
3
mPW1PW91                 1.6872
3
M06-2X                 1.6837
3
PBEPBE                 1.6758
6
PBEPBEultrafine                 1.7063
3
PBE1PBE                 1.6879
3
HSEh1PBE                 1.6877
3
TPSSh                 1.6959
3
wB97X-D 1.6861
3
1.7050
3
1.6868
3
1.7036
3
1.6843
3
1.6858
3
    1.6862
3
B97D3                 1.7060
3
Moller Plesset perturbation MP2 1.7004
6
1.6718
6
1.6918
5
1.6717
6
1.6965
6
1.6951
6
    1.6587
6
MP2=FULL                 1.6929
3
MP3                 1.6864
3
MP3=FULL                 1.6821
3
MP4                 1.6982
3
MP4=FULL                 1.6937
3
B2PLYP                 1.6925
3
B2PLYP=FULL                 1.6910
3
B2PLYP=FULLultrafine                 1.6910
3
Configuration interaction CISD                 1.6794
3
Quadratic configuration interaction QCISD                 1.6915
3
QCISD(T)                 1.6953
3
Coupled Cluster CCD                 1.6888
3
CCSD                 1.6905
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.