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Comparison of levels of theory for Al-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 2.4139
3
PM3 2.5149
3
PM6 2.5178
6
composite G2 2.7230
3
G3 2.7230
3
G3B3 2.7378
3
G3MP2 2.5394
1
G4 2.7849
5
CBS-Q 2.7230
3

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-pCVDZ cc-pCVTZ
hartree fock HF 2.4918
2
2.8378
3
2.7024
3
2.8350
3
2.7922
5
2.7208
3
2.7157
3
2.7282
3
2.8021
3
2.6250
3
2.2557
1
2.7299
6
2.6937
6
2.7450
3
2.7275
3
2.7195
3
2.6418
3
2.7242
3
2.7182
3
2.7687
1
2.6903
2
ROHF         2.7769
3
                               
density functional LSDA 2.4724
3
2.7594
2
2.6795
3
2.7641
3
2.7025
3
2.7011
3
2.6977
3
2.7019
3
2.7004
3
2.6873
3
  2.5902
1
  2.7145
3
2.6931
3
  2.7071
3
2.8059
2
    2.5803
1
BLYP 2.5618
2
2.8267
3
2.7399
3
2.8382
3
2.7016
6
2.7683
3
2.7634
3
2.7738
3
2.8632
3
2.7517
3
  2.6430
1
  2.7792
3
2.7585
3
  2.8060
1
      2.6329
1
B1B95 2.4721
3
  2.6890
3
2.7793
3
2.7064
3
2.7070
3
2.7017
3
2.7117
3
2.7101
3
2.6985
3
  2.6084
1
  2.7215
3
2.7057
3
3.0213
1
2.7640
2
2.8120
2
3.0169
1
  2.5997
1
B3LYP 2.4890
3
2.8037
3
2.7092
3
2.8117
3
2.7367
3
2.7347
3
2.7301
3
2.7395
3
2.8231
3
2.7217
3
2.5025
1
2.7287
6
2.6895
6
2.7480
3
2.7284
3
2.8307
2
2.7393
3
2.7248
3
2.7198
3
2.7689
1
2.6142
1
B3LYPultrafine         2.7367
3
                2.6333
1
2.6176
1
  2.6278
1
2.7881
5
    2.6142
1
B3PW91 2.5256
2
2.7886
3
2.6971
3
2.7895
3
2.7167
3
2.7150
3
2.7125
3
2.7204
3
2.8056
3
2.7058
3
  2.6167
1
  2.7303
3
2.7126
3
  2.7500
1
      2.6067
1
mPW1PW91 2.4575
3
2.7832
3
2.6906
3
2.8642
3
2.7091
3
2.7075
3
2.7048
3
2.7138
3
2.7981
3
2.6994
3
  2.6120
1
  2.7234
3
2.7064
3
  2.6797
2
2.6050
1
    2.6022
1
M06-2X 2.4685
1
2.6550
1
2.6806
6
2.6786
1
2.6982
5
2.6125
1
2.6122
1
2.6116
1
2.6046
1
2.6017
1
  2.6087
1
  2.6149
1
2.6027
1
  2.6116
1
2.6027
1
    2.5992
1
PBEPBE 2.5428
2
2.7972
3
2.8383
2
2.9280
2
2.7378
3
2.7362
3
2.7326
3
2.7421
3
2.8323
3
2.7244
3
2.4892
1
2.6274
1
2.6390
6
2.7489
3
2.7314
3
3.0755
1
2.8587
2
2.8462
2
3.0705
1
  2.6185
1
PBEPBEultrafine         2.5647
2
                2.6367
1
2.6219
1
  2.6317
1
2.6211
1
    2.6185
1
PBE1PBE 2.4710
1
  2.5939
1
2.6845
1
2.7477
6
2.6161
1
2.6109
1
2.6103
1
2.6044
1
2.5998
1
  2.6117
1
  2.6189
1
2.6060
1
  2.6150
1
2.6049
1
    2.6019
1
HSEh1PBE 2.4735
1
2.7730
4
2.5959
1
2.6884
1
2.7516
4
2.6139
1
2.7504
4
2.6122
1
2.6066
1
2.6017
1
  2.6138
1
  2.6215
1
2.7470
4
  2.6173
1
2.6066
1
    2.6035
1
TPSSh         2.7258
4
  2.7256
4
    2.6833
6
        2.7247
4
          2.6047
1
wB97X-D     2.5996
6
  2.6135
6
  2.6131
6
  2.6117
6
    2.6128
6
  2.6131
6
2.6146
6
    2.6153
6
     
B97D3   2.7115
6
    2.6822
6
  2.6761
6
  2.6532
6
  2.6696
6
      2.6931
6
    2.6979
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 Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pCVDZ cc-pCVTZ
Moller Plesset perturbation MP2 2.5060
2
2.7548
3
2.6668
3
2.8317
3
2.6795
6
2.6856
3
2.6810
3
2.6794
6
2.7676
3
2.6216
3
  2.7139
6
2.6789
6
2.7237
3
2.6941
3
2.5317
2
2.7998
3
2.6919
3
2.5324
2
2.7441
1
2.6620
2
MP2=FULL 2.5040
2
2.8300
3
2.6595
3
2.8311
3
2.6798
3
2.6770
3
2.6732
3
2.6881
3
2.7652
3
2.7695
2
  2.6122
1
  2.7157
3
2.6737
3
2.5880
2
2.7088
3
2.6038
4
2.5312
1
2.7379
1
2.6496
2
ROMP2                                         2.6068
1
MP3         2.7607
3
  2.6943
5
                          2.6076
1
MP3=FULL         2.6910
5
  2.6885
5
                          2.5946
1
MP4   3.0026
2
    2.6913
3
    2.4750
1
2.8010
2
    2.6183
1
  2.6314
1
2.7940
3
    2.6134
1
    2.6096
1
MP4=FULL   2.6946
1
    2.6073
1
      2.6036
1
        2.6218
1
2.5960
1
  2.6226
1
2.5979
1
    2.5956
1
B2PLYP 2.4809
1
2.6813
1
2.5963
1
2.7055
1
2.7513
4
2.6154
1
2.6148
1
2.6163
1
2.6107
1
2.6054
1
  2.6170
1
  2.6262
1
2.7044
5
  2.6237
1
2.6102
1
    2.6065
1
B2PLYP=FULL 2.4802
1
2.7330
2
2.5938
1
2.7051
1
2.6803
2
2.6122
1
2.6771
2
2.6154
1
2.6083
1
2.5970
1
  2.6155
1
  2.6232
1
2.6054
1
  2.6194
1
2.6052
1
    2.6021
1
Configuration interaction CID   2.9878
2
2.7696
2
2.9788
2
2.6175
3
    2.6202
3
                        2.6073
1
CISD   2.9913
2
2.7715
2
2.9815
2
2.6215
3
    2.8007
2
                        2.6072
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-pCVDZ cc-pCVTZ
Quadratic configuration interaction QCISD   2.8637
3
2.7663
2
3.0028
2
2.6914
3
2.6894
3
2.6187
3
2.6930
3
2.7957
2
2.7886
2
  2.6185
1
  2.6659
3
2.6976
3
  2.6364
1
2.6140
1
    2.6099
1
QCISD(T)         2.6919
3
    2.3073
1
      2.6192
1
  2.8403
2
2.7992
2
  3.0261
1
2.7962
2
    2.6103
1
QCISD(T)=FULL                                         2.5967
1
Coupled Cluster CCD   2.8602
3
2.7632
2
2.9960
2
2.6884
3
2.7830
2
2.7760
2
2.6895
3
2.7919
2
2.7872
2
  2.6179
1
  2.8316
2
2.7947
2
  2.8234
2
2.7916
2
    2.6098
1
CCSD         2.6910
3
    2.2851
1
      2.6184
1
  2.6312
1
2.6153
1
2.6031
1
2.6364
1
2.6140
1
    2.6099
1
CCSD=FULL         2.6088
1
            2.6146
1
  2.6220
1
2.5973
1
2.5226
1
2.6225
1
2.5984
1
    2.5973
1
CCSD(T)         2.6913
3
2.4914
1
  2.3021
1
    2.7174
1
2.6192
1
  2.8136
3
2.7747
3
2.7860
2
2.8961
2
2.7734
3
2.6039
1
2.7589
1
2.6668
2
CCSD(T)=FULL         2.7555
3
            2.6153
1
  2.6875
2
2.6512
2
2.7374
2
2.6905
2
2.6462
2
2.5332
1
2.7527
1
2.6563
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 Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pCVDZ cc-pCVTZ

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         2.8910
3
2.8842
2
2.8831
3
2.8818
2
2.9097
3
2.9567
3
density functional B1B95         2.8350
1
2.5317
1
       
B3LYP         2.9114
3
2.9295
2
2.9034
3
2.9254
2
2.9254
3
2.9397
3
Moller Plesset perturbation MP2         2.9110
3
2.8581
2
2.9010
3
2.8558
2
2.9244
3
2.9549
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.