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III.G.1.a.

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 2.4564
4
PM3 2.4921
5
PM6 2.5178
6
composite G2 2.7922
5
G3 2.7922
5
G3B3 2.8150
5
G4 2.7849
5
CBS-Q 2.7922
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 cc-pCVDZ cc-pCVTZ
hartree fock HF 2.4495
4
2.9257
5
2.7756
5
2.9099
5
2.8219
7
2.7909
5
2.7960
5
2.8113
5
2.8556
5
2.7467
5
2.2557
1
2.7299
6
2.8234
5
2.8125
5
2.7195
3
2.7675
5
2.8151
5
2.7182
3
     
ROHF         2.7769
3
                               
density functional LSDA 2.4604
5
2.7528
5
2.7425
5
2.8306
5
2.7674
5
2.7666
5
2.7677
5
2.7750
5
2.7742
5
2.6873
3
  2.5902
1
2.7833
5
2.7668
5
  2.7794
5
2.8425
4
       
SVWN   2.7582
4
    2.7756
3
2.5931
1
2.7410
4
2.5899
1
2.5855
1
2.5798
1
    2.6015
1
2.5837
1
  2.5968
1
2.5832
1
       
BLYP 2.5236
4
2.9294
5
2.8309
5
2.9317
5
2.8584
5
2.8570
5
2.8573
5
2.8703
5
2.9240
5
2.8477
5
  2.6430
1
2.8697
5
2.8555
5
  2.8060
1
         
B1B95 2.4609
5
2.7725
5
2.7607
5
2.8559
5
2.7797
5
2.7801
5
2.7808
5
2.7959
5
2.7949
5
2.7810
5
  2.6084
1
2.7996
5
2.7900
5
3.0213
1
2.6992
3
2.8662
4
3.0169
1
     
B3LYP 2.4771
5
2.8972
5
2.7880
5
2.8939
5
2.8144
5
2.8131
5
2.8145
5
2.8269
5
2.9050
4
2.8093
5
2.5025
1
2.7287
6
2.8301
5
2.8169
5
2.7212
3
2.8270
5
2.8169
5
2.7198
3
     
B3LYPultrafine         2.8142
5
              2.6333
1
2.6176
1
  2.6278
1
2.7881
5
       
B3PW91 2.4862
4
2.8712
5
2.7630
5
2.8602
5
2.7842
5
2.7831
5
2.7865
5
2.8000
5
2.8775
4
2.7844
5
  2.6167
1
2.8037
5
2.7923
5
  2.7500
1
         
mPW1PW91 2.4503
5
2.8631
5
2.8274
4
2.8999
5
2.7746
5
2.7736
5
2.7765
5
2.7910
5
2.8416
5
2.7761
5
  2.6120
1
2.7945
5
2.7840
5
  2.6797
2
2.6050
1
       
M06-2X 2.4685
1
2.6550
1
2.5851
1
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
       
PBEPBE 2.5030
4
2.8828
5
2.8641
4
2.9590
4
2.8089
5
2.8079
5
2.8093
5
2.8238
5
2.8780
5
2.8052
5
2.4892
1
2.6274
1
2.8242
5
2.8132
5
3.0755
1
2.8587
2
2.7281
3
3.0705
1
     
PBEPBEultrafine         2.5647
2
              2.6367
1
2.6219
1
  2.6317
1
2.6211
1
       
PBE1PBE 2.4710
1
2.5939
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
       
HSEh1PBE 2.4735
1
2.6684
1
2.5959
1
2.6884
1
2.7516
4
2.6139
1
2.6133
1
2.6122
1
2.6066
1
2.6017
1
  2.6138
1
2.6215
1
2.6076
1
  2.6173
1
2.6066
1
       
TPSSh         2.7258
4
  2.7256
4
            2.7247
4
             
Moller Plesset perturbation MP2 2.4676
4
2.8757
5
2.7295
5
2.9085
5
2.7502
5
2.7489
5
2.7524
5
2.7660
5
2.8123
5
2.7244
5
  2.7139
6
2.7982
5
2.7711
5
2.5317
2
2.8486
5
2.7328
5
2.5324
2
  2.7441
1
2.7179
1
MP2=FULL 2.4653
4
2.9212
5
2.7229
5
2.9085
5
2.7422
5
2.7405
5
2.7457
5
2.7637
5
2.8368
4
2.8063
4
  2.6122
1
2.7907
5
2.7487
5
2.4577
2
2.7088
3
2.7763
2
2.5312
1
  2.7379
1
2.7080
1
MP3         2.7913
5
  2.6943
5
                           
MP3=FULL         2.7120
4
  2.7111
4
                           
MP4   3.0430
4
    2.7492
5
    2.4750
1
2.8362
4
    2.6183
1
2.6314
1
2.7940
3
    2.6134
1
       
MP4=FULL   2.6946
1
    2.6073
1
      2.6036
1
      2.6218
1
2.5960
1
  2.6226
1
2.5979
1
       
B2PLYP         2.7946
3
                2.7278
4
             
Configuration interaction CID   3.0330
4
2.7918
4
3.0158
4
2.7058
5
    2.7224
5
                         
CISD   3.0330
4
2.7935
4
3.0154
4
2.7086
5
    2.8388
4
                         
Quadratic configuration interaction QCISD   2.9516
5
2.7908
4
3.0316
4
2.7509
5
2.7497
5
2.7142
5
2.7671
5
2.8370
4
2.8350
4
  2.6185
1
2.7671
5
2.7737
5
  2.6364
1
2.6140
1
       
QCISD(T)         2.7494
5
    2.3073
1
      2.6192
1
2.8787
4
2.8417
4
  2.9628
3
2.8438
4
       
Coupled Cluster CCD   2.9505
5
2.7878
4
3.0295
4
2.7481
5
2.8103
4
2.8155
4
2.7640
5
2.8338
4
2.8338
4
  2.6179
1
2.8057
5
2.8410
4
  2.8786
4
2.8439
4
       
CCSD         2.7506
5
    2.2851
1
      2.6184
1
2.6312
1
2.6153
1
2.6031
1
2.6364
1
2.6140
1
       
CCSD=FULL         2.6088
1
            2.6146
1
2.6220
1
2.5973
1
2.5226
1
2.6225
1
2.5984
1
       
CCSD(T)         2.7489
5
2.4914
1
  2.3021
1
    2.7174
1
2.6192
1
2.8549
5
2.8183
5
2.7860
2
2.9135
4
2.8206
5
2.6039
1
2.8853
3
2.7589
1
2.7234
1
CCSD(T)=FULL         2.7843
5
            2.6153
1
2.6875
2
2.6512
2
2.7374
2
2.6905
2
2.6462
2
2.5332
1
  2.7527
1
2.7160
1

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 2.9295
5
2.8971
4
2.9317
5
2.8973
4
2.9500
5
3.0168
5
density functional B1B95 2.8350
1
2.5317
1
       
B3LYP 2.9526
5
2.9388
4
2.9532
5
2.9392
4
2.9641
5
3.0102
5
Moller Plesset perturbation MP2 2.9421
5
2.8656
4
2.9430
5
2.8651
4
2.9571
5
3.0160
5
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.