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III.G.1.a.

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 1.5554
2
PM3 1.6062
3
PM6 1.5417
3
composite G2 1.6456
3
G3 1.6456
3
G3B3 1.6347
3
G4 1.6277
3
CBS-Q 1.6530
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 cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(T+d)Z
hartree fock HF 1.6399
3
1.6999
3
1.6508
3
1.7543
3
1.6456
6
1.6456
3
1.6531
3
1.6455
3
1.6453
3
1.6303
3
1.6858
1
1.6490
3
1.6824
3
1.6393
3
1.6319
3
1.6700
3
1.6395
3
1.6320
3
1.6819
1
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
 
SVWN   1.6616
3
    1.6372
2
  1.6333
3
                       
BLYP 1.6220
3
1.6822
3
1.6527
3
1.7050
3
1.6504
3
1.6504
3
1.6587
3
1.6535
3
1.6535
3
1.6372
3
    1.6708
3
1.6463
3
  1.6694
1
     
B1B95 1.6022
3
1.6439
3
1.6342
3
1.6881
3
1.6299
3
1.6303
3
1.6372
3
1.6314
3
1.6314
3
1.6182
3
    1.6538
3
1.6257
3
1.6180
2
1.6471
2
1.6248
2
1.6183
2
 
B3LYP 1.6082
3
1.6680
3
1.6386
3
1.6925
3
1.6346
3
1.6346
3
1.6426
3
1.6368
3
1.6351
2
1.6221
3
1.6275
1
1.6388
3
1.6572
3
1.6309
3
1.6250
3
1.6529
3
1.6318
3
1.6253
3
1.6240
1
B3LYPultrafine         1.6346
3
                      1.6356
3
   
B3PW91 1.6058
2
1.6666
3
1.6369
3
1.6894
3
1.6311
3
1.6311
3
1.6378
3
1.6323
3
1.6312
2
1.6189
3
    1.6545
3
1.6267
3
  1.6507
1
     
mPW1PW91 1.6024
2
1.6638
3
1.6320
2
1.6875
3
1.6280
3
1.6280
3
1.6347
3
1.6291
3
1.6291
3
1.6158
3
    1.6520
3
1.6236
3
  1.6486
1
     
M06-2X         1.6219
3
                           
PBEPBE 1.6190
2
1.6806
3
1.6500
2
1.7015
2
1.6462
3
1.6462
3
1.6533
3
1.6479
3
1.6479
3
1.6333
3
1.6351
1
  1.6680
3
1.6412
3
1.6348
2
  1.6423
1
1.6353
2
1.6314
1
PBEPBEultrafine         1.6465
1
                           
PBE1PBE         1.6289
3
                           
HSEh1PBE         1.6295
3
                           
TPSSh         1.6451
3
  1.6515
3
            1.6429
3
         
Moller Plesset perturbation MP2 1.5635
2
1.6696
3
1.6427
3
1.6913
3
1.6325
3
1.6325
3
1.6293
3
1.6293
3
1.6294
3
1.6194
3
  1.6330
3
1.6547
3
1.6238
3
1.6173
3
1.6497
3
1.6271
3
1.6172
1
1.6076
1
MP2=FULL 1.5647
2
1.6705
3
1.6303
2
1.6660
2
1.6332
3
1.6332
3
1.6299
3
1.6294
3
1.6220
2
1.6137
2
    1.6553
3
1.6175
2
1.5990
3
1.6554
1
    1.5901
1
MP3         1.6429
3
  1.6450
3
                       
MP3=FULL         1.6406
3
  1.6538
3
                       
MP4   1.9208
2
    1.6547
3
      1.6478
2
        1.6353
3
         
B2PLYP         1.6279
3
                1.6344
3
         
Configuration interaction CID   1.6534
2
1.6299
2
1.6775
2
1.6397
3
    1.6355
3
                     
CISD   1.6723
2
1.6416
2
1.6980
2
1.6420
3
    1.6283
2
                     
Quadratic configuration interaction QCISD   1.7047
3
1.6678
2
1.7354
2
1.6559
3
1.6572
2
1.6622
3
1.6503
3
1.6503
3
1.6380
2
    1.6822
3
1.6427
3
        1.6328
1
QCISD(T)         1.6566
2
              1.6830
2
1.6435
2
  1.6778
2
1.6466
2
   
Coupled Cluster CCD   1.6538
2
1.6326
2
1.6763
2
1.6430
3
1.6293
2
1.6384
2
1.6389
3
1.6255
2
1.6176
2
    1.6483
2
1.6221
2
  1.6500
2
1.6252
2
   
CCSD         1.6471
3
                           
CCSD(T)   1.6777
1
    1.6542
1
1.6541
1
1.6595
1
  1.6475
1
      1.6768
2
1.6395
3
1.6135
1
1.6735
2
1.6420
2
  1.6305
1
CCSD(T)=FULL         1.6516
2
                  1.6181
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 1.7596
3
1.6462
3
1.7625
3
1.6527
3
1.7383
3
1.7378
3
density functional B1B95 1.6909
1
1.6357
1
       
B3LYP 1.6914
3
1.6360
3
1.6946
3
1.6411
3
1.6796
3
1.6791
3
Moller Plesset perturbation MP2 1.6916
3
1.6259
3
1.6622
2
1.6275
3
1.6855
3
1.6819
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.