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Comparison of levels of theory for Al-H


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 1.4693
23
PM3 1.5943
21
PM6 1.6415
36
composite G2 1.6118
16
G3 1.6167
19
G3B3 1.6512
26
G3MP2 1.5993
8
G4 1.6498
36
CBS-Q 1.6167
19

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(D+d)Z cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
hartree fock HF 1.5422
28
1.6735
31
1.6476
31
1.6759
31
1.6465
36
1.6401
31
1.6418
29
1.6367
31
1.6426
31
1.6422
31
1.6066
9
1.6366
33
1.6429
31
1.6381
31
1.6419
27
1.6502
31
1.6443
31
1.6393
27
1.6512
1
1.6146
10
1.5849
3
1.6354
11
1.6375
3
1.6414
36
ROHF 1.5028
3
1.7383
11
1.6913
11
1.7614
9
1.6798
13
1.6704
11
1.6844
11
1.6677
11
1.6718
9
1.6072
3
1.6329
3
1.6458
3
1.6695
11
1.6643
11
1.6749
9
1.6826
9
1.6738
9
1.7066
6
        1.5848
3
1.5810
3
density functional LSDA 1.5584
28
1.6558
20
1.6490
28
1.6706
28
1.6510
28
1.6472
28
1.6466
28
1.6447
28
1.6440
28
1.6404
28
  1.6461
11
1.6546
28
1.6432
28
1.6231
7
1.6510
28
1.6414
21
1.6196
7
1.6872
1
1.6752
1
  1.6586
8
   
BLYP 1.5730
28
1.6574
31
1.6393
31
1.6625
31
1.6541
36
1.6385
31
1.6377
31
1.6378
31
1.6469
31
1.6428
31
1.6352
3
1.6490
14
1.6457
31
1.6362
31
  1.6275
9
1.6102
6
  1.6851
1
1.6737
1
  1.6634
8
1.6244
3
 
B1B95 1.5585
27
1.6330
6
1.6436
27
1.6672
27
1.6434
27
1.6425
27
1.6394
27
1.6440
27
1.6425
27
1.6360
27
1.6284
3
1.6406
14
1.6485
27
1.6402
27
1.6144
7
1.6215
13
1.6358
19
1.6098
7
1.6686
1
1.6608
1
  1.6551
8
1.6292
3
1.6205
3
B3LYP 1.5595
31
1.6514
31
1.6327
31
1.6555
31
1.6441
31
1.6312
31
1.6303
31
1.6302
31
1.6377
30
1.6350
31
1.6241
6
1.6390
33
1.6369
31
1.6297
31
1.6362
25
1.6441
31
1.6362
31
1.6312
27
1.6704
1
1.6148
10
  1.6341
11
1.6277
3
1.6181
3
B3LYPultrafine   1.6308
6
    1.6441
31
1.6124
6
1.6101
6
1.6110
6
  1.6322
3
1.6282
3
1.6139
6
1.6458
14
1.6326
16
  1.6414
14
1.6495
36
        1.6543
8
1.6277
3
 
B3PW91 1.5603
28
1.6567
31
1.6384
31
1.6590
31
1.6482
31
1.6355
31
1.6341
31
1.6344
31
1.6422
30
1.6403
31
1.6341
3
1.6449
14
1.6419
31
1.6346
31
  1.6223
9
1.6101
6
  1.6717
1
1.6638
1
  1.6594
8
1.6377
3
1.6301
3
mPW1PW91 1.5567
31
1.6679
31
1.6472
30
1.6698
31
1.6468
31
1.6444
31
1.6430
31
1.6430
31
1.6417
31
1.6391
31
1.6326
3
1.6433
14
1.6510
31
1.6436
31
  1.6557
20
1.6533
17
  1.6685
1
1.6613
1
  1.6582
8
1.6369
3
1.6301
3
M06-2X 1.5471
14
1.6463
14
1.6455
36
1.6535
14
1.6345
33
1.6338
14
1.6325
14
1.6307
14
1.6306
14
1.6277
14
1.6236
33
1.6333
14
1.6376
14
1.6295
14
  1.6340
14
1.6270
14
  1.6589
1
1.6491
1
  1.6468
8
1.6273
3
1.6197
3
PBEPBE 1.5676
25
1.6781
31
1.6597
28
1.6824
28
1.6588
31
1.6558
31
1.6549
31
1.6549
31
1.6533
31
1.6503
31
1.6390
6
1.6552
14
1.6637
31
1.6545
31
1.6298
7
1.6699
17
1.6630
18
1.6253
7
1.6889
1
1.6794
1
  1.6701
8
1.6378
3
1.6274
3
PBEPBEultrafine   1.6458
6
    1.6550
17
1.6264
6
1.6249
6
1.6253
6
  1.6458
3
1.6420
3
1.6283
6
1.6611
14
1.6519
14
  1.6566
14
1.6488
14
        1.6701
8
1.6378
3
1.6274
3
PBE1PBE 1.5572
14
1.6480
3
1.6476
14
1.6662
14
1.6444
33
1.6468
14
1.6435
14
1.6418
14
1.6413
14
1.6391
14
1.6346
3
1.6456
14
1.6505
14
1.6428
14
  1.6466
14
1.6403
14
        1.6604
8
1.6384
3
1.6316
3
HSEh1PBE 1.5576
14
1.6622
33
1.6473
14
1.6664
14
1.6446
33
1.6445
14
1.6409
33
1.6416
14
1.6410
14
1.6385
14
1.6339
3
1.6451
14
1.6501
14
1.6402
33
  1.6461
14
1.6395
14
  1.6721
1
1.6643
1
  1.6597
8
1.6369
3
1.6291
3
TPSSh 1.5633
3
1.6346
6
1.6210
6
1.6344
6
1.6387
28
1.6147
6
1.6354
28
1.6133
6
1.6394
3
1.6341
36
1.6336
3
1.6163
6
1.6202
6
1.6357
28
1.6352
3
1.6144
6
1.6091
6
1.6295
3
      1.6570
8
1.6352
3
 
wB97X-D 1.5301
6
1.6372
6
1.6468
36
1.6359
6
1.6435
36
1.6162
6
1.6402
36
1.6145
6
1.6390
36
1.6103
6
1.6347
3
1.6417
36
1.6414
36
1.6393
36
1.6089
6
1.6163
6
1.6370
36
1.6056
6
        1.6416
3
1.6344
3
B97D3 1.5832
3
1.6743
36
1.6597
3
1.6783
3
1.6543
36
1.6536
3
1.6490
36
1.6564
3
1.6512
36
1.6480
3
1.6483
36
1.6601
36
1.6617
3
1.6523
36
1.6470
3
1.6530
3
1.6547
36
1.6380
3
          1.6431
30
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(D+d)Z cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Moller Plesset perturbation MP2 1.5547
28
1.6765
31
1.6439
31
1.6835
31
1.6406
36
1.6289
31
1.6263
31
1.6341
36
1.6341
31
1.6327
31
1.6279
3
1.6303
33
1.6366
31
1.6308
31
1.6500
18
1.6481
31
1.6382
27
1.6498
18
1.6500
1
1.6102
10
1.5834
3
1.6306
11
1.6356
3
1.6285
3
MP2=FULL 1.5506
30
1.6885
31
1.6568
28
1.7007
28
1.6421
31
1.6358
31
1.6258
31
1.6342
31
1.6325
30
1.6298
28
1.6223
3
1.6334
14
1.6450
31
1.6389
28
1.6084
18
1.6531
20
1.6299
27
1.6072
17
1.6491
1
1.6051
10
1.5822
3
1.6243
11
1.6314
3
1.6217
3
ROMP2 1.5788
9
1.7063
9
1.6991
9
1.7679
9
1.6941
9
1.6674
9
1.6650
9
1.6777
9
1.6586
9
1.6593
9
1.6281
3
1.6358
3
1.6739
9
1.6674
9
1.6038
3
1.6773
9
1.6058
3
        1.6509
8
1.5864
3
1.5796
3
MP3         1.6553
31
  1.6333
36
      1.6306
3
1.6067
6
1.6125
6
1.6094
6
        1.6500
1
1.6489
1
  1.6529
8
1.6383
3
1.6314
3
MP3=FULL   1.6421
6
1.6182
6
1.6461
6
1.6479
36
1.6017
6
1.6315
36
1.6112
6
1.5995
6
1.5942
6
1.6253
3
1.6070
6
1.6123
6
1.6068
6
  1.6107
6
1.6001
6
        1.6468
8
1.6343
3
1.6247
3
MP4   1.6967
34
    1.6577
34
    1.6053
6
1.6374
31
  1.6329
3
1.6352
14
1.6419
14
1.6505
26
  1.6160
6
1.6372
14
  1.6512
1
1.5977
4
  1.6549
8
1.6410
3
1.6334
3
MP4=FULL   1.6720
14
    1.6463
14
      1.6282
14
  1.6275
3
  1.6404
14
1.6347
14
  1.6395
14
1.6300
14
        1.6492
8
1.6362
3
1.6266
3
B2PLYP 1.5521
14
1.6572
14
1.6387
14
1.6623
14
1.6376
33
1.6345
14
1.6248
19
1.6337
14
1.6315
14
1.6293
14
1.6258
3
1.6358
14
1.6412
14
1.6330
36
  1.6384
14
1.6314
14
        1.6509
8
1.6307
3
1.6238
3
B2PLYP=FULL 1.5522
14
1.6498
19
1.6383
14
1.6623
14
1.6315
19
1.6338
14
1.6242
19
1.6336
14
1.6311
14
1.6273
14
1.6240
3
1.6357
14
1.6407
14
1.6328
14
  1.6370
14
1.6293
14
        1.6490
8
1.6294
3
1.6217
3
B2PLYP=FULLultrafine 1.5260
6
1.6304
6
1.6140
6
1.6328
6
1.6445
33
1.6068
6
1.6042
6
1.6073
6
1.6041
6
1.6006
6
1.6240
3
1.6095
6
1.6391
33
1.6305
33
  1.6083
6
1.6267
33
          1.6294
3
1.6217
3
Configuration interaction CID   1.7002
28
1.6601
28
1.7079
28
1.6566
31
    1.6383
31
    1.6313
3
  1.6407
3
1.6119
9
              1.6511
8
1.6391
3
1.6319
3
CISD   1.6844
31
1.6596
28
1.7090
28
1.6566
31
    1.6513
28
    1.6319
3
  1.6418
3
1.6127
9
              1.6514
8
1.6397
3
1.6323
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(D+d)Z cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Quadratic configuration interaction QCISD   1.6868
31
1.6642
31
1.7117
28
1.6581
31
1.6385
31
1.6368
31
1.6425
28
1.6350
31
1.6358
28
1.6342
3
1.6360
14
1.6363
27
1.6432
27
  1.6659
17
1.6562
17
  1.6513
1
1.5981
4
  1.6555
8
1.6413
3
1.6345
3
QCISD(T)         1.6591
34
1.5978
6
1.5969
6
1.6203
9
    1.6348
3
1.6368
14
1.6496
30
1.6449
30
  1.6301
16
1.6350
18
    1.5814
3
  1.6562
8
1.6428
3
1.6350
3
QCISD(T)=FULL         1.6234
6
  1.6026
6
      1.6294
3
  1.6162
6
1.6108
6
1.5820
6
1.6143
6
1.6038
6
1.5727
6
      1.6506
8
1.6380
3
1.6279
3
QCISD(TQ)         1.6244
6
  1.6037
6
      1.6351
3
  1.6165
6
1.6136
6
1.5824
3
1.6181
6
1.6110
6
1.5827
3
      1.5826
3
1.6432
3
 
QCISD(TQ)=FULL         1.6236
6
  1.5798
3
      1.6296
3
  1.5893
3
1.5830
3
1.5600
3
1.6147
6
1.6040
6
        1.5779
3
   
Coupled Cluster CCD   1.6984
31
1.6613
28
1.7103
28
1.6580
31
1.6380
31
1.6363
31
1.6398
31
1.6373
28
1.6355
28
1.6335
3
1.6351
14
1.6472
27
1.6431
27
  1.6542
24
1.6501
21
  1.6500
1
1.5973
4
  1.6549
8
1.6415
3
1.6344
3
CCSD         1.6585
34
1.5768
9
1.5747
9
1.5838
9
1.6290
3
1.6011
6
1.6341
3
1.6359
14
1.6403
20
1.6510
20
1.6338
14
1.6445
14
1.6377
14
1.6055
6
  1.5804
3
  1.6353
11
1.6413
3
1.6345
3
CCSD=FULL         1.6475
14
        1.5967
6
1.6287
3
1.6358
14
1.6411
14
1.6354
14
1.6004
14
1.6400
14
1.6307
14
1.5721
6
      1.6296
11
1.6373
3
1.6275
3
CCSD(T)   1.7148
1
    1.6626
26
1.6093
9
1.6068
9
1.6202
9
1.6343
4
1.6256
3
1.6348
3
1.6368
14
1.6496
30
1.6448
30
1.6519
17
1.6510
19
1.6498
21
1.6515
17
1.6526
1
1.6215
8
1.5871
3
1.6360
11
1.6428
3
1.6350
3
CCSD(T)=FULL         1.6651
23
          1.6294
3
1.6367
14
1.6600
17
1.6527
17
1.6091
17
1.6605
17
1.6483
17
1.6071
17
1.6521
1
1.5948
4
1.5864
3
1.6307
11
1.6381
3
1.6279
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(D+d)Z cc-pV(T+d)Z cc-pCVDZ 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 1.6834
31
1.6568
23
1.6762
31
1.6521
23
1.6743
31
1.6628
31
    1.6334
36
ROHF                 1.6405
3
density functional BLYP                 1.6425
3
B1B95 1.6361
6
1.6199
6
            1.6358
3
B3LYP 1.6717
31
1.6487
23
1.6666
31
1.6503
23
1.6654
31
1.6509
31
    1.6345
36
B3LYPultrafine                 1.6351
3
B3PW91                 1.6393
3
mPW1PW91                 1.6378
3
M06-2X                 1.6282
3
PBEPBE                 1.6472
36
PBEPBEultrafine                 1.6481
3
PBE1PBE                 1.6399
3
HSEh1PBE                 1.6393
3
TPSSh                 1.6386
3
wB97X-D 1.6445
6
1.6322
6
1.6397
6
1.6332
6
1.6383
6
1.6168
6
    1.6397
3
B97D3                 1.6506
3
Moller Plesset perturbation MP2 1.6945
31
1.6600
23
1.6848
31
1.6540
23
1.6860
31
1.6686
31
    1.6296
36
MP2=FULL                 1.6264
3
ROMP2                 1.6318
3
MP3                 1.6336
3
MP3=FULL                 1.6288
3
MP4=FULL                 1.6311
3
B2PLYP                 1.6316
3
B2PLYP=FULL                 1.6300
3
B2PLYP=FULLultrafine                 1.6300
3
Configuration interaction CID                 1.6345
3
CISD                 1.6351
3
Quadratic configuration interaction QCISD                 1.6370
3
QCISD(T)                 1.6377
3
QCISD(T)=FULL                 1.6330
3
QCISD(TQ)                 1.6379
3
Coupled Cluster CCD                 1.6363
3
CCSD                 1.6369
3
CCSD=FULL                 1.6328
3
CCSD(T)                 1.6377
3
CCSD(T)=FULL                 1.6330
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.