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Computational Chemistry Comparison and Benchmark DataBase
Release 17bSeptember 2015
NIST Standard Reference Database 101
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III.G.1.a.

Comparison of levels of theory for H-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 1.4726
22
PM3 1.6360
23
PM6 1.6461
33
composite G2 1.6230
27
G3 1.6230
27
G3B3 1.6508
33
G3MP2 1.5887
5
G4 1.6514
33
CBS-Q 1.6230
27

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
hartree fock HF 1.5470
30
1.6744
33
1.6477
33
1.6774
33
1.6468
33
1.6415
33
1.6424
31
1.6374
33
1.6440
33
1.6432
33
1.5935
6
1.6366
33
1.6448
33
1.6398
33
1.6425
29
1.6520
33
1.6459
33
1.6412
29
1.6512
1
1.6146
10
1.5849
3
1.6354
11
ROHF 1.5274
10
1.7126
15
1.6725
15
1.7269
13
1.6657
17
1.6553
15
1.6664
15
1.6542
15
1.6539
13
1.6171
10
    1.6564
15
1.6511
15
1.6575
13
1.6640
13
1.6560
13
1.6691
10
       
density functional LSDA 1.5643
33
1.6622
33
1.6521
33
1.6748
33
1.6541
33
1.6505
33
1.6500
33
1.6477
33
1.6476
33
1.6440
33
  1.6461
11
1.6582
33
1.6468
33
1.6338
9
1.6546
33
1.6442
23
1.6301
9
1.6872
1
1.6752
1
  1.6586
8
SVWN   1.6667
30
    1.6484
27
1.6472
11
1.6470
30
1.6440
11
1.6436
11
1.6405
11
  1.6415
25
1.6537
11
1.6426
11
  1.6507
11
1.6415
11
        1.6586
8
BLYP 1.5785
30
1.6621
33
1.6432
33
1.6675
33
1.6544
33
1.6424
33
1.6417
33
1.6415
33
1.6504
33
1.6459
33
  1.6486
11
1.6499
33
1.6401
33
  1.6208
6
1.5896
3
  1.6851
1
1.6737
1
  1.6634
8
B1B95 1.5638
29
1.6490
29
1.6458
29
1.6709
29
1.6459
29
1.6450
29
1.6425
29
1.6462
29
1.6451
29
1.6385
29
  1.6399
11
1.6514
29
1.6430
29
1.6287
12
1.6320
14
1.6418
20
1.6251
12
1.6686
1
1.6608
1
  1.6551
8
B3LYP 1.5643
33
1.6550
33
1.6355
33
1.6601
33
1.6474
29
1.6343
33
1.6335
33
1.6329
33
1.6403
32
1.6378
33
1.6199
3
1.6390
33
1.6404
33
1.6329
33
1.6389
27
1.6477
33
1.6394
33
1.6345
29
1.6704
1
1.6148
10
  1.6341
11
B3LYPultrafine   1.6050
3
    1.6466
33
1.5863
3
1.5862
3
1.5841
3
      1.5853
3
1.6457
11
1.6313
13
  1.6433
11
1.6516
33
        1.6543
8
B3PW91 1.5655
30
1.6597
33
1.6407
33
1.6627
33
1.6500
33
1.6380
33
1.6367
33
1.6365
33
1.6442
32
1.6422
33
  1.6445
11
1.6447
33
1.6370
33
  1.6132
6
1.5867
3
  1.6717
1
1.6638
1
  1.6594
8
mPW1PW91 1.5614
33
1.6702
33
1.6487
32
1.6730
33
1.6485
33
1.6464
33
1.6452
33
1.6447
33
1.6438
33
1.6409
33
  1.6429
11
1.6533
33
1.6454
33
  1.6586
17
1.6577
14
  1.6685
1
1.6613
1
  1.6582
8
M06-2X 1.5458
11
1.6462
11
1.6369
33
1.6537
11
1.6343
30
1.6340
11
1.6335
11
1.6303
11
1.6305
11
1.6280
11
  1.6325
11
1.6373
11
1.6290
11
  1.6353
11
1.6285
11
  1.6589
1
1.6491
1
  1.6468
8
PBEPBE 1.5741
27
1.6815
33
1.6625
30
1.6866
30
1.6617
33
1.6587
33
1.6580
33
1.6572
33
1.6563
33
1.6534
33
1.6361
3
1.6550
11
1.6670
33
1.6571
33
1.6400
9
1.6745
14
1.6676
15
1.6354
9
1.6889
1
1.6794
1
  1.6701
8
PBEPBEultrafine   1.6208
3
    1.6550
14
1.6015
3
1.6013
3
1.5991
3
      1.6008
3
1.6613
11
1.6520
11
  1.6587
11
1.6511
11
        1.6701
8
PBE1PBE 1.5558
11
1.6475
11
1.6475
11
1.6669
11
1.6443
30
1.6470
11
1.6446
11
1.6417
11
1.6415
11
1.6395
11
  1.6453
11
1.6504
11
1.6427
11
  1.6482
11
1.6419
11
        1.6604
8
HSEh1PBE 1.5562
11
1.6623
30
1.6471
11
1.6671
11
1.6445
30
1.6448
11
1.6411
30
1.6415
11
1.6412
11
1.6389
11
  1.6447
11
1.6501
11
1.6400
30
  1.6478
11
1.6412
11
  1.6721
1
1.6643
1
  1.6597
8
TPSSh   1.6070
3
1.5942
3
1.6054
3
1.6379
25
1.5875
3
1.6350
25
1.5855
3
  1.6339
33
  1.5874
3
1.5913
3
1.6350
25
  1.5899
3
1.5847
3
        1.6570
8
wB97X-D 1.4979
3
1.6090
3
1.6467
36
1.6064
3
1.6434
36
1.5881
3
1.5876
3
1.5857
3
1.6391
36
1.5828
3
  1.5871
3
1.5919
3
1.6393
36
1.5810
3
1.5901
3
1.6372
36
1.5810
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
Moller Plesset perturbation MP2 1.5593
30
1.6784
33
1.6454
33
1.6856
33
1.6405
33
1.6304
33
1.6283
33
1.6341
33
1.6355
33
1.6340
33
  1.6303
33
1.6383
33
1.6322
33
1.6521
17
1.6494
33
1.6396
29
1.6522
17
1.6500
1
1.6102
10
1.5834
3
1.6306
11
MP2=FULL 1.5551
32
1.6897
33
1.6577
30
1.7019
30
1.6439
33
1.6370
33
1.6279
33
1.6364
33
1.6340
32
1.6312
30
  1.6329
11
1.6463
33
1.6398
30
1.6094
17
1.6567
17
1.6284
27
1.6076
16
1.6491
1
1.6051
10
1.5822
3
1.6243
11
ROMP2 1.5735
13
1.6972
13
1.6791
13
1.7367
13
1.6754
13
1.6528
13
1.6516
13
1.6628
13
1.6473
13
1.6467
13
    1.6608
13
1.6539
13
1.6184
10
1.6639
13
1.6204
10
1.6225
7
      1.6509
8
MP3         1.6569
33
  1.6343
33
        1.5788
3
1.5852
3
1.5814
3
        1.6500
1
1.6489
1
  1.6529
8
MP3=FULL   1.6159
3
1.5944
3
1.6180
3
1.6484
33
1.5764
3
1.6324
33
1.5860
3
1.5742
3
1.5711
3
  1.5789
3
1.5853
3
1.5787
3
  1.5861
3
1.5762
3
        1.6468
8
MP4   1.6997
33
    1.6594
33
    1.6053
6
1.6390
30
    1.6347
11
1.6422
11
1.6519
23
  1.5907
3
1.6381
11
  1.6512
1
1.5977
4
  1.6549
8
MP4=FULL   1.6720
11
    1.6465
11
      1.6286
11
      1.6403
11
1.6340
11
  1.6401
11
1.6311
11
        1.6492
8
B2PLYP 1.5506
11
1.6574
11
1.6386
11
1.6627
11
1.6374
30
1.6349
11
1.6286
13
1.6337
11
1.6318
11
1.6299
11
  1.6353
11
1.6410
11
1.6327
33
  1.6399
11
1.6330
11
        1.6509
8
B2PLYP=FULL 1.5506
11
1.6520
13
1.6381
11
1.6627
11
1.6337
13
1.6341
11
1.6280
13
1.6336
11
1.6314
11
1.6278
11
  1.6351
11
1.6404
11
1.6323
11
  1.6385
11
1.6310
11
        1.6490
8
B2PLYP=FULLultrafine 1.4941
3
1.6042
3
1.5890
3
1.6047
3
1.5931
5
1.5809
3
1.5805
3
1.5809
3
1.5782
3
1.5758
3
  1.5810
3
1.5862
3
1.5786
3
  1.5850
3
1.5774
3
         
Configuration interaction CID   1.7033
30
1.6623
30
1.7114
30
1.6589
33
    1.6417
33
          1.5987
6
              1.6511
8
CISD   1.6888
33
1.6622
30
1.7133
30
1.6593
33
    1.6546
30
          1.5996
6
              1.6514
8
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
Quadratic configuration interaction QCISD   1.6912
33
1.6665
33
1.7161
30
1.6609
33
1.6412
33
1.6395
33
1.6465
30
1.6378
33
1.6386
30
  1.6354
11
1.6403
29
1.6457
29
  1.6711
14
1.6608
14
  1.6513
1
1.5981
4
  1.6555
8
QCISD(T)         1.6612
33
1.5978
6
1.5969
6
1.6089
6
      1.6363
11
1.6517
29
1.6464
29
  1.6327
15
1.6373
17
    1.5814
3
  1.6562
8
QCISD(T)=FULL         1.5980
3
  1.5796
3
          1.5890
3
1.5828
3
1.5598
3
1.5897
3
1.5801
3
1.5530
3
      1.6506
8
QCISD(TQ)         1.5989
3
  1.5804
3
          1.5890
3
1.5856
3
1.5824
3
1.5928
3
1.5862
3
1.5827
3
      1.5826
3
QCISD(TQ)=FULL         1.5982
3
  1.5798
3
          1.5893
3
1.5830
3
1.5600
3
1.5900
3
1.5804
3
        1.5779
3
Coupled Cluster CCD   1.7015
33
1.6635
30
1.7138
30
1.6603
33
1.6398
33
1.6387
33
1.6431
33
1.6393
30
1.6374
30
  1.6346
11
1.6493
29
1.6445
29
  1.6562
26
1.6523
20
  1.6500
1
1.5973
4
  1.6549
8
CCSD         1.6607
33
1.5493
6
1.5490
6
1.5548
6
  1.5773
3
  1.6354
11
1.6398
17
1.6528
17
1.6339
11
1.6453
11
1.6385
11
1.5815
3
  1.5804
3
  1.6353
11
CCSD=FULL         1.6474
11
        1.5732
3
  1.6351
11
1.6407
11
1.6345
11
1.5993
11
1.6405
11
1.6316
11
1.5525
3
      1.6296
11
CCSD(T)   1.7148
1
    1.6643
23
1.5977
6
1.5969
6
1.6088
6
1.6481
1
    1.6363
11
1.6517
29
1.6463
29
1.6552
16
1.6542
18
1.6525
20
1.6551
16
1.6526
1
1.6215
8
1.5871
3
1.6360
11
CCSD(T)=FULL         1.6675
20
            1.6361
11
1.6636
14
1.6557
14
1.6109
16
1.6650
14
1.6528
14
1.6080
16
1.6521
1
1.5948
4
1.5864
3
1.6307
11
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

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 1.6861
33
1.6574
25
1.6781
33
1.6540
25
1.6765
33
1.6627
33
density functional B1B95 1.6361
6
1.6199
6
       
B3LYP 1.6751
33
1.6523
25
1.6704
33
1.6540
25
1.6680
33
1.6529
33
wB97X-D 1.6148
3
1.6021
3
1.6087
3
1.6029
3
1.6075
3
1.5868
3
Moller Plesset perturbation MP2 1.6964
33
1.6622
25
1.6872
33
1.6575
25
1.6876
33
1.6695
33
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.