National Institute of Standards and Technology
Computational Chemistry Comparison and Benchmark DataBase
Release 18October 2016
NIST Standard Reference Database 101
IIntroduction
IIExperimental data
IIICalculated data
IVData comparisons
VCost comparisons
VIInput and output files
VIITutorials and Units
VIIILinks to other sites
IXFeedback
XOlder CCCBDB versions
XIIGeometries
XIII Vibrations
XIVReaction data
XVEntropy data
XVIBibliographic data
XVIIIon data
XVIIIBad calculations
XIXIndex of properties
XXH-bond dimers
XXIOddities

NIST policy on privacy, security, and accessibility.

Please rate our products
© 2013 copyright by the U.S. Secretary of Commerce on behalf of the United States of America. All rights reserved.

The National Institute of Standards and Technology (NIST) is an agency of the U.S. Department of Commerce.

Please send questions, comments, corrections, additions and suggestions to cccbdb@nist.gov.

return to home page

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 1.4825
17
PM3 1.6075
15
PM6 1.6461
33
composite G2 1.6215
22
G3 1.6215
22
G3B3 1.6528
28
G3MP2 1.5887
5
G4 1.6514
33
CBS-Q 1.6215
22

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 1.5479
22
1.6802
25
1.6514
25
1.6825
25
1.6468
33
1.6431
25
1.6472
23
1.6400
25
1.6474
25
1.6469
25
1.5935
6
1.6366
33
1.6451
25
1.6403
25
1.6479
21
1.6571
25
1.6508
25
1.6470
21
1.6512
1
1.6146
10
1.5849
3
1.6354
11
ROHF   1.8499
5
1.7635
5
1.9882
3
1.7230
7
1.7227
5
1.7599
5
1.7224
5
1.7713
3
      1.7134
5
1.7077
5
1.7842
3
1.8075
3
1.7895
3
1.7839
3
       
density functional LSDA 1.5620
25
1.6609
25
1.6517
25
1.6742
25
1.6542
25
1.6502
25
1.6498
25
1.6477
25
1.6471
25
1.6435
25
  1.6461
11
1.6579
25
1.6463
25
1.6317
4
1.6547
25
1.6464
18
1.6287
4
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 1.5753
22
1.6585
25
1.6396
25
1.6643
25
1.6544
33
1.6396
25
1.6395
25
1.6389
25
1.6507
25
1.6464
25
  1.6486
11
1.6470
25
1.6373
25
  1.6208
6
1.5896
3
  1.6851
1
1.6737
1
  1.6634
8
B1B95 1.5627
21
1.6510
21
1.6466
21
1.6731
21
1.6470
21
1.6462
21
1.6439
21
1.6494
21
1.6477
21
1.6401
21
  1.6399
11
1.6526
21
1.6442
21
1.6198
4
1.6175
10
1.6449
13
1.6167
4
1.6686
1
1.6608
1
  1.6551
8
B3LYP 1.5620
25
1.6530
25
1.6332
25
1.6577
25
1.6475
25
1.6324
25
1.6323
25
1.6317
25
1.6414
24
1.6387
25
1.6199
3
1.6390
33
1.6381
25
1.6311
25
1.6421
19
1.6496
25
1.6414
25
1.6373
21
1.6704
1
1.6148
10
  1.6341
11
B3LYPultrafine   1.6050
3
    1.6476
25
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 1.5638
22
1.6579
25
1.6385
25
1.6609
25
1.6514
25
1.6364
25
1.6357
25
1.6355
25
1.6457
24
1.6438
25
  1.6445
11
1.6430
25
1.6357
25
  1.6132
6
1.5867
3
  1.6717
1
1.6638
1
  1.6594
8
mPW1PW91 1.5598
25
1.6723
25
1.6500
24
1.6746
25
1.6502
25
1.6478
25
1.6470
25
1.6466
25
1.6454
25
1.6427
25
  1.6429
11
1.6547
25
1.6472
25
  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 1.5697
19
1.6824
25
1.6634
22
1.6883
22
1.6623
25
1.6595
25
1.6591
25
1.6586
25
1.6571
25
1.6541
25
1.6361
3
1.6550
11
1.6675
25
1.6582
25
1.6368
4
1.6745
14
1.6676
15
1.6332
4
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
1.6403
36
1.5857
3
1.6391
36
1.5828
3
  1.6417
36
1.6407
36
1.6393
36
1.5810
3
1.5901
3
1.6372
36
1.5810
3
       
B97D3   1.6667
36
    1.6518
36
      1.6479
36
              1.6453
36
         
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 1.5606
22
1.6823
25
1.6472
25
1.6900
25
1.6405
33
1.6315
25
1.6297
25
1.6341
33
1.6389
25
1.6376
25
  1.6303
33
1.6389
25
1.6329
25
1.6544
15
1.6539
25
1.6442
21
1.6549
15
1.6500
1
1.6102
10
1.5834
3
1.6306
11
MP2=FULL 1.5549
24
1.6971
25
1.6643
22
1.7128
22
1.6453
25
1.6405
25
1.6293
25
1.6373
25
1.6373
24
1.6359
22
  1.6329
11
1.6494
25
1.6442
22
1.6100
15
1.6567
17
1.6284
27
1.6113
14
1.6491
1
1.6051
10
1.5822
3
1.6243
11
ROMP2 1.6709
3
1.8367
3
1.8367
3
1.9906
3
1.8219
3
1.7666
3
1.7700
3
1.7899
3
1.7473
3
1.7524
3
    1.7676
3
1.7576
3
  1.7833
3
          1.6509
8
MP3         1.6607
25
  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   1.7061
25
    1.6626
25
    1.6053
6
1.6431
22
    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   1.7111
22
1.6670
22
1.7197
22
1.6617
25
    1.6409
25
          1.5987
6
              1.6511
8
CISD   1.6898
25
1.6660
22
1.7207
22
1.6614
25
    1.6576
22
          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   1.6922
25
1.6706
25
1.7235
22
1.6629
25
1.6427
25
1.6418
25
1.6425
25
1.6393
25
1.6416
22
  1.6354
11
1.6380
21
1.6475
21
  1.6711
14
1.6608
14
  1.6513
1
1.5981
4
  1.6555
8
QCISD(T)         1.6630
25
1.5978
6
1.5969
6
1.6089
6
      1.6363
11
1.6533
21
1.6479
21
  1.6154
7
1.6349
15
    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   1.7071
25
1.6681
22
1.7222
22
1.6631
25
1.6424
25
1.6415
25
1.6424
25
1.6432
22
1.6416
22
  1.6346
11
1.6524
21
1.6477
21
  1.6625
18
1.6527
18
  1.6500
1
1.5973
4
  1.6549
8
CCSD         1.6627
25
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
    1.6702
17
1.5977
6
1.5969
6
1.6088
6
1.6481
1
    1.6363
11
1.6532
21
1.6479
21
1.6558
14
1.6594
10
1.6522
18
1.6560
14
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
1.6101
14
1.6650
14
1.6528
14
1.6103
14
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 1.6906
25
1.6631
17
1.6843
25
1.6573
17
1.6812
25
1.6703
25
density functional B1B95 1.6361
6
1.6199
6
       
B3LYP 1.6763
25
1.6520
17
1.6708
25
1.6535
17
1.6697
25
1.6557
25
wB97X-D 1.6148
3
1.6021
3
1.6087
3
1.6029
3
1.6075
3
1.5868
3
Moller Plesset perturbation MP2 1.7016
25
1.6662
17
1.6925
25
1.6595
17
1.6931
25
1.6767
25
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.