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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 1.4848
17
PM3 1.6436
24
PM6 1.6461
33
composite G2 1.6339
27
G3 1.6339
27
G3B3 1.6603
33
G4 1.6514
33
CBS-Q 1.6339
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 1.5549
27
1.6848
33
1.6569
33
1.6879
33
1.6341
60
1.6503
33
1.6482
33
1.6458
33
1.6440
33
1.6432
33
1.5935
6
1.6366
33
1.6539
33
1.6485
33
1.6425
29
1.6520
33
1.6459
33
1.6412
29
1.6512
1
1.6146
10
1.5849
3
1.5790
3
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
1.6747
33
1.6541
33
1.6505
33
1.6500
33
1.6477
33
1.6476
33
1.6440
33
  1.6649
8
1.6582
33
1.6468
33
1.6338
9
1.6546
33
1.6520
20
1.6301
9
1.6872
1
1.6752
1
   
SVWN   1.6667
30
    1.6484
27
1.6658
8
1.6470
30
1.6624
8
1.6621
8
1.6585
8
    1.6727
8
1.6612
8
  1.6695
8
1.6602
8
         
BLYP 1.5858
27
1.6737
33
1.6536
33
1.6792
33
1.6562
33
1.6523
33
1.6517
33
1.6513
33
1.6504
33
1.6459
33
  1.6692
8
1.6603
33
1.6497
33
  1.6208
6
    1.6851
1
1.6737
1
   
B1B95 1.5640
29
1.6491
29
1.6459
29
1.6710
29
1.6459
29
1.6451
29
1.6426
29
1.6463
29
1.6452
29
1.6386
29
  1.6603
8
1.6515
29
1.6430
29
1.6287
12
1.6320
14
1.6523
17
1.6251
12
1.6686
1
1.6608
1
   
B3LYP 1.5643
33
1.6659
33
1.6452
33
1.6709
33
1.6468
33
1.6435
33
1.6427
33
1.6419
33
1.6494
27
1.6378
33
1.6199
3
1.6390
33
1.6499
33
1.6417
33
1.6360
29
1.6477
33
1.6394
33
1.6345
29
1.6704
1
1.6148
10
   
B3LYPultrafine         1.6466
33
  1.6055
2
          1.6664
8
1.6313
13
  1.6637
8
1.6516
33
         
B3PW91 1.5726
27
1.6710
33
1.6509
33
1.6739
33
1.6500
33
1.6476
33
1.6463
33
1.6459
33
1.6535
27
1.6422
33
  1.6650
8
1.6546
33
1.6463
33
  1.6132
6
    1.6717
1
1.6638
1
   
mPW1PW91 1.5614
33
1.6702
33
1.6577
27
1.6730
33
1.6485
33
1.6464
33
1.6451
33
1.6447
33
1.6438
33
1.6409
33
  1.6633
8
1.6533
33
1.6454
33
  1.6586
17
1.6774
11
  1.6685
1
1.6613
1
   
M06-2X 1.5672
8
1.6662
8
1.6501
8
1.6756
8
1.6343
30
1.6540
8
1.6536
8
1.6499
8
1.6502
8
1.6476
8
  1.6524
8
1.6576
8
1.6490
8
  1.6555
8
1.6484
8
  1.6589
1
1.6491
1
   
PBEPBE 1.5817
24
1.6815
33
1.6686
27
1.6940
27
1.6617
33
1.6587
33
1.6580
33
1.6572
33
1.6563
33
1.6534
33
1.6361
3
1.6754
8
1.6670
33
1.6571
33
1.6400
9
1.6937
11
1.6615
17
1.6354
9
1.6889
1
1.6794
1
   
PBEPBEultrafine         1.6436
19
              1.6820
8
1.6723
8
  1.6792
8
1.6714
8
         
PBE1PBE 1.5770
8
1.6662
8
1.6662
8
1.6885
8
1.6443
30
1.6670
8
1.6647
8
1.6616
8
1.6615
8
1.6592
8
  1.6656
8
1.6709
8
1.6630
8
  1.6686
8
1.6621
8
         
HSEh1PBE 1.5774
8
1.6839
8
1.6658
8
1.6889
8
1.6445
30
1.6650
8
1.6645
8
1.6614
8
1.6613
8
1.6587
8
  1.6651
8
1.6706
8
1.6623
8
  1.6682
8
1.6615
8
  1.6721
1
1.6643
1
   
TPSSh         1.6379
25
  1.6350
25
            1.6350
25
               
Moller Plesset perturbation MP2 1.5670
27
1.6897
33
1.6551
33
1.6971
33
1.6544
33
1.6388
33
1.6238
43
1.6453
33
1.6355
33
1.6340
33
  1.6303
33
1.6474
33
1.6408
33
1.6684
14
1.6494
33
1.6396
29
1.6683
14
1.6500
1
1.6102
10
1.5834
3
1.5767
3
MP2=FULL 1.5670
27
1.6897
33
1.6651
27
1.7120
27
1.6533
33
1.6370
33
1.6361
33
1.6452
33
1.6441
27
1.6379
27
  1.6531
8
1.6463
33
1.6468
27
1.6210
14
1.6567
17
1.6444
21
1.6212
13
1.6491
1
1.6051
10
1.5822
3
1.5712
3
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
       
MP3         1.6569
33
  1.6343
33
                      1.6500
1
1.6489
1
   
MP3=FULL         1.6437
25
  1.6276
25
                             
MP4   1.6997
33
    1.6594
33
    1.6053
6
1.6459
27
    1.6551
8
1.6628
8
1.6519
23
    1.6583
8
  1.6512
1
1.6513
1
   
MP4=FULL   1.6918
8
    1.6655
8
      1.6484
8
      1.6602
8
1.6539
8
  1.6596
8
1.6509
8
         
B2PLYP         1.6293
22
                1.6260
25
               
B2PLYP=FULLultrafine         1.5931
5
                                 
Configuration interaction CID   1.7127
27
1.6695
27
1.7215
27
1.6589
33
    1.6511
33
          1.5987
6
               
CISD   1.7012
33
1.6694
27
1.7235
27
1.6593
33
    1.6619
27
          1.5996
6
               
Quadratic configuration interaction QCISD   1.7037
33
1.6665
33
1.7263
27
1.6609
33
1.6412
33
1.6395
33
1.6570
30
1.6378
33
1.6454
27
  1.6557
8
1.6509
29
1.6457
29
  1.6929
11
1.6815
11
  1.6513
1
1.6509
1
   
QCISD(T)         1.6612
33
1.5978
6
1.5969
6
1.6089
6
      1.6565
8
1.6517
29
1.6464
29
  1.6428
12
1.6483
14
         
Coupled Cluster CCD   1.7015
33
1.6707
27
1.7238
27
1.6603
33
1.6398
33
1.6387
33
1.6526
33
1.6463
27
1.6442
27
  1.6549
8
1.6493
29
1.6445
29
  1.6648
23
1.6644
17
  1.6500
1
1.6500
1
   
CCSD         1.6607
33
1.5969
6
1.5960
6
1.6078
6
      1.6556
8
1.6579
17
1.6528
17
1.6537
8
1.6656
8
1.6586
8
         
CCSD=FULL         1.6663
8
            1.6552
8
1.6606
8
1.6544
8
1.6143
8
1.6599
8
1.6514
8
         
CCSD(T)   1.7148
1
    1.6643
23
1.5977
6
1.5969
6
1.6088
6
1.6481
1
    1.6565
8
1.6517
29
1.6463
29
1.6720
13
1.6542
18
1.6525
20
1.6718
13
1.6526
1
1.6232
12
1.5871
3
1.5824
3
CCSD(T)=FULL         1.6687
22
            1.6561
8
1.6636
14
1.6557
14
1.6226
13
1.6650
14
1.6660
17
1.6207
13
1.6521
1
1.6500
1
1.5864
3
1.5777
3

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 1.6365
6
1.6199
6
       
B3LYP 1.6751
33
1.6523
25
1.6704
33
1.6540
25
1.6680
33
1.6529
33
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.