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Comparison of levels of theory for Al-S


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 1.7849
3
PM3 1.9053
3
PM6 1.9992
3
composite G2 2.0441
3
G3 2.0441
3
G3B3 2.0640
3
G3MP2 2.0259
1
G4 2.0514
3
CBS-Q 2.0441
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 Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(T+d)Z
hartree fock HF 1.9758
3
2.1714
3
2.0373
3
2.1878
3
2.0443
3
2.0441
3
2.0456
3
2.0426
3
2.0425
3
2.0383
3
2.0179
1
2.0490
3
2.0353
3
2.0640
3
2.0467
3
2.0394
3
2.0706
3
2.0477
3
2.0398
3
2.0196
1
ROHF   2.1006
1
2.0058
1
  2.0100
1
2.0100
1
2.0103
1
2.0077
1
          2.0236
1
2.0099
1
         
density functional LSDA 1.9608
3
2.0657
3
2.0418
3
2.1188
3
2.0480
3
2.0480
3
2.0482
3
2.0442
3
2.0442
3
2.0376
3
      2.0639
3
2.0435
3
2.0900
1
2.0660
3
2.0478
2
2.0900
1
 
BLYP 1.9880
3
2.1504
3
2.0747
3
2.1588
3
2.0623
3
2.0841
3
2.0850
3
2.0819
3
2.0817
3
2.0735
3
      2.0989
3
2.0798
3
  2.0917
1
     
B1B95 1.9611
3
  2.0432
3
2.1258
3
2.0477
3
2.0485
3
2.0534
2
2.0463
3
2.0463
3
2.0420
3
      2.0661
3
2.0480
3
2.0926
1
2.0750
2
2.0535
2
2.0930
1
 
B3LYP 1.9738
3
2.1365
3
2.0558
3
2.1437
3
2.0639
3
2.0639
3
2.0648
3
2.0620
3
2.0620
3
2.0550
3
2.0452
1
2.0659
3
2.0441
3
2.0798
3
2.0614
3
2.0588
2
2.0838
3
2.0619
3
2.0547
3
2.0448
1
B3LYPultrafine         2.0640
3
                        2.0560
3
   
B3PW91 1.9667
3
2.1273
3
2.0480
3
2.1310
3
2.0530
3
2.0530
3
2.0534
3
2.0506
3
2.0507
3
2.0455
3
      2.0700
3
2.0517
3
  2.0608
1
     
mPW1PW91 1.9630
3
2.1243
3
2.0441
3
2.1277
3
2.0485
3
2.0485
3
2.0489
3
2.0463
3
2.0464
3
2.0415
3
      2.0656
3
2.0477
3
  2.0566
1
     
M06-2X     2.0381
3
  2.0476
3
                             
PBEPBE 1.9766
3
2.1383
3
2.0683
2
2.1488
2
2.0690
3
2.0690
3
2.0692
3
2.0669
3
2.0669
3
2.0604
3
2.0492
1
  2.1028
3
2.0853
3
2.0663
3
2.1147
1
    2.1151
1
2.0488
1
PBEPBEultrafine         2.0591
1
                             
PBE1PBE         2.0491
3
                             
HSEh1PBE   2.1269
3
    2.0507
3
  2.0511
3
              2.0496
3
         
TPSSh         2.0452
3
  2.0450
3
    2.0404
3
        2.0444
3
         
wB97X-D     2.0357
3
  2.0385
3
  2.0387
3
  2.0366
3
    2.0402
3
  2.0387
3
2.0383
3
    2.0384
3
   
B97D3   2.1029
3
    2.1092
3
  2.0562
3
  2.1641
3
  2.1041
3
      2.1073
3
    2.0944
2
   
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 Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(T+d)Z
Moller Plesset perturbation MP2 1.9382
3
2.1151
3
2.0320
3
2.1179
3
2.0319
3
2.0365
3
2.0378
3
2.0303
3
2.0355
3
2.0386
3
  2.0437
3
2.0337
3
2.0607
3
2.0459
3
2.0237
1
2.0731
3
2.0488
3
2.0243
1
2.0271
1
MP2=FULL 1.9438
3
2.1157
3
2.0353
2
2.1317
2
2.0346
3
2.0346
3
2.0360
3
2.0354
3
2.0355
3
2.0370
2
      2.0596
3
2.0473
2
2.0024
1
2.0548
1
    2.0230
1
MP3         2.0420
3
  2.0379
3
                         
MP3=FULL         2.0369
3
  2.0375
3
                         
MP4   2.1475
2
    2.0530
3
    2.0416
1
2.0552
2
          2.0611
3
         
B2PLYP         2.0551
3
  2.0458
1
              2.0468
3
         
B2PLYP=FULL   2.0944
1
    2.0405
1
  2.0407
1
                         
Configuration interaction CID   2.1552
2
2.0415
2
2.1627
2
2.0424
3
    2.0402
3
                       
CISD   2.1657
2
2.0465
2
2.1731
2
2.0476
3
    2.0510
2
                       
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 Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(T+d)Z
Quadratic configuration interaction QCISD   2.1762
3
2.0582
2
2.1931
2
2.0608
3
2.0661
2
2.0619
3
2.0574
3
2.0575
3
2.0634
2
      2.0896
3
2.0658
3
        2.0467
1
QCISD(T)         2.0629
3
    2.0482
1
          2.0987
2
2.0747
2
  2.1108
2
2.0780
2
   
Coupled Cluster CCD   2.1544
2
2.0446
2
2.1616
2
2.0462
3
2.0514
2
2.0532
2
2.0439
3
2.0497
2
2.0532
2
      2.0807
2
2.0615
2
  2.0948
2
2.0647
2
   
CCSD         2.0545
3
    2.0396
1
                       
CCSD(T)         2.0482
1
2.0482
1
  2.0441
1
    2.0463
1
    2.0942
2
2.0660
3
2.1011
1
2.1070
2
2.0750
2
   
CCSD(T)=FULL         2.0604
2
                             
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 Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(T+d)Z

average calculated bond lengths (Å)
Methods with effective core potentials (select basis sets)
daug-cc-pVDZ daug-cc-pVTZ daug-cc-pVQZ Sadlej_pVTZ CEP-31G CEP-31G* CEP-121G CEP-121G* LANL2DZ SDD
hartree fock HF         2.1916
3
2.0526
3
2.1880
3
2.0531
3
2.1843
3
2.1810
3
density functional B1B95         2.1401
1
2.0650
1
       
B3LYP         2.1550
3
2.0983
2
2.1551
3
2.0768
3
2.1526
3
2.1320
3
Moller Plesset perturbation MP2         2.1294
3
2.0585
3
2.1253
3
2.0501
3
2.1237
3
2.1040
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.