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Comparison of levels of theory for F-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 1.5803
3
PM3 1.6443
3
PM6 1.6265
9
composite G2 1.6260
7
G3 1.6260
7
G3B3 1.6443
7
G4 1.6388
9
CBS-Q 1.6400
7

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) 6-311+G(3df,2pd) 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 1.5993
7
1.6352
7
1.6212
7
1.6723
7
1.6308
9
1.6248
7
1.6373
4
1.6357
7
1.6358
7
1.6184
7
1.6210
7
1.6147
3
1.6380
9
1.6624
7
1.6256
7
1.6203
4
1.6387
7
1.6230
7
1.6199
4
1.6310
3
1.6152
7
1.6630
4
1.6208
4
density functional LSDA 1.6246
7
1.6542
7
1.6289
7
1.6886
7
1.6373
7
1.6373
7
1.6513
7
1.6503
7
1.6503
7
1.6276
7
1.6293
3
1.6293
3
1.6410
3
1.6739
7
1.6432
7
1.6276
3
1.6598
7
1.6339
3
1.6274
3
1.6383
3
1.6240
3
1.6650
3
1.6275
3
SVWN 1.6276
3
1.6627
9
1.6242
3
1.6786
3
1.6429
9
1.6319
3
1.6580
9
1.6433
3
1.6433
3
1.6227
3
1.6293
3
1.6293
3
1.6574
9
1.6677
3
1.6364
3
1.6276
3
1.6516
3
1.6339
3
1.6274
3
1.6383
3
1.6240
3
1.6650
3
1.6275
3
BLYP 1.6395
7
1.6736
7
1.6481
7
1.7100
7
1.6532
9
1.6591
7
1.6764
7
1.6741
7
1.6742
7
1.6478
7
1.6560
3
1.6560
3
1.6665
3
1.6936
7
1.6685
7
1.6538
3
1.6846
7
1.6603
3
1.6542
3
1.6612
3
1.6498
3
1.6856
3
1.6530
3
B1B95 1.6247
7
1.6534
7
1.6330
7
1.6861
7
1.6399
7
1.6409
7
1.6531
7
1.6522
7
1.6522
7
1.6341
7
1.6328
3
1.6328
3
1.6425
3
1.6739
7
1.6451
7
1.6304
3
1.6582
7
1.6659
1
1.6303
3
1.6434
3
1.6277
3
1.6668
3
1.6306
3
B3LYP 1.6251
7
1.6575
7
1.6352
7
1.6937
7
1.6442
7
1.6442
7
1.6592
7
1.6582
7
1.6513
3
1.6363
7
1.6441
7
1.6390
3
1.6664
9
1.6798
7
1.6515
7
1.6462
4
1.6662
7
1.6499
7
1.6464
4
1.6470
3
1.6396
7
1.6801
4
1.6365
3
B3LYPultrafine 1.6310
3
1.6486
3
1.6308
3
1.6841
3
1.6443
7
1.6391
3
1.6510
3
1.6513
3
1.6513
3
1.6315
3
1.6391
3
1.6391
3
1.6491
3
1.6735
3
1.6457
6
1.6371
3
1.6580
3
1.6493
9
1.6372
3
1.6471
3
1.6334
3
1.6716
3
1.6365
3
B3PW91 1.6237
3
1.6590
7
1.6369
7
1.6941
7
1.6441
7
1.6440
7
1.6571
7
1.6570
7
1.6499
3
1.6362
7
1.6370
3
1.6370
3
1.6471
3
1.6808
7
1.6497
7
1.6348
3
1.6643
7
1.6477
4
1.6347
3
1.6480
3
1.6317
3
1.6726
3
1.6346
3
mPW1PW91 1.6207
3
1.6552
7
1.6316
3
1.6905
7
1.6407
7
1.6407
7
1.6537
7
1.6534
7
1.6535
7
1.6323
7
1.6335
3
1.6335
3
1.6434
3
1.6776
7
1.6458
7
1.6313
3
1.6606
7
1.6372
3
1.6313
3
1.6450
3
1.6282
3
1.6695
3
1.6310
3
M06-2X 1.6212
3
1.6359
3
1.6362
9
1.6722
3
1.6417
9
1.6305
3
1.6393
3
1.6401
3
1.6401
3
1.6310
4
1.6280
3
1.6280
3
1.6367
3
1.6648
3
1.6403
4
1.6261
3
1.6460
3
1.6386
4
1.6263
3
1.6399
3
1.6231
3
1.6632
3
1.6261
3
PBEPBE 1.6343
3
1.6720
7
    1.6538
7
1.6538
7
1.6677
7
1.6659
7
1.6708
7
1.6487
7
1.6580
7
1.6521
3
1.6628
3
1.6932
7
1.6601
7
1.6497
3
  1.6635
7
1.6500
3
1.6609
3
1.6549
4
1.6852
3
1.6491
3
PBEPBEultrafine 1.6454
3
1.6641
3
1.6433
3
1.6991
3
1.6529
7
1.6518
3
1.6646
3
1.6640
3
1.6640
3
1.6439
3
1.6523
3
1.6523
3
1.6629
3
1.6872
3
1.6577
3
1.6499
3
1.6728
3
1.6563
3
1.6501
3
1.6611
3
1.6461
3
1.6853
3
1.6492
3
PBE1PBE 1.6262
3
1.6465
3
1.6297
3
1.6814
3
1.6467
9
1.6360
3
1.6464
3
1.6467
3
1.6467
3
1.6288
3
1.6340
3
1.6340
3
1.6439
3
1.6718
3
1.6395
3
1.6318
3
1.6531
3
1.6375
3
1.6317
3
1.6456
3
1.6284
3
1.6698
3
1.6313
3
HSEh1PBE 1.6264
3
1.6640
9
1.6297
3
1.6814
3
1.6468
9
1.6361
3
1.6612
9
1.6470
3
1.6470
3
1.6288
3
1.6342
3
1.6342
3
1.6442
3
1.6715
3
1.6540
9
1.6322
3
1.6534
3
1.6380
3
1.6321
3
1.6452
3
1.6288
3
1.6695
3
1.6318
3
TPSSh         1.6453
9
  1.6541
9
    1.6391
9
        1.6487
9
               
wB97X-D     1.6362
9
  1.6401
9
  1.6491
9
  1.6498
9
      1.6472
9
1.6491
9
1.6440
9
    1.6413
9
         
B97D3   1.6672
9
    1.6524
9
      1.6614
9
                1.6536
9
         
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) 6-311+G(3df,2pd) 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 1.6090
3
1.6529
7
1.6353
7
1.6974
7
1.6461
9
1.6490
7
1.6626
7
1.6502
9
1.6547
7
1.6386
7
1.6434
3
1.6434
3
1.6667
9
1.6850
7
1.6506
7
1.6473
4
1.6721
7
1.6531
4
1.6484
4
1.6552
3
1.6416
7
1.6853
4
1.6471
4
MP2=FULL 1.6121
3
1.6538
7
1.6322
3
1.6888
3
1.6481
7
1.6493
7
1.6647
7
1.6543
7
1.6481
3
1.6390
4
1.6392
3
1.6392
3
1.6508
3
1.6856
7
1.6504
4
1.6327
4
1.6716
7
1.6468
4
1.6229
3
1.6545
3
1.6371
7
1.6851
4
1.6425
4
MP3 1.6165
3
1.6393
3
1.6268
3
1.6812
3
1.6420
7
1.6372
3
1.6441
9
1.6396
3
1.6396
3
1.6279
3
1.6313
3
1.6313
3
1.6395
3
1.6714
3
1.6347
3
1.6271
3
1.6539
3
1.6344
3
1.6274
3
1.6465
3
1.6248
3
1.6694
3
1.6272
3
MP3=FULL         1.6410
9
  1.6490
9
                               
MP4 1.6213
3
1.6462
3
1.6337
3
1.6903
3
1.6506
7
1.6454
3
1.6598
3
1.6581
4
1.6496
3
1.6376
3
1.6446
3
1.6446
3
1.6524
3
1.6818
3
1.6653
6
1.6397
3
1.6672
3
1.6481
3
1.6406
3
1.6570
3
1.6367
3
1.6800
3
1.6390
3
MP4=FULL 1.6221
3
1.6470
3
1.6345
3
1.6909
3
1.6456
3
1.6456
3
1.6583
3
1.6491
3
1.6491
3
1.6340
3
1.6405
3
1.6405
3
1.6520
3
1.6824
3
1.6446
3
1.6244
3
1.6665
3
1.6411
3
1.6231
3
1.6566
3
1.6321
3
1.6796
3
1.6344
3
B2PLYP         1.6488
9
        1.6562
1
        1.6477
6
    1.6696
1
         
B2PLYP=FULLultrafine         1.6399
6
                                   
Configuration interaction CID 1.6172
3
1.6373
3
1.6252
3
1.6782
3
1.6382
7
1.6331
3
1.6428
3
1.6455
4
1.6364
3
1.6229
3
1.6252
3
1.6252
3
1.6350
3
1.6672
3
1.6294
3
1.6212
3
1.6477
3
1.6281
3
1.6212
3
1.6424
3
1.6195
3
1.6651
3
1.6218
3
CISD 1.6193
3
1.6383
3
1.6261
3
1.6791
3
1.6393
7
1.6337
3
1.6435
3
1.6370
3
1.6370
3
1.6233
3
1.6257
3
1.6257
3
1.6357
3
1.6679
3
1.6299
3
1.6216
3
1.6483
3
1.6286
3
1.6216
3
1.6431
3
1.6200
3
1.6659
3
1.6223
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) 6-311+G(3df,2pd) 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 1.6216
3
1.6531
7
1.6309
3
1.6868
3
1.6461
7
  1.6959
1
1.6518
7
1.6516
7
1.6387
4
1.6369
3
1.6369
3
1.6458
3
1.6853
4
1.6466
4
1.6321
3
1.6602
3
1.6467
4
1.6325
3
1.6525
3
1.6382
4
1.6753
3
1.6325
3
QCISD(T) 1.6227
3
1.6450
3
1.6321
3
1.6878
3
1.6498
4
1.6428
3
1.6554
3
1.6555
4
1.6469
3
1.6345
3
1.6403
3
1.6403
3
1.6485
3
1.6790
3
1.6430
3
1.6356
3
1.6627
3
1.6436
3
1.6362
3
1.6542
3
1.6330
3
1.6771
3
1.6354
3
QCISD(TQ) 1.6224
3
      1.6416
3
      1.6457
3
1.6331
3
1.6384
3
1.6384
3
    1.6414
3
  1.6608
3
1.6417
3
  1.6527
3
1.6314
3
1.6756
3
1.6338
3
Coupled Cluster CCD 1.6184
3
1.6404
3
1.6280
3
1.6833
3
1.6432
7
1.6390
3
1.6502
3
1.6506
4
1.6422
3
1.6300
3
1.6339
3
1.6339
3
1.6425
3
1.6815
4
1.6373
3
1.6296
3
1.6565
3
1.6370
3
1.6299
3
1.6489
3
1.6274
3
1.6796
4
1.6379
4
CCSD 1.6202
3
1.6423
3
1.6298
3
1.6853
3
1.6447
7
1.6404
3
1.6520
3
1.6525
4
1.6439
3
1.6373
4
1.6355
3
1.6355
3
1.6443
3
1.6756
3
1.6453
4
1.6309
3
1.6583
3
1.6453
4
1.6312
3
1.6509
3
1.6289
3
1.6737
3
1.6312
3
CCSD=FULL 1.6209
3
1.6431
3
1.6305
3
1.6860
3
1.6463
4
1.6407
3
1.6507
3
1.6435
3
1.6435
3
1.6343
4
1.6317
3
1.6317
3
1.6439
3
1.6762
3
1.6436
4
1.6167
3
1.6576
3
1.6395
4
1.6148
3
1.6504
3
1.6245
3
1.6733
3
1.6267
3
CCSD(T) 1.6218
3
1.6537
4
1.6317
3
1.6874
3
1.6475
7
1.6493
4
1.6651
4
1.6550
4
1.6550
4
1.6340
3
1.6489
4
1.6397
3
1.6479
3
1.6784
3
1.6510
4
1.6350
3
1.6621
3
1.6430
3
1.6356
3
1.6536
3
1.6405
4
1.6845
4
1.6431
4
CCSD(T)=FULL 1.6227
3
1.6453
3
1.6325
3
1.6880
3
1.6497
4
1.6426
3
1.6534
3
1.6460
3
1.6460
3
1.6305
3
1.6358
3
1.6358
3
1.6474
3
1.6870
4
1.6490
4
1.6204
3
1.6614
3
1.6363
3
  1.6532
3
1.6280
3
1.6844
4
1.6389
4
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) 6-311+G(3df,2pd) 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 1.6918
7
1.6380
7
1.6826
7
1.6342
7
1.6791
7
1.6774
7
density functional LSDA 1.7089
3
1.6633
3
1.7083
3
1.6630
3
1.6943
3
1.6785
3
SVWN 1.7089
3
1.6633
3
1.7083
3
1.6630
3
1.6943
3
1.6785
3
BLYP 1.7100
3
1.6641
3
1.7098
3
1.6637
3
1.7014
3
1.7033
3
B1B95 1.7000
7
1.6560
7
1.6908
3
1.6464
3
1.6845
3
1.6805
3
B3LYP 1.7107
7
1.6594
7
1.7074
7
1.6587
7
1.6979
7
1.6966
7
B3LYPultrafine 1.6975
3
1.6525
3
1.6963
3
1.6513
3
1.6883
3
1.6870
3
B3PW91 1.6974
3
1.6514
3
1.6960
3
1.6502
3
1.6884
3
1.6865
3
mPW1PW91 1.6941
3
1.6483
3
1.6925
3
1.6469
3
1.6858
3
1.6832
3
M06-2X 1.6826
3
1.6398
3
1.6801
3
1.6384
3
1.6817
3
1.6736
3
PBEPBE 1.7096
3
1.6627
3
1.7091
3
1.6621
3
1.7020
3
1.7013
3
PBEPBEultrafine 1.7096
3
1.6627
3
1.7091
3
1.6621
3
1.7019
3
1.7013
3
PBE1PBE 1.6948
3
1.6488
3
1.6930
3
1.6474
3
1.6868
3
1.6838
3
HSEh1PBE 1.6951
3
1.6495
3
1.6933
3
1.6481
3
1.6868
3
1.6838
3
Moller Plesset perturbation MP2 1.7257
7
1.6693
7
1.7174
7
1.6663
7
1.7093
7
1.7072
7
MP2=FULL 1.7120
3
1.6625
3
1.7065
3
1.6589
3
1.7002
3
1.6985
3
MP3 1.7046
3
1.6533
3
1.6968
3
1.6489
3
1.6921
3
1.6896
3
MP4 1.7153
3
1.6635
3
1.7103
3
1.6603
3
1.7022
3
1.6997
3
MP4=FULL 1.7153
3
1.6635
3
1.7103
3
1.6603
3
1.7022
3
1.7006
3
Configuration interaction CID 1.7002
3
1.6476
3
1.6925
3
1.6433
3
1.6885
3
1.6860
3
CISD 1.7013
3
1.6481
3
1.6937
3
1.6439
3
1.6894
3
1.6869
3
Quadratic configuration interaction QCISD 1.7111
3
1.6589
3
1.7047
3
1.6549
3
1.6985
3
1.6960
3
QCISD(T) 1.7116
3
1.6597
3
1.7058
3
1.6562
3
1.6989
3
1.6964
3
QCISD(TQ) 1.7100
3
1.6581
3
1.7035
3
1.6544
3
1.6976
3
1.6950
3
Coupled Cluster CCD 1.7070
3
1.6557
3
1.7001
3
1.6515
3
1.6949
3
1.6923
3
CCSD 1.7089
3
1.6570
3
1.7023
3
1.6529
3
1.6967
3
1.6942
3
CCSD=FULL 1.7089
3
1.6570
3
1.7023
3
1.6529
3
1.6967
3
1.6950
3
CCSD(T) 1.7112
3
1.6592
3
1.7051
3
1.6556
3
1.6985
3
1.6959
3
CCSD(T)=FULL 1.7112
3
1.6592
3
1.7051
3
1.6556
3
1.6985
3
1.6968
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.