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III.G.1.a.

Comparison of levels of theory for F-H


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 1.1511
2
PM3 1.0994
4
PM6 1.0841
10
composite G2 1.0803
8
G3 1.0803
8
G3B3 1.1130
8
G4 1.0595
10
CBS-Q 1.0802
8
molecular mechanics DREIDING 0.9310
1

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-pCVDZ cc-pCVTZ cc-pCVQZ
hartree fock HF 1.0618
10
1.1024
8
1.1024
8
1.0952
8
1.0737
14
1.0692
8
1.2400
8
1.0589
8
1.0548
8
1.0314
10
0.8970
2
0.8973
1
1.0249
10
1.0700
8
1.0612
8
1.0031
6
0.9896
7
0.9684
9
0.9742
7
0.9014
1
0.8980
1
0.8969
1
ROHF   1.1454
2
1.1454
2
1.1437
2
1.2288
4
1.1221
2
1.1339
2
1.1301
2
1.1178
2
      1.1232
2
1.1277
2
1.1216
2
1.1219
2
1.1285
2
1.1228
2
1.1222
2
     
density functional LSDA 1.1457
8
1.1525
8
1.1525
8
1.1243
8
1.1068
8
1.0969
8
1.1081
8
1.0680
8
1.0422
8
1.0905
8
0.9305
1
0.9305
1
1.0755
3
1.0903
8
1.0469
8
0.9300
1
1.0175
8
1.0396
4
0.9309
1
     
SVWN 0.9978
1
1.1524
8
0.9743
1
0.9563
1
1.1157
7
1.0755
3
1.1081
8
1.0831
3
1.0719
3
1.0681
3
0.9305
1
0.9305
1
0.9324
1
1.0798
3
1.0741
3
0.9300
1
1.0794
3
1.0754
3
0.9309
1
     
BLYP 1.1395
10
1.1886
8
1.1886
8
1.1620
8
1.1436
8
1.1301
8
1.1347
8
1.1151
8
1.1055
8
1.0854
10
0.9330
1
0.9331
1
1.0895
3
1.1301
8
1.0967
8
0.9322
1
0.9367
2
0.9351
1
0.9332
1
     
B1B95 1.1815
6
1.1941
6
1.1941
6
1.1682
6
1.1498
6
1.1432
6
1.1617
6
1.1226
6
1.1112
6
1.1341
6
0.9169
1
0.9169
1
1.0692
3
1.1384
6
1.1012
6
1.0032
3
1.0308
5
1.0273
5
0.9628
2
     
B3LYP 1.1145
10
1.1547
8
1.1547
8
1.1289
8
1.1130
8
1.1022
8
1.1159
8
1.0884
8
1.1026
7
1.2767
10
0.9247
4
0.9224
1
1.0388
10
1.1020
8
1.0736
8
1.0471
6
1.0173
7
1.0145
7
1.0015
7
0.9270
1
0.9227
1
 
B3LYPultrafine 0.9953
1
0.9688
1
0.9688
1
0.9493
1
1.1130
8
0.9256
1
0.9280
1
0.9246
1
0.9203
1
0.9197
1
0.9222
1
0.9224
1
0.9250
1
0.9271
1
0.9225
1
0.9216
1
0.9259
1
1.0496
10
0.9224
1
     
B3PW91 1.1618
7
1.1469
8
1.1469
8
1.1208
8
1.1050
8
1.0941
8
1.1086
8
1.0766
8
1.0860
7
1.0556
10
0.9196
1
0.9198
1
1.0717
3
1.0929
8
1.0596
8
0.9192
1
0.9233
2
0.9216
1
0.9198
1
     
mPW1PW91 1.1553
7
1.1391
8
1.1645
7
1.1144
8
1.0988
8
1.0877
8
1.1051
8
1.0706
8
1.0578
8
1.0502
10
0.9172
1
0.9171
1
1.0682
3
1.0866
8
1.0541
8
0.9168
1
1.0345
4
1.0307
4
0.9174
1
     
M06-2X 1.0925
3
1.1008
3
1.1008
3
1.0887
3
1.0956
8
1.0674
3
1.0691
3
1.0726
3
1.0637
3
1.0621
3
0.9177
1
0.9177
1
1.0676
3
1.0716
3
1.0662
3
0.9177
1
1.0707
3
1.0674
3
0.9183
1
     
PBEPBE 1.1851
7
1.1404
10
1.2028
7
1.1705
7
1.0916
10
1.0801
10
1.0871
10
1.0634
10
1.0818
8
1.0738
10
0.9330
4
0.9301
1
1.0844
3
1.0790
10
1.0464
10
1.0311
3
1.0886
3
1.0458
4
0.9766
2
     
PBEPBEultrafine 1.0057
1
0.9784
1
0.9784
1
0.9585
1
0.9469
4
0.9329
1
0.9357
1
0.9332
1
0.9279
1
0.9272
1
0.9301
1
0.9301
1
0.9327
1
0.9352
1
0.9302
1
0.9296
1
0.9343
1
0.9323
1
0.9305
1
     
PBE1PBE 0.9871
1
0.9623
1
0.9623
1
0.9440
1
1.0828
6
0.9206
1
0.9231
1
0.9196
1
0.9160
1
0.9294
3
0.9178
1
0.9180
1
0.9205
1
0.9225
1
0.9182
1
0.9175
1
0.9214
1
0.9199
1
0.9182
1
     
HSEh1PBE 1.1046
3
1.1050
3
1.1050
3
1.0927
3
1.1000
8
1.0693
3
1.0712
3
1.0756
3
1.0655
3
1.0628
3
0.9182
1
0.9183
1
1.0696
3
1.0741
3
1.0678
3
0.9177
1
1.0734
3
1.0691
3
0.9184
1
     
TPSSh         1.0704
10
  1.0670
10
              1.0569
10
             
Moller Plesset perturbation MP2 1.0430
6
1.1235
8
1.1235
8
1.1196
8
1.0824
9
1.0815
8
1.1477
8
1.0719
8
1.0174
8
1.0989
7
0.9179
1
0.9171
1
1.0125
10
1.0737
8
1.0271
9
1.0328
6
1.0067
8
1.0265
5
1.0098
6
0.9198
1
0.9181
1
0.9173
1
MP2=FULL 1.0333
7
1.1234
8
1.1234
8
1.1195
8
1.0823
9
1.0812
8
1.1473
8
1.0716
8
1.0317
7
1.0753
8
0.9173
1
0.9160
1
1.0687
3
1.0735
8
1.0238
9
1.0315
6
0.9965
8
1.0306
4
1.0233
5
0.9195
1
0.9176
1
0.9167
1
MP3 0.9858
1
0.9583
1
0.9583
1
0.9442
1
1.0952
8
0.9185
1
1.0483
10
0.9140
1
0.9089
1
0.9108
1
0.9122
1
0.9114
1
0.9168
1
0.9168
1
0.9130
1
0.9113
1
0.9194
1
0.9158
1
0.9123
1
     
MP3=FULL         1.0622
10
  1.0577
10
                             
MP4 0.9909
1
1.1231
8
0.9620
1
0.9480
1
1.0988
8
0.9208
1
0.9263
1
0.9181
2
1.0186
8
0.9138
1
0.9183
1
0.9176
1
0.9220
1
0.9195
1
1.0411
8
0.9174
1
0.9253
1
0.9225
1
0.9193
1
     
MP4=FULL 0.9909
1
0.9620
1
0.9620
1
0.9480
1
0.9348
1
0.9204
1
0.9260
1
0.9178
1
0.9125
1
0.9132
1
0.9175
1
0.9165
1
0.9219
1
0.9192
1
0.9169
1
0.9163
1
0.9250
1
0.9207
1
0.9182
1
     
B2PLYP         1.0856
6
                  1.0265
8
             
Configuration interaction CID 0.9938
1
1.1189
8
1.1189
8
1.1126
8
1.0941
8
0.9176
1
0.9207
1
1.0632
8
0.9083
1
0.9094
1
0.9105
1
0.9099
1
0.9157
1
0.9160
1
0.9114
2
0.9096
1
0.9181
1
0.9142
1
0.9106
1
     
CISD 0.9946
1
1.1206
8
1.1206
8
1.1152
8
1.0953
8
  0.9217
1
1.0642
8
0.9092
1
0.9100
1
0.9115
1
0.9109
1
0.9170
1
0.9168
1
0.9125
2
0.9105
1
0.9191
1
0.9152
1
0.9115
1
     
Quadratic configuration interaction QCISD 0.9946
1
1.1231
8
1.1037
9
1.1198
8
1.0991
8
1.0795
8
1.0922
10
1.0686
8
1.0185
8
1.0728
8
0.9154
1
0.9147
1
1.0648
3
1.0619
8
1.0702
6
0.9143
1
1.0362
4
1.0280
4
0.9156
1
     
QCISD(T) 0.9944
1
0.9634
1
0.9634
1
0.9486
1
1.0989
8
0.9210
2
0.9254
2
0.9182
2
0.9128
1
0.9138
1
0.9171
1
0.9164
1
1.0667
3
1.1074
6
1.0702
6
0.9162
1
1.0374
5
1.0293
5
0.9178
1
     
QCISD(TQ)   0.9635
1
0.9635
1
0.9489
1
0.9354
1
0.9212
1
0.9252
1
0.9183
1
0.9128
1
0.9139
1
0.9167
1
0.9160
1
0.9211
1
0.9200
1
0.9170
1
0.9159
1
0.9239
1
0.9206
1
0.9173
1
     
Coupled Cluster CCD 0.9938
1
1.1209
8
1.1209
8
1.1150
8
1.0966
8
1.0768
8
1.1353
8
1.0663
8
1.0143
8
1.0707
8
0.9138
1
0.9129
1
1.0629
3
1.1042
6
1.0628
6
0.9127
1
1.0282
5
1.0208
5
0.9138
1
     
CCSD 0.9946
1
0.9621
1
0.9621
1
0.9479
1
1.0395
5
0.9202
2
0.9240
2
0.9167
2
0.9117
1
0.9129
1
0.9149
1
0.9140
1
0.9196
1
1.0654
3
1.0600
3
0.9139
1
0.9222
1
0.9184
1
0.9151
1
     
CCSD=FULL 0.9946
1
0.9620
1
0.9620
1
0.9479
1
0.9343
1
0.9202
1
0.9241
1
0.9166
1
0.9113
1
0.9123
1
0.9141
1
0.9129
1
0.9195
1
0.9188
1
0.9143
1
0.9129
1
0.9219
1
0.9166
1
0.9141
1
     
CCSD(T) 0.9944
1
0.9634
1
0.9634
1
0.9486
1
1.1573
5
0.9209
2
0.9252
2
0.9181
2
0.9126
1
0.9137
1
0.9171
2
0.9161
1
1.0664
3
1.1074
6
1.0699
6
1.0306
6
1.0182
6
1.0110
6
1.0084
6
0.9196
1
0.9170
1
0.9164
1
CCSD(T)=FULL 0.9944
1
0.9633
1
0.9633
1
0.9486
1
1.0398
5
0.9205
1
0.9249
1
0.9179
1
0.9122
1
0.9134
1
0.9161
1
0.9150
1
1.0662
3
1.0296
4
1.0244
4
1.0293
6
1.0378
4
1.0284
4
1.0072
6
0.9193
1
0.9165
1
0.9158
1

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 1.2174
8
1.2052
8
1.0840
8
1.0581
8
1.1614
8
1.1619
8
density functional LSDA 0.9605
1
0.9436
1
0.9564
1
0.9403
1
0.9566
1
0.9565
1
SVWN 0.9605
1
0.9436
1
0.9564
1
0.9403
1
0.9566
1
0.9565
1
BLYP 0.9621
1
0.9449
1
0.9569
1
0.9410
1
0.9614
1
0.9614
1
B1B95 0.9445
2
0.9292
2
0.9386
2
0.9246
2
0.9436
2
0.9436
2
B3LYP 1.1230
8
1.1103
8
1.0946
8
1.0696
8
1.1238
8
1.1237
8
B3LYPultrafine 0.9502
1
0.9347
1
0.9451
1
0.9307
1
0.9488
1
0.9488
1
B3PW91 0.9463
1
0.9311
1
0.9414
1
0.9271
1
0.9455
1
0.9455
1
mPW1PW91 0.9433
1
0.9285
1
0.9383
1
0.9245
1
0.9428
1
0.9428
1
M06-2X 0.9407
1
0.9260
1
0.9362
1
0.9227
1
0.9434
1
0.9434
1
PBEPBE 0.9574
1
0.9405
1
0.9523
1
0.9365
1
0.9577
1
0.9577
1
PBEPBEultrafine 0.9574
1
0.9405
1
0.9523
1
0.9365
1
0.9577
1
0.9577
1
PBE1PBE 0.9438
1
0.9289
1
0.9388
1
0.9249
1
0.9435
1
0.9435
1
HSEh1PBE 0.9444
1
0.9294
1
0.9394
1
0.9253
1
0.9440
1
0.9440
1
Moller Plesset perturbation MP2 1.1468
8
1.1270
8
1.1028
8
1.0661
8
1.1390
8
1.1391
8
MP2=FULL 0.9504
1
0.9361
1
0.9453
1
0.9319
1
0.9495
1
0.9495
1
MP3 0.9476
1
0.9334
1
0.9415
1
0.9285
1
0.9455
1
0.9455
1
MP4 0.9513
1
0.9363
1
0.9462
1
0.9320
1
0.9495
1
0.9496
1
MP4=FULL 0.9513
1
0.9363
1
0.9462
1
0.9320
1
0.9495
1
0.9495
1
Configuration interaction CID 0.9473
1
0.9322
1
0.9414
1
0.9274
1
0.9453
1
0.9453
1
CISD 0.9485
1
0.9329
1
0.9426
1
0.9282
1
0.9465
1
0.9465
1
Quadratic configuration interaction QCISD 0.9511
1
0.9358
1
0.9457
1
0.9314
1
0.9494
1
0.9494
1
QCISD(T) 0.9511
1
0.9361
1
0.9459
1
0.9318
1
0.9495
1
0.9495
1
QCISD(TQ) 0.9511
1
0.9362
1
0.9458
1
0.9318
1
0.9497
1
0.9497
1
Coupled Cluster CCD 0.9496
1
0.9348
1
0.9440
1
0.9302
1
0.9478
1
0.9478
1
CCSD 0.9507
1
0.9355
1
0.9452
1
0.9310
1
0.9490
1
0.9491
1
CCSD=FULL 0.9507
1
0.9355
1
0.9452
1
0.9310
1
0.9490
1
0.9490
1
CCSD(T) 0.9509
1
0.9360
1
0.9457
1
0.9316
1
0.9494
1
0.9494
1
CCSD(T)=FULL 0.9509
1
0.9360
1
0.9457
1
0.9316
1
0.9494
1
0.9494
1
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.