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Comparison of levels of theory for H-F


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 0.8263
1
PM3 0.9378
1
PM6 1.2489
11
composite G2 0.9997
6
G3 0.9997
6
G3B3 1.0428
6
G3MP2 0.9109
1
G4 1.1279
11
CBS-Q 0.9976
6
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 Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pCVDZ cc-pCVTZ cc-pCVQZ
hartree fock HF 1.0674
9
1.0219
6
1.0219
6
1.0105
6
1.0686
9
0.9888
6
0.9908
6
0.9887
6
0.9845
6
1.0647
9
0.8970
2
0.8973
1
1.1060
11
1.1035
13
0.9920
6
0.9872
6
1.0094
4
0.9907
6
1.0744
9
1.1106
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
1.0579
6
1.0579
6
1.1243
8
1.1068
8
1.0192
6
1.0218
6
1.0681
8
1.0155
6
1.0135
6
0.9305
1
0.9305
1
1.0755
3
  1.0233
6
1.0181
6
0.9300
1
1.0225
6
1.0396
4
0.9309
1
     
BLYP 1.1145
9
1.0712
6
1.0712
6
1.0538
6
1.1459
13
1.0288
6
1.0299
6
1.0315
6
1.0238
6
1.1090
9
0.9330
1
0.9331
1
1.0895
3
  1.0330
6
1.0259
6
0.9322
1
0.9367
2
0.9351
1
0.9332
1
     
B1B95 1.0766
4
1.0688
4
1.0688
4
1.0556
4
1.0381
4
1.0363
4
1.0343
4
1.0358
4
1.0281
4
1.0258
4
0.9169
1
0.9169
1
1.0692
3
  1.0360
4
1.0301
4
0.9164
1
1.0350
4
1.0314
4
0.9171
1
     
B3LYP 1.0957
9
1.0540
6
1.0540
6
1.0383
6
1.0213
7
1.0152
6
1.0170
6
1.0171
6
1.0106
6
1.2200
9
1.1026
5
0.9224
1
1.1091
11
1.1241
13
1.0191
6
1.0095
7
1.0348
4
1.0171
6
1.1570
9
1.1149
7
0.9270
1
0.9227
1
 
B3LYPultrafine 0.9953
1
0.9688
1
0.9688
1
0.9493
1
1.0240
6
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
1.1222
11
0.9224
1
     
B3PW91 1.0563
6
1.0488
6
1.0488
6
1.0345
6
1.0205
6
1.0116
6
1.0135
6
1.0139
6
1.0075
6
1.0995
9
0.9196
1
0.9198
1
1.0717
3
  1.0159
6
1.0099
6
0.9192
1
0.9233
2
0.9208
1
0.9198
1
     
mPW1PW91 1.0515
6
1.0461
6
1.0461
6
1.0316
6
1.0179
6
1.0088
6
1.0107
6
1.0106
6
1.0045
6
1.0965
9
0.9172
1
0.9171
1
1.0682
3
  1.0129
6
1.0069
6
0.9168
1
1.0345
4
1.0307
4
0.9174
1
     
M06-2X 1.0925
3
1.1008
3
1.1236
11
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
1.0661
3
0.9177
1
1.0707
3
1.0672
3
0.9183
1
     
PBEPBE 1.0751
6
1.1210
9
1.0655
6
1.0489
6
1.1120
9
1.1050
9
1.0918
9
1.1189
9
1.0194
6
1.1026
9
1.1060
5
0.9301
1
1.0844
3
1.1307
13
1.1104
9
1.0868
9
0.9296
1
1.0500
4
1.0458
4
0.9305
1
     
PBEPBEultrafine 1.0057
1
0.9784
1
0.9784
1
0.9585
1
1.1385
5
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
1.1279
4
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
1.1405
8
1.1050
3
1.0927
3
1.1000
8
1.0693
3
1.1066
8
1.0756
3
1.0655
3
1.0628
3
0.9182
1
0.9183
1
1.0696
3
  1.0741
3
1.0558
8
0.9177
1
1.0734
3
1.0691
3
0.9184
1
     
TPSSh   0.9693
1
0.9693
1
0.9512
1
1.1537
11
0.9275
1
1.1535
11
0.9269
1
  1.1383
11
    0.9264
1
  0.9298
1
1.1439
11
  0.9287
1
0.9258
1
       
wB97X-D     1.1491
13
  1.1268
13
  1.1261
13
  1.1155
13
      1.1180
13
  1.1261
13
1.1172
13
    1.1039
14
       
B97D3   1.1628
13
    1.1404
13
  1.1380
13
  1.1292
13
  1.1188
14
        1.1306
13
    1.0759
14
       
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 Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pCVDZ cc-pCVTZ cc-pCVQZ
Moller Plesset perturbation MP2 1.0317
6
1.0424
6
1.0424
6
1.0372
6
1.1346
12
1.0094
6
1.0152
6
1.1332
11
1.0008
6
1.0035
6
0.9179
1
0.9171
1
1.0886
11
1.1185
13
1.0096
6
1.0041
7
1.0285
4
1.0066
7
1.0325
4
1.0118
5
0.9198
1
0.9181
1
0.9173
1
MP2=FULL 1.0317
6
1.0423
6
1.0423
6
1.0371
6
1.0231
6
1.0091
6
1.0148
6
1.0094
6
1.0004
6
1.0031
6
0.9173
1
0.9160
1
1.0687
3
  1.0093
6
1.0052
6
1.0274
4
1.1062
8
1.0308
4
1.0295
4
0.9195
1
0.9176
1
0.9167
1
MP3 0.9858
1
0.9583
1
0.9583
1
0.9442
1
1.0197
6
0.9185
1
1.1202
11
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         1.1345
11
  1.1303
11
          0.9167
1
  0.9165
1
0.9120
1
             
MP4 0.9909
1
1.0431
6
0.9620
1
0.9480
1
1.0233
6
0.9208
1
0.9263
1
0.9181
2
1.0000
6
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 0.9851
1
0.9634
1
0.9634
1
0.9466
1
1.0853
6
0.9224
1
0.9259
1
0.9204
1
0.9163
1
0.9158
1
0.9198
1
0.9197
1
0.9226
1
  0.9229
1
1.1170
9
0.9191
1
0.9243
1
0.9216
1
0.9202
1
     
B2PLYP=FULL 0.9851
1
0.9547
1
0.9634
1
0.9466
1
0.9298
1
0.9223
1
0.9245
1
0.9203
1
0.9162
1
0.9161
1
    0.9226
1
  0.9228
1
0.9194
1
  0.9242
1
0.9220
1
       
B2PLYP=FULLultrafine 0.9851
1
0.9634
1
0.9634
1
0.9466
1
0.9322
1
0.9223
1
0.9260
1
0.9203
1
0.9162
1
0.9161
1
    0.9226
1
  0.9228
1
0.9195
1
  0.9239
1
0.9220
1
       
Configuration interaction CID 0.9938
1
1.0387
6
1.0387
6
1.0313
6
1.0179
6
0.9176
1
0.9207
1
1.0024
6
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
1.0402
6
1.0402
6
1.0327
6
1.0187
6
  0.9217
1
1.0033
6
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
     
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 Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pCVDZ cc-pCVTZ cc-pCVQZ
Quadratic configuration interaction QCISD 0.9946
1
1.0428
6
1.0428
6
1.0364
6
1.0220
6
1.0075
6
1.0891
9
1.0074
6
0.9984
6
1.0011
6
0.9154
1
0.9147
1
1.0648
3
  1.1101
7
1.0242
4
0.9143
1
1.0362
4
1.0279
4
0.9156
1
     
QCISD(T) 0.9944
1
0.9634
1
0.9634
1
0.9486
1
1.0233
6
0.9210
2
0.9254
2
0.9182
2
0.9128
1
0.9138
1
0.9171
1
0.9164
1
1.0667
3
  1.0299
4
1.0262
4
0.9162
1
1.0764
3
1.0674
3
0.9178
1
     
QCISD(T)=FULL         0.9351
1
  0.9251
1
              0.9195
1
0.9162
1
0.9152
1
0.9239
1
0.9193
1
0.9167
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
     
QCISD(TQ)=FULL         0.9353
1
  0.9249
1
              0.9197
1
0.9160
1
0.9148
1
0.9236
1
0.9187
1
0.9164
1
     
Coupled Cluster CCD 0.9938
1
1.0408
6
1.0408
6
1.0342
6
1.0208
6
1.0062
6
1.0100
6
1.0059
6
0.9970
6
1.0001
6
0.9138
1
0.9129
1
1.0629
3
  1.0277
4
1.0228
4
0.9127
1
1.0338
4
1.0260
4
0.9138
1
     
CCSD 0.9946
1
0.9621
1
0.9621
1
0.9479
1
1.0392
5
0.9202
2
0.9240
2
0.9167
2
0.9117
1
0.9126
1
0.9149
1
0.9140
1
0.9196
1
  1.0654
3
1.0395
4
0.9139
1
0.9222
1
0.9492
2
0.9151
1
     
CCSD=FULL 0.9946
1
0.9620
1
0.9620
1
0.9479
1
0.9329
1
0.9202
1
0.9241
1
0.9166
1
0.9113
1
0.9121
1
0.9141
1
0.9129
1
0.9195
1
  0.9188
1
0.9140
1
0.9129
1
0.9219
1
0.9162
1
0.9141
1
     
CCSD(T) 0.9944
1
0.9634
1
0.9634
1
0.9486
1
1.0418
4
0.9209
2
0.9252
2
0.9181
2
0.9126
1
0.9137
1
0.9171
2
0.9161
1
1.0664
3
  1.0298
4
1.0260
4
1.0265
4
1.0380
4
1.0305
4
1.0286
4
0.9196
1
0.9170
1
0.9164
1
CCSD(T)=FULL 0.9944
1
0.9633
1
0.9633
1
0.9486
1
1.0416
4
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
1.0254
4
1.0378
4
1.0284
4
1.0274
4
0.9193
1
0.9165
1
0.9158
1
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 Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pCVDZ cc-pCVTZ cc-pCVQZ

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         1.0065
6
0.9966
6
1.0030
6
0.9934
6
1.0055
6
1.0055
6
density functional LSDA         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         1.0329
6
1.0202
6
1.0294
6
1.0172
6
1.0319
6
1.0319
6
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         1.0358
6
1.0223
6
1.0327
6
1.0194
6
1.0353
6
1.0354
6
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
B2PLYP         0.9481
1
0.9333
1
0.9432
1
0.9293
1
0.9470
1
0.9470
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.