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Computational Chemistry Comparison and Benchmark DataBase
Release 18October 2016
NIST Standard Reference Database 101
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III.G.1.a.

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 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
1.0803
8
0.9888
6
0.9908
6
0.9887
6
0.9845
6
1.0647
9
0.8970
2
0.8973
1
1.1060
11
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
     
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
1.0654
9
1.0798
3
1.0741
3
0.9300
1
1.0794
3
1.0754
3
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
1.0240
6
1.0152
6
1.0170
6
1.0171
6
1.0106
6
1.2200
9
1.1026
5
0.9224
1
1.1091
11
1.0191
6
1.0131
6
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
1.1264
13
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
1.1104
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
    1.1133
13
       
B97D3   1.1628
13
    1.1404
13
      1.1292
13
                1.1260
13
       
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
Moller Plesset perturbation MP2 1.0317
6
1.0424
6
1.0424
6
1.0372
6
1.1453
11
1.0094
6
1.0152
6
1.1332
11
1.0008
6
1.0035
6
0.9179
1
0.9171
1
1.0886
11
1.0096
6
1.0066
6
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 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
1.0600
3
0.9139
1
0.9222
1
0.9179
1
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 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)
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
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 1.0329
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.