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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 0.9935
4
PM3 1.1043
4
PM6 1.2306
12
composite G2 1.1058
7
G3 1.1058
7
G3B3 1.1573
7
G3MP2 0.9109
1
G4 1.1046
13
CBS-Q 1.1067
7
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 daug-cc-pVDZ daug-cc-pVTZ
hartree fock HF 1.1014
12
1.0881
9
1.0885
9
1.0796
9
1.0570
10
1.0545
9
1.2363
9
1.0445
9
1.0410
9
1.0934
12
0.9463
5
0.8973
1
1.0570
12
1.0555
9
1.0471
9
0.9930
7
0.9750
9
1.0414
12
1.0595
10
0.9014
1
0.8980
1
0.8969
1
0.9297
4
1.0458
14
ROHF   1.2391
4
1.2391
4
1.2532
4
1.2288
4
1.2227
4
1.9374
4
1.1889
4
1.1790
4
  0.9988
2
  1.0771
4
1.2166
4
1.2264
4
1.0548
4
1.0383
4
1.0342
4
1.0328
4
      0.9423
2
0.9415
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 1.1613
12
1.1705
9
1.1707
9
1.1445
9
1.1515
14
1.1135
9
1.1176
9
1.0998
9
1.0909
9
1.1501
12
1.1111
4
0.9331
1
1.1314
6
1.1140
9
1.0832
9
0.9322
1
0.9717
5
0.9766
4
0.9332
1
      0.9750
4
0.9728
4
B1B95 1.1567
7
1.1647
7
1.1647
7
1.1398
7
1.1228
7
1.1217
7
1.1327
7
1.0968
7
1.0872
7
1.1068
7
1.0585
4
0.9169
1
1.0928
6
1.1120
7
1.0795
7
0.9164
1
1.0079
7
1.0043
7
0.9171
1
      0.9549
4
0.9530
4
B3LYP 1.1392
12
1.1386
9
1.1388
9
1.1135
9
1.0889
10
1.0872
9
1.0996
9
1.0745
9
1.0666
9
1.2213
12
1.1140
8
0.9224
1
1.0972
12
1.0875
9
1.0541
10
1.0350
7
1.0047
9
1.0599
12
1.0726
10
0.9270
1
0.9227
1
0.9214
1
0.9615
4
0.9597
4
B3LYPultrafine 0.9953
1
1.2231
4
0.9688
1
0.9493
1
1.0982
9
1.1548
4
1.1807
4
1.1232
4
0.9203
1
1.1486
4
1.0804
4
0.9224
1
1.0820
4
1.1500
4
1.0992
4
0.9216
1
0.9665
4
1.0594
12
0.9224
1
      0.9615
4
0.9597
4
B3PW91 1.1272
9
1.1313
9
1.1315
9
1.1059
9
1.0909
9
1.0798
9
1.0928
9
1.0638
9
1.0532
9
1.1272
12
1.0287
4
0.9198
1
1.0822
6
1.0794
9
1.0487
9
0.9192
1
0.9548
5
0.9589
4
0.9198
1
      0.9580
4
0.9555
4
mPW1PW91 1.1213
9
1.1241
9
1.1243
9
1.1000
9
1.0852
9
1.0741
9
1.0895
9
1.0580
9
1.0465
9
1.1220
12
1.0184
4
0.9171
1
1.0765
6
1.0734
9
1.0435
9
0.9168
1
1.0079
7
1.0039
7
0.9174
1
      0.9549
4
0.9527
4
M06-2X 1.1671
6
1.1808
6
1.1139
12
1.1588
6
1.0827
9
1.1344
6
1.1610
6
1.1133
6
1.0939
6
1.1285
6
1.0724
15
0.9177
1
1.0707
6
1.1307
6
1.0918
6
0.9177
1
1.0218
6
1.0186
6
0.9183
1
      0.9554
4
0.9542
4
PBEPBE 1.1487
9
1.1764
12
1.1580
9
1.1285
9
1.1511
12
1.1412
12
1.1367
12
1.1363
12
1.0694
9
1.1378
12
1.0949
9
0.9301
1
1.1004
6
1.1420
12
1.1012
12
0.9296
1
1.0244
7
1.0201
7
0.9305
1
      0.9712
4
0.9689
4
PBEPBEultrafine 1.0057
1
1.2516
4
0.9784
1
0.9585
1
1.1871
8
1.1706
4
1.1876
4
1.1247
4
0.9279
1
1.1643
4
1.0644
4
0.9301
1
1.0705
4
1.1612
4
1.0909
4
0.9296
1
0.9763
4
0.9724
4
0.9305
1
      0.9712
4
0.9689
4
PBE1PBE 1.1916
4
1.1997
4
1.1997
4
1.1631
4
1.0677
7
1.1443
4
1.1666
4
1.0933
4
1.0731
4
1.1578
7
1.0158
4
0.9180
1
1.0392
4
1.1254
4
1.0630
4
0.9175
1
0.9601
4
0.9569
4
0.9182
1
      0.9557
4
0.9537
4
HSEh1PBE 1.1825
6
1.1255
9
1.1936
6
1.1656
6
1.0864
9
1.1379
6
1.0910
9
1.1153
6
1.0994
6
1.1314
6
1.0257
4
0.9183
1
1.0795
6
1.1350
6
1.0452
9
0.9177
1
1.0236
6
1.0196
6
0.9184
1
      0.9562
4
0.9542
4
TPSSh 1.2069
4
1.2262
4
1.2266
4
1.1855
4
1.1367
13
1.1567
4
1.1500
12
1.1273
4
1.1205
4
1.1303
12
1.0921
4
  1.0955
4
1.1239
5
1.1253
12
1.0735
4
0.9676
4
0.9631
4
0.9617
4
      0.9628
4
0.9593
4
wB97X-D 1.1925
4
1.2042
4
1.1497
14
1.1712
4
1.1210
14
1.1430
4
1.1249
14
1.1221
4
1.1029
14
1.1374
4
1.0813
4
  1.0977
14
1.1156
14
1.1012
14
0.9580
3
0.9582
4
1.0551
15
0.9521
4
      0.9534
4
0.9505
4
B97D3 1.2311
4
1.1789
14
1.2755
4
1.2339
4
1.1471
14
1.1932
4
1.1395
14
1.1692
4
1.1258
14
1.1857
4
1.1035
15
  1.1104
15
1.1954
4
1.1229
14
1.1007
4
0.9680
4
1.0687
15
0.9613
4
      0.9624
4
1.0772
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 cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pCVDZ cc-pCVTZ cc-pCVQZ daug-cc-pVDZ daug-cc-pVTZ
Moller Plesset perturbation MP2 1.0928
9
1.1100
9
1.1104
9
1.1051
9
1.1258
13
1.0688
9
1.1278
9
1.1129
12
1.0105
9
1.0632
9
1.0770
4
0.9171
1
1.0782
12
1.0618
9
1.0278
10
1.0227
7
1.0024
9
1.0054
7
1.0031
7
0.9198
1
0.9181
1
0.9173
1
0.9571
4
0.9538
4
MP2=FULL 1.0928
9
1.1100
9
1.1104
9
1.1050
9
1.0881
9
1.0684
9
1.1275
9
1.0591
9
1.0100
9
1.0628
9
1.0733
4
0.9160
1
1.0635
6
1.0615
9
1.0289
9
1.0214
7
1.0765
10
1.0037
7
1.0018
7
0.9195
1
0.9176
1
0.9167
1
0.9568
4
0.9520
4
ROMP2 1.3199
2
1.3668
2
1.3668
2
1.3487
2
1.3179
2
1.2838
2
1.5709
2
1.2352
2
1.0754
2
1.2779
2
1.1682
2
  1.1107
2
1.2495
2
1.1392
2
  0.9777
2
          0.9680
2
0.9642
2
MP3 0.9858
1
0.9583
1
0.9583
1
0.9442
1
1.0822
9
0.9185
1
1.1067
12
0.9140
1
0.9089
1
0.9108
1
0.9311
2
0.9114
1
0.9350
2
0.9370
2
0.9323
2
0.9113
1
0.9194
1
0.9158
1
0.9123
1
      0.9565
1
0.9538
1
MP3=FULL   0.9949
1
0.9981
1
0.9794
1
1.1214
12
0.9575
1
1.1160
12
0.9485
1
0.9454
1
0.9523
1
0.9492
1
  0.9349
2
0.9367
2
0.9311
2
  0.9566
1
0.9518
1
        0.9562
1
0.9519
1
MP4 0.9909
1
1.1097
9
0.9620
1
0.9480
1
1.0860
9
0.9208
1
0.9263
1
0.9181
2
1.0113
9
0.9138
1
0.9388
2
0.9176
1
0.9421
2
0.9417
2
1.0321
9
0.9174
1
0.9456
2
0.9432
2
0.9193
1
      0.9657
1
0.9640
1
MP4=FULL 0.9909
1
0.9823
2
0.9620
1
0.9480
1
0.9594
2
0.9204
1
0.9260
1
0.9178
1
0.9325
2
0.9132
1
0.9379
2
0.9165
1
0.9219
1
0.9414
2
0.9381
2
0.9163
1
0.9454
2
0.9413
2
0.9182
1
      0.9654
1
0.9616
1
B2PLYP 1.1770
4
1.1930
4
1.1935
4
1.1681
4
1.0707
7
1.1332
4
1.1868
4
1.1052
4
1.0841
4
1.1268
4
1.0817
4
0.9197
1
1.0646
4
1.1260
4
1.0868
10
0.9191
1
0.9630
4
0.9596
4
0.9202
1
      0.9581
4
0.9560
4
B2PLYP=FULL 1.1770
4
1.1930
4
1.1935
4
1.1681
4
1.1490
4
1.1330
4
1.1866
4
1.1051
4
1.0839
4
1.1266
4
1.0810
4
  1.0644
4
1.1258
4
1.0787
4
  0.9629
4
0.9592
4
        0.9580
4
0.9555
4
B2PLYP=FULLultrafine 1.1770
4
1.1930
4
1.1936
4
1.1681
4
1.1277
15
1.1331
4
1.1867
4
1.1052
4
1.0840
4
1.1266
4
1.0810
4
  1.0645
4
1.1188
15
1.0869
15
  0.9629
4
1.0577
15
        0.9580
4
0.9555
4
Configuration interaction CID 0.9938
1
1.1049
9
1.1051
9
1.0976
9
1.0807
9
0.9176
1
0.9207
1
1.0501
9
0.9083
1
0.9094
1
0.9873
4
0.9099
1
0.9157
1
1.0965
4
1.0070
5
0.9096
1
0.9181
1
0.9142
1
0.9106
1
      0.9487
4
0.9447
4
CISD 0.9946
1
1.1067
9
1.1068
9
1.1002
9
1.0819
9
  0.9217
1
1.0511
9
0.9092
1
0.9100
1
0.9910
4
0.9109
1
0.9170
1
1.0988
4
1.0113
5
0.9105
1
0.9191
1
0.9152
1
0.9115
1
      0.9499
4
0.9458
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-pCVDZ cc-pCVTZ cc-pCVQZ daug-cc-pVDZ daug-cc-pVTZ
Quadratic configuration interaction QCISD 0.9946
1
1.1094
9
1.1097
9
1.1048
9
1.0860
9
1.0663
9
1.1464
12
1.0557
9
1.0108
9
1.0597
9
0.9550
3
0.9147
1
1.0592
6
1.1263
10
1.0537
7
0.9143
1
1.0083
7
1.0009
7
0.9156
1
      0.9544
4
0.9501
4
QCISD(T) 0.9944
1
0.9634
1
0.9634
1
0.9486
1
1.0859
9
0.9210
2
0.9254
2
1.0593
5
0.9128
1
0.9138
1
1.0577
4
0.9164
1
1.0622
6
1.0866
7
1.0541
7
0.9162
1
1.0249
6
1.0179
6
0.9178
1
      0.9563
4
0.9530
4
QCISD(T)=FULL         1.1421
4
  1.2136
4
      1.0503
4
    1.1016
4
1.0433
4
0.9868
4
0.9609
4
0.9546
4
0.9520
4
      0.9561
4
0.9511
4
QCISD(TQ)   0.9635
1
0.9635
1
0.9489
1
0.9586
2
0.9212
1
0.9442
2
0.9183
1
0.9128
1
0.9139
1
0.9363
2
0.9160
1
0.9211
1
0.9409
2
0.9369
2
0.9361
2
0.9429
2
0.9402
2
0.9173
1
         
QCISD(TQ)=FULL         0.9585
2
  0.9249
1
      0.9550
1
    0.9197
1
0.9160
1
0.9148
1
0.9427
2
0.9187
1
0.9164
1
         
Coupled Cluster CCD 0.9938
1
1.1070
9
1.1073
9
1.1001
9
1.0834
9
1.0636
9
1.1158
9
1.0534
9
1.0068
9
1.0576
9
0.9980
4
0.9129
1
1.0527
6
1.0834
7
1.0470
7
0.9127
1
1.0058
7
0.9988
7
0.9138
1
      0.9521
4
0.9483
4
CCSD 0.9946
1
0.9621
1
0.9621
1
0.9479
1
1.1039
8
1.0775
5
1.1583
5
1.0579
5
1.0029
4
1.1097
4
1.0027
4
0.9140
1
1.0166
4
1.1144
6
1.0612
7
0.9819
4
0.9582
4
0.9582
5
0.9494
4
    0.9138
1
0.9536
4
0.9495
4
CCSD=FULL 0.9946
1
0.9620
1
0.9620
1
0.9479
1
1.1419
4
0.9202
1
0.9241
1
0.9166
1
0.9113
1
1.1093
4
1.0004
4
0.9129
1
1.0160
4
1.1019
4
1.0413
4
0.9804
4
0.9580
4
0.9508
4
0.9482
4
    0.9131
1
0.9534
4
0.9477
4
CCSD(T) 0.9944
1
0.9634
1
0.9634
1
0.9486
1
1.1144
7
1.0773
5
1.1567
5
1.0592
5
1.0049
4
1.1103
4
1.0141
5
0.9161
1
1.0612
6
1.0866
7
1.0538
7
1.0201
7
1.0102
7
1.0037
7
1.0012
7
0.9196
1
0.9170
1
0.9164
1
0.9560
4
0.9527
4
CCSD(T)=FULL 0.9944
1
0.9633
1
0.9633
1
0.9486
1
1.1142
7
0.9205
1
0.9249
1
0.9179
1
0.9122
1
0.9134
1
1.0250
4
0.9150
1
1.0606
6
1.0865
7
1.0503
7
1.0188
7
1.0099
7
1.0016
7
0.9999
7
0.9193
1
0.9165
1
0.9158
1
0.9558
4
0.9508
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-pCVDZ cc-pCVTZ cc-pCVQZ daug-cc-pVDZ daug-cc-pVTZ

average calculated bond lengths (Å)
Methods with effective core potentials (select basis sets)
CEP-31G CEP-31G* CEP-121G CEP-121G* LANL2DZ SDD cc-pVTZ-PP aug-cc-pVTZ-PP Def2TZVPP
hartree fock HF 1.1872
9
1.1761
9
1.0683
9
1.0450
9
1.1379
9
1.1381
9
    1.0511
14
ROHF                 1.0106
2
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
    1.1107
4
B1B95 0.9445
2
0.9292
2
0.9386
2
0.9246
2
0.9436
2
0.9436
2
    1.0593
4
B3LYP 1.1077
9
1.0953
9
1.0818
9
1.0586
9
1.1084
9
1.1082
9
    1.1011
14
B3LYPultrafine 0.9502
1
0.9347
1
0.9451
1
0.9307
1
0.9488
1
0.9488
1
    1.0781
4
B3PW91 0.9463
1
0.9311
1
0.9414
1
0.9271
1
0.9455
1
0.9455
1
    1.0369
4
mPW1PW91 0.9433
1
0.9285
1
0.9383
1
0.9245
1
0.9428
1
0.9428
1
    1.0265
4
M06-2X 0.9407
1
0.9260
1
0.9362
1
0.9227
1
0.9434
1
0.9434
1
    1.0214
4
PBEPBE 0.9574
1
0.9405
1
0.9523
1
0.9365
1
0.9577
1
0.9577
1
    1.1020
14
PBEPBEultrafine 0.9574
1
0.9405
1
0.9523
1
0.9365
1
0.9577
1
0.9577
1
    1.0615
4
PBE1PBE 0.9438
1
0.9289
1
0.9388
1
0.9249
1
0.9435
1
0.9435
1
    1.0226
4
HSEh1PBE 0.9444
1
0.9294
1
0.9394
1
0.9253
1
0.9440
1
0.9440
1
    1.0338
4
TPSSh                 1.0962
4
wB97X-D 1.1700
4
1.1578
4
1.1248
4
1.0948
4
1.1721
4
1.1718
4
    1.0832
4
B97D3                 1.1185
4
Moller Plesset perturbation MP2 1.1288
9
1.1108
9
1.0891
9
1.0561
9
1.1221
9
1.1220
9
    1.0795
14
MP2=FULL 0.9504
1
0.9361
1
0.9453
1
0.9319
1
0.9495
1
0.9495
1
    1.0137
4
ROMP2                 1.0962
2
MP3 0.9476
1
0.9334
1
0.9415
1
0.9285
1
0.9455
1
0.9455
1
    0.9509
1
MP3=FULL                 0.9510
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
    0.9608
1
B2PLYP 0.9481
1
0.9333
1
0.9432
1
0.9293
1
0.9470
1
0.9470
1
    1.0587
4
B2PLYP=FULL                 1.0578
4
B2PLYP=FULLultrafine                 1.0578
4
Configuration interaction CID 0.9473
1
0.9322
1
0.9414
1
0.9274
1
0.9453
1
0.9453
1
    0.9929
4
CISD 0.9485
1
0.9329
1
0.9426
1
0.9282
1
0.9465
1
0.9465
1
    0.9958
4
Quadratic configuration interaction QCISD 0.9511
1
0.9358
1
0.9457
1
0.9314
1
0.9494
1
0.9494
1
    1.0087
4
QCISD(T) 0.9511
1
0.9361
1
0.9459
1
0.9318
1
0.9495
1
0.9495
1
    1.0145
4
QCISD(T)=FULL                 1.0131
4
QCISD(TQ) 0.9511
1
0.9362
1
0.9458
1
0.9318
1
0.9497
1
0.9497
1
    0.9563
1
Coupled Cluster CCD 0.9496
1
0.9348
1
0.9440
1
0.9302
1
0.9478
1
0.9478
1
    1.0018
4
CCSD 0.9507
1
0.9355
1
0.9452
1
0.9310
1
0.9490
1
0.9491
1
    1.0057
4
CCSD=FULL 0.9507
1
0.9355
1
0.9452
1
0.9310
1
0.9490
1
0.9490
1
    1.0047
4
CCSD(T) 0.9509
1
0.9360
1
0.9457
1
0.9316
1
0.9494
1
0.9494
1
    1.0132
4
CCSD(T)=FULL 0.9509
1
0.9360
1
0.9457
1
0.9316
1
0.9494
1
0.9494
1
    1.0119
4
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.