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III.G.1.a.

Comparison of levels of theory for F-S


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 1.6935
29
PM3 1.5719
40
PM6 1.5710
47
composite G2 1.6029
46
G3 1.6017
47
G3B3 1.6413
45
G4 1.5809
35
CBS-Q 1.6118
41

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) 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 aug-cc-pV(T+d)Z cc-pCVTZ
hartree fock HF 1.8082
45
1.6748
47
1.6057
47
1.7126
47
1.5901
73
1.5938
47
1.5992
47
1.5928
47
1.5928
47
1.5699
47
1.5442
14
1.6142
51
1.6133
47
1.5750
47
1.6013
24
1.6110
47
1.5767
45
1.5792
20
1.6051
4
1.5511
27
1.5470
11
1.5896
3
ROHF 1.6134
2
1.7743
14
1.6924
14
1.7684
14
1.6400
15
1.6493
14
1.6614
14
1.6551
14
1.6551
14
1.4816
2
  1.6849
12
1.6725
14
1.6359
14
1.6314
14
1.6736
14
1.6391
14
1.5929
12
  1.5890
3
  1.5896
3
density functional LSDA 1.7391
47
1.6468
47
1.6170
47
1.7598
47
1.6239
47
1.6239
47
1.6387
47
1.6361
47
1.6361
47
1.6001
47
  1.6739
21
1.6465
47
1.6175
47
1.5659
4
1.6528
47
1.6278
29
1.5646
4
1.6523
4
1.6049
14
1.6005
11
1.6340
3
SVWN   1.7027
42
    1.6181
40
1.6306
19
1.6317
42
1.6440
19
1.6440
19
1.6062
19
    1.6548
19
1.6265
19
  1.6626
19
1.6291
19
  1.6523
4
1.6049
14
1.6005
11
1.6340
3
BLYP 1.7835
45
1.7563
47
1.6648
47
1.8091
47
1.6720
47
1.6720
47
1.6928
47
1.6883
47
1.6883
47
1.6474
47
  1.7060
19
1.6956
47
1.6676
47
  1.6587
8
    1.7022
4
1.6518
14
1.6495
11
1.6793
3
B1B95 1.7351
45
1.6365
45
1.6146
45
1.7523
45
1.6204
47
1.6216
45
1.6334
45
1.6305
45
1.6305
45
1.5998
45
  1.6672
21
1.6440
45
1.6109
45
1.5479
5
1.6506
43
1.6228
33
1.5469
5
1.6445
4
1.5950
15
1.5893
11
1.6237
3
B3LYP 1.7497
45
1.7163
47
1.6343
47
1.7695
47
1.6404
47
1.6404
47
1.6551
47
1.6514
47
1.6602
39
1.6160
47
1.5814
8
1.6776
51
1.6626
47
1.6317
47
1.6615
22
1.6687
46
1.6436
36
1.6377
20
1.6642
4
1.6058
27
1.6105
11
1.6439
3
B3LYPultrafine         1.6410
43
  1.6302
3
        1.6195
5
1.7039
19
1.6588
26
  1.7114
19
1.6213
46
    1.6068
10
1.5929
7
1.6440
3
B3PW91 1.7493
37
1.7095
47
1.6259
47
1.7550
45
1.6317
47
1.6317
47
1.6440
47
1.6412
47
1.6497
39
1.6088
47
  1.6805
21
1.6535
47
1.6217
47
  1.6154
8
    1.6558
4
1.6064
14
1.6011
11
1.6347
3
mPW1PW91 1.7413
37
1.7007
47
1.6194
45
1.7537
45
1.6246
47
1.6246
47
1.6365
47
1.6331
47
1.6331
47
1.6020
47
  1.6714
21
1.6463
47
1.6152
46
  1.6571
32
1.6402
24
  1.6478
4
1.5990
14
1.5935
11
1.6275
3
M06-2X 1.7430
21
1.7194
21
1.6349
21
1.7599
21
1.6171
44
1.6431
21
1.6569
21
1.6547
21
1.6534
21
1.6222
21
  1.6608
21
1.6666
21
1.6389
21
  1.6693
21
1.6407
21
  1.6362
4
1.5934
14
1.5876
11
1.6218
3
PBEPBE 1.7743
37
1.7452
47
1.6558
39
1.7901
37
1.6545
47
1.6545
47
1.6727
47
1.6694
47
1.6694
47
1.6328
47
1.6120
12
1.7117
21
1.6777
47
1.6490
47
1.5802
5
1.7053
25
1.6573
34
1.5792
5
1.6852
4
1.6351
14
1.6318
11
1.6625
3
PBEPBEultrafine         1.6604
40
            1.6390
5
1.7158
19
1.6904
19
  1.7263
19
1.7125
14
    1.6253
10
1.6122
7
1.6623
3
PBE1PBE 1.7709
19
1.6500
19
1.6500
19
1.7844
19
1.6256
45
1.6583
19
1.6758
19
1.6720
19
1.6720
19
1.6368
19
  1.6795
19
1.6832
19
1.6533
19
  1.6883
19
1.6560
19
    1.5911
10
1.5775
7
1.6267
3
HSEh1PBE 1.7704
21
1.7301
21
1.6414
21
1.7832
21
1.6290
43
1.6525
21
1.6693
21
1.6654
21
1.6654
21
1.6297
21
  1.6732
21
1.6773
21
1.6465
21
  1.6823
21
1.6490
21
  1.6496
4
1.6006
14
1.5953
11
1.6291
3
TPSSh   1.6848
5
1.5946
5
1.7476
5
1.6347
47
1.6075
5
1.6406
47
1.6135
5
      1.6171
5
1.6249
5
1.6260
47
  1.6277
5
1.5978
5
    1.5849
5
1.5861
5
 
Moller Plesset perturbation MP2 1.7423
40
1.6973
47
1.6201
47
1.7608
45
1.6289
57
1.6307
47
1.6452
61
1.6321
47
1.6321
47
1.6034
46
  1.6589
51
1.6519
47
1.6112
56
1.7038
10
1.6648
43
1.6278
29
1.6744
8
1.6625
4
1.5911
27
1.5975
11
1.6254
3
MP2=FULL 1.7283
34
1.6974
46
1.6201
45
1.7585
40
1.6263
57
1.6279
47
1.6458
47
1.6315
47
1.6406
37
1.6038
37
  1.6719
21
1.6514
46
1.6088
56
1.7009
10
1.6807
29
1.6242
25
1.6813
7
1.6618
4
1.5888
27
1.5940
11
1.6239
3
ROMP2 1.7711
12
1.6818
14
1.6697
14
1.8095
14
1.6734
14
1.6734
14
1.7001
14
1.6847
14
1.6847
14
1.6480
14
  1.7926
7
1.7021
14
1.6609
14
1.5087
2
1.7125
14
1.5189
2
1.5093
2
  1.6258
3
  1.6263
3
MP3         1.6234
47
  1.6229
47
        1.5892
5
1.6089
5
1.5676
5
        1.6478
4
1.5831
14
1.5780
11
1.6103
3
MP3=FULL         1.6204
47
  1.6274
47
        1.5882
5
1.6079
5
1.5658
5
          1.5566
5
1.5576
5
 
MP4 1.7643
4
1.7092
45
    1.6444
40
    1.6397
1
1.6511
37
1.6074
4
  1.6922
19
1.6936
19
1.6339
28
  1.7346
14
1.6892
14
  1.6713
4
1.6067
14
1.6053
11
1.6352
3
MP4=FULL   1.7390
19
    1.6658
19
      1.6789
19
      1.6718
17
1.6536
19
  1.7095
19
1.6609
19
    1.5956
10
1.5829
7
1.6338
3
B2PLYP 1.7206
5
1.6736
5
1.5894
5
1.7462
5
1.6112
28
1.6044
5
1.6134
5
1.6063
5
1.6063
5
1.5765
5
  1.6113
5
1.6208
5
1.5941
31
  1.6256
5
1.5921
5
    1.5784
5
1.5800
5
 
B2PLYP=FULL 1.7205
5
1.6734
5
1.5893
5
1.7460
5
1.6035
5
1.6035
5
1.6125
5
1.6062
5
1.6062
5
1.5749
5
  1.6110
5
1.6205
5
1.5884
5
  1.6247
5
1.5909
5
    1.5778
5
1.5795
5
 
B2PLYP=FULLultrafine         1.6187
7
                                 
Configuration interaction CID 1.7378
4
1.6853
39
1.6084
45
1.7369
45
1.6104
47
    1.6071
46
1.5996
4
1.5748
4
                  1.5613
10
1.5461
7
1.5985
3
CISD 1.7384
4
1.6887
39
1.6171
39
1.7464
39
1.6115
47
    1.6083
45
1.6006
4
1.5754
4
                  1.5620
10
1.5467
7
1.5996
3
Quadratic configuration interaction QCISD 1.7586
4
1.7047
47
1.6251
45
1.7742
45
1.6316
46
1.6315
45
1.6531
40
1.6309
46
1.6281
41
1.6124
31
  1.6681
21
1.6520
46
1.6164
33
  1.6877
21
1.6511
19
  1.6557
4
1.5906
14
1.5856
11
1.6207
3
QCISD(T)         1.6424
40
    1.6395
1
      1.6764
21
1.6719
26
1.6263
23
  1.6800
26
1.6339
26
    1.5915
10
1.5785
7
1.6288
3
Coupled Cluster CCD 1.7561
4
1.6915
45
1.6180
45
1.7545
45
1.6247
47
1.6255
45
1.6448
39
1.6236
46
1.6304
33
1.6014
33
  1.6605
21
1.6449
46
1.6103
32
  1.6632
26
1.6175
26
  1.6478
4
1.5853
15
1.5796
11
1.6126
3
CCSD         1.6350
40
    1.6301
1
      1.6510
17
1.6579
19
1.6124
19
1.7423
7
1.6924
19
1.6736
14
1.7034
5
  1.5811
10
1.5676
7
1.6169
3
CCSD=FULL         1.6592
19
            1.6734
19
1.6848
19
1.6398
19
1.8306
4
1.7100
14
1.6613
14
1.8231
2
  1.5788
10
1.5648
7
 
CCSD(T)         1.6406
41
1.6370
1
  1.6377
1
    1.6123
1
1.6912
16
1.6700
33
1.6247
33
1.7198
8
1.6778
33
1.6297
29
1.7302
3
  1.5914
11
1.5772
7
1.6268
3
CCSD(T)=FULL         1.6546
24
            1.6901
16
1.7009
17
1.6368
22
1.7168
8
1.6889
22
1.6726
15
1.7263
3
1.6639
4
1.5963
15
1.5884
7
1.6251
3

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 1.8259
49
1.6025
47
1.8256
44
1.6029
47
1.7969
45
1.7936
45
density functional B1B95 1.7658
14
1.6170
14
       
B3LYP 1.7980
45
1.6572
47
1.7940
45
1.6586
47
1.7860
46
1.7817
46
Moller Plesset perturbation MP2 1.8170
44
1.6536
47
1.8091
47
1.6536
47
1.7895
47
1.7894
47
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.