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III.G.1.a.

Comparison of levels of theory for C-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 1.5855
19
PM3 1.7838
124
PM6 1.7432
132
composite G2 1.7725
106
G3 1.7705
126
G3B3 1.7873
134
G4 1.7794
132
CBS-Q 1.7573
69

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-pCVDZ cc-pCVTZ Sadlej_pVTZ
hartree fock HF 1.7574
125
1.8358
134
1.7644
126
1.8281
125
1.7863
355
1.7648
124
1.7674
132
1.7660
126
1.7660
126
1.7613
126
1.7746
115
1.7730
135
1.7715
126
1.7624
125
1.6522
23
1.7728
126
1.7626
126
1.6218
14
1.5938
1
1.7102
25
1.7561
2
1.5584
3
1.5561
3
1.8117
2
ROHF 1.5971
5
1.6411
8
1.6108
9
1.6448
8
1.6053
11
1.6159
9
1.6151
9
1.6132
9
1.5935
7
1.5717
5
  1.6430
2
1.6216
9
1.6112
9
1.5738
6
1.6024
7
1.5912
7
1.5732
6
           
density functional LSDA 1.7891
131
1.8310
132
1.7683
131
1.8309
132
1.7676
132
1.7675
132
1.7670
132
1.7673
130
1.7677
130
1.7575
132
  1.6839
5
1.7708
131
1.7582
132
1.5937
4
1.7701
130
1.6488
11
1.5874
4
1.6067
1
1.7428
2
1.8918
1
     
SVWN   1.7878
122
    1.7981
117
1.6861
5
1.7460
122
1.6810
5
1.6815
5
1.6760
5
    1.6921
5
1.6768
5
  1.6881
5
1.6733
5
    1.7428
2
1.8918
1
     
BLYP 1.8248
125
1.8798
125
1.7908
71
1.8774
125
1.8066
124
1.8076
126
1.8071
124
1.7868
71
1.8073
126
1.7982
126
  1.7119
5
1.8121
122
1.7990
123
  1.8312
106
    1.6275
1
1.7710
2
1.9330
1
     
B1B95 1.7833
123
1.8275
123
1.7682
123
1.8294
123
1.7650
123
1.7667
123
1.7671
125
1.7661
118
1.7657
123
1.7604
120
  1.6849
5
1.7701
123
1.7584
123
1.5808
6
1.7795
115
1.6716
14
1.5932
4
1.6024
1
1.6383
5
1.7527
2
1.5670
3
1.5652
3
 
B3LYP 1.7979
126
1.8559
134
1.7864
125
1.8502
126
1.7870
135
1.7851
126
1.7864
131
1.7838
126
1.6849
20
1.7777
125
1.7897
106
1.7830
135
1.7889
126
1.7779
123
1.6291
14
1.7496
50
1.7328
48
1.6268
14
1.6129
1
1.7193
25
1.7635
2
1.5740
3
1.5718
3
1.8234
2
B3LYPultrafine         1.7844
124
  1.8151
31
        1.9314
1
1.7030
5
1.8021
55
  1.7003
5
1.7763
135
    1.5986
1
       
B3PW91 1.7070
20
1.8422
125
1.7749
126
1.8372
126
1.7939
125
1.7929
126
1.7553
71
1.7720
125
1.6776
20
1.7657
125
  1.6918
5
1.7777
126
1.7661
123
  1.7961
106
    1.6084
1
1.7559
2
1.9156
1
     
mPW1PW91 1.6931
21
1.8344
125
1.7010
27
1.8314
126
1.7693
126
1.7699
124
1.7686
126
1.7677
126
1.7682
126
1.7618
126
  1.6887
5
1.7716
123
1.7236
49
  1.7880
112
1.7201
6
  1.6053
1
1.7532
2
1.9126
1
     
M06-2X 1.6751
5
1.7191
5
1.6806
5
1.7251
5
1.7519
122
1.6866
5
1.6854
5
1.6831
5
1.6835
5
1.6781
5
  1.6854
5
1.6919
5
1.6792
5
  1.6900
5
1.6775
5
  1.6027
1
1.7509
2
1.9110
1
     
PBEPBE 1.7174
21
1.8573
126
1.6879
20
1.7510
20
1.7869
125
1.7873
126
1.7870
126
1.7860
126
1.7865
126
1.7792
124
1.7912
106
1.7034
5
1.7891
120
1.7801
126
1.5967
6
1.7714
8
1.7738
37
1.5922
6
1.6201
1
1.6262
7
1.9230
1
1.5650
2
1.5631
2
1.8215
2
PBEPBEultrafine         1.8065
166
            1.9332
1
1.7100
5
1.6962
5
  1.7063
5
1.6930
5
    1.6073
1
       
PBE1PBE 1.6810
5
1.6833
5
1.6833
5
1.7295
5
1.7938
125
1.6894
5
1.6876
5
1.6857
5
1.6861
5
1.6813
5
  1.6890
5
1.6949
5
1.6820
5
  1.6923
5
1.6799
5
    1.9120
1
1.9127
1
     
HSEh1PBE 1.6818
5
1.7236
5
1.6835
5
1.7301
5
1.7497
121
1.6901
5
1.6881
5
1.6862
5
1.6866
5
1.6818
5
  1.6894
5
1.6956
5
1.6824
5
  1.6929
5
1.6802
5
  1.6059
1
1.7539
2
1.9130
1
     
TPSSh   1.9356
1
1.9132
1
1.9483
1
1.7930
134
1.9265
1
1.7926
134
1.9218
1
      1.9267
1
1.9328
1
1.7869
134
  1.9313
1
1.9193
1
    1.9149
1
1.9155
1
     
Moller Plesset perturbation MP2 1.7110
20
1.8602
134
1.7785
126
1.8541
125
1.7654
160
1.7646
126
1.7832
322
1.7618
120
1.7628
126
1.7552
70
  1.7735
135
1.7766
126
1.7543
108
1.6143
5
1.7451
51
1.6396
21
1.6116
5
1.6175
1
1.7159
23
1.7622
2
1.5821
3
1.5751
3
1.8198
2
MP2=FULL 1.7107
20
1.8194
52
1.7082
27
1.7824
27
1.7622
150
1.7459
72
1.7458
72
1.7618
125
1.6700
20
1.6597
20
  1.6888
5
1.7416
52
1.7121
54
1.6110
5
1.6455
11
1.6151
13
1.6263
4
1.6158
1
1.7051
25
1.7517
2
1.5797
3
1.5717
3
 
ROMP2 1.6539
5
1.6476
5
1.6189
5
1.6948
5
1.6142
5
1.6142
5
1.6114
5
1.6104
5
1.6103
5
1.6066
5
  1.6421
2
1.6278
5
1.6093
5
1.5614
2
1.6272
5
1.5676
2
1.5616
2
  1.9130
1
1.9139
1
     
MP3         1.7681
126
  1.7821
135
        1.9206
1
1.9362
1
1.9162
1
        1.6131
1
1.9130
1
1.9138
1
     
MP3=FULL         1.7829
134
  1.7819
133
        1.9191
1
1.9322
1
1.9066
1
          1.9020
1
1.8998
1
     
MP4   1.7568
21
1.5812
1
1.6758
1
1.7053
36
1.5723
1
1.5692
1
1.6728
3
1.6578
15
    1.7018
5
1.6914
6
1.6332
16
  1.7136
5
1.6383
3
  1.6271
1
1.6144
1
       
MP4=FULL   1.7534
5
    1.6982
5
      1.6954
5
      1.7106
5
1.7183
3
  1.7104
5
1.6997
4
             
B2PLYP 1.9238
1
1.9381
1
1.9115
1
1.9518
1
1.7613
118
1.9258
1
1.9275
1
1.9218
1
1.9226
1
1.9157
1
  1.9255
1
1.9340
1
1.7918
131
  1.9340
1
1.9205
1
    1.9156
1
1.9168
1
     
B2PLYP=FULL 1.9236
1
1.9379
1
1.9107
1
1.9515
1
1.9244
1
1.9245
1
1.9262
1
1.9210
1
1.9218
1
1.9124
1
  1.9250
1
1.9326
1
1.9162
1
  1.9319
1
1.9166
1
    1.9121
1
1.9124
1
     
B2PLYP=FULLultrafine         1.8078
96
                                     
Configuration interaction CID   1.7685
27
1.7014
27
1.7714
27
1.7453
72
1.7597
5
1.5277
1
1.6828
26
        1.7266
3
1.5263
1
          1.7486
2
1.9103
1
     
CISD   1.7812
29
1.6935
25
1.7739
24
1.7467
72
1.7535
5
1.5331
1
1.6652
21
        1.7288
3
1.5302
1
          1.7491
2
1.9102
1
     
Quadratic configuration interaction QCISD 1.8291
5
1.8461
84
1.7159
27
1.7851
25
1.7399
52
1.7168
29
1.7131
39
1.7384
52
1.7353
50
1.6781
19
  1.6967
5
1.7208
36
1.6299
20
  1.7072
5
1.6878
5
  1.6209
1
1.6213
7
1.9155
1
     
QCISD(T)   1.6206
1
1.5647
1
1.6250
1
1.6873
30
1.5689
2
1.5667
2
1.6682
3
1.7381
3
    1.7011
5
1.6389
15
1.6208
15
  1.6477
13
1.6269
12
    1.7619
2
1.9160
1
     
Coupled Cluster CCD 1.7980
5
1.7680
25
1.6993
25
1.7718
25
1.7894
74
1.6926
25
1.6870
26
1.6970
28
1.6729
19
1.6689
19
  1.6882
5
1.7132
36
1.6283
17
  1.6331
13
1.6133
14
  1.6132
1
1.6432
5
1.7602
2
1.5755
3
1.5678
3
 
CCSD   1.6020
1
1.5506
1
1.6072
1
1.6919
28
1.5570
2
1.5552
2
1.6589
3
1.7315
3
    1.6936
5
1.6656
7
1.6479
7
1.6223
3
1.7044
5
1.6998
4
1.6319
2
  1.7576
2
1.9156
1
     
CCSD=FULL         1.6910
5
            1.6928
5
1.7021
5
1.6809
5
1.6191
3
1.7014
5
1.6195
3
1.6169
3
  1.9037
1
1.9013
1
     
CCSD(T)   1.6223
4
1.5620
1
1.6212
1
1.7137
23
1.7002
12
1.5667
5
1.6267
5
1.6378
7
  1.5437
1
1.6999
5
1.6351
18
1.6153
19
1.6423
2
1.6430
16
1.6224
15
1.6390
2
1.6273
1
1.6289
6
1.7675
2
1.5876
3
1.5799
3
 
CCSD(T)=FULL         1.6348
11
            1.6992
5
1.6667
8
1.6468
8
1.6268
3
1.6721
7
1.6002
5
1.6246
3
1.6255
1
1.6574
4
1.5750
3
1.5855
3
1.5770
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 1.8336
126
1.7778
126
1.8324
125
1.7763
126
1.8259
123
1.8209
126
density functional B1B95 1.8615
118
1.8008
117
1.8837
4
1.8222
4
1.8761
4
1.8664
4
B3LYP 1.8627
125
1.8000
125
1.8607
125
1.7971
117
1.8519
123
1.8402
123
Moller Plesset perturbation MP2 1.8676
125
1.7842
123
1.8644
125
1.7802
125
1.8566
125
1.8542
125
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.