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III.G.1.a.

Comparison of levels of theory for H-Si


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 1.4501
21
PM3 1.4933
49
PM6 1.4986
56
composite G2 1.4850
47
G3 1.4860
49
G3B3 1.5032
54
G4 1.4995
51
CBS-Q 1.4870
47

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(T+d)Z aug-cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ
hartree fock HF 1.4407
46
1.4995
49
1.4844
49
1.5066
49
1.4827
110
1.4867
49
1.4852
49
1.4854
49
1.4875
49
1.4862
49
1.4789
30
1.4932
56
1.4977
49
1.4895
49
1.4866
46
1.4966
49
1.4884
49
1.4872
44
1.4754
36
1.4905
4
1.4939
5
1.4839
5
ROHF 1.4610
10
1.5152
19
1.4955
19
1.5274
15
1.4979
19
1.4984
19
1.4961
19
1.4975
19
1.5025
15
1.4991
10
  1.5087
5
1.5108
19
1.5017
19
1.4999
15
1.5108
15
1.5020
15
1.4985
15
1.4904
4
1.4905
4
   
density functional LSDA 1.4708
49
1.5230
49
1.5112
49
1.5331
49
1.5132
49
1.5123
49
1.5115
49
1.5105
49
1.5103
49
1.5086
49
  1.5335
5
1.5228
49
1.5089
49
1.5257
12
1.5193
49
1.5255
19
1.5244
12
1.5143
4
1.5142
4
   
SVWN   1.5172
56
    1.4963
51
1.5334
5
1.5016
56
1.5321
5
1.5314
5
1.5278
5
    1.5440
5
1.5288
5
  1.5393
5
1.5273
5
  1.5143
4
1.5142
4
   
BLYP 1.4807
46
1.5254
49
1.5083
47
1.5310
47
1.5128
49
1.5109
49
1.5085
47
1.5076
47
1.5086
49
1.5071
49
  1.5344
5
1.5217
49
1.5059
47
  1.5090
30
    1.5137
4
1.5136
4
   
B1B95 1.4631
49
1.5052
49
1.4975
49
1.5175
49
1.4984
49
1.4985
49
1.4974
49
1.4970
49
1.4972
49
1.4956
49
  1.5196
5
1.5084
49
1.4962
49
1.5127
12
1.5070
46
1.5106
19
1.5113
12
1.5006
4
1.5005
4
   
B3LYP 1.4667
49
1.5144
49
1.4989
49
1.5197
47
1.5017
49
1.5003
49
1.4993
49
1.4971
47
1.5134
21
1.4972
49
1.4865
30
1.5051
56
1.5097
47
1.4979
49
1.4959
44
1.5062
47
1.4968
49
1.4953
44
1.4824
36
1.5029
4
1.5038
5
1.4905
5
B3LYPultrafine         1.5017
49
  1.5018
4
        1.5107
4
1.5329
5
1.4891
23
  1.5283
5
1.4938
45
  1.5221
2
1.5221
2
   
B3PW91 1.4857
21
1.5162
49
1.5001
47
1.5201
47
1.5024
49
1.5017
49
1.4993
47
1.4999
47
1.5151
21
1.4994
49
  1.5240
5
1.5107
47
1.4995
47
  1.5021
30
    1.5048
4
1.5048
4
   
mPW1PW91 1.4776
24
1.5137
49
1.5084
23
1.5194
49
1.5000
49
1.4994
49
1.4982
49
1.4989
49
1.4991
49
1.4973
49
  1.5215
5
1.5097
49
1.4989
49
  1.5019
33
1.5162
5
  1.5029
4
1.5028
4
   
M06-2X 1.4750
5
1.5312
5
1.5080
5
1.5409
5
1.4815
56
1.5117
5
1.5103
5
1.5104
5
1.5104
5
1.5070
5
  1.5130
5
1.5220
5
1.5078
5
  1.5182
5
1.5061
5
  1.4940
4
1.4940
4
   
PBEPBE 1.4991
21
1.5287
49
1.5270
21
1.5547
21
1.5151
49
1.5139
49
1.5129
49
1.5132
49
1.5127
49
1.5111
49
1.5008
30
1.5367
5
1.5252
48
1.5123
49
1.5290
12
1.5333
7
1.5054
35
1.5274
12
1.5228
5
1.5173
4
   
PBEPBEultrafine         1.5064
55
            1.5244
4
1.5460
5
1.5326
5
  1.5418
5
1.5308
5
  1.5379
2
1.5378
2
   
PBE1PBE 1.4850
5
1.5198
5
1.5198
5
1.5498
5
1.5018
52
1.5222
5
1.5200
5
1.5215
5
1.5210
5
1.5178
5
  1.5240
5
1.5321
5
1.5203
5
  1.5289
5
1.5188
5
  1.5056
4
1.5055
4
   
HSEh1PBE 1.4857
5
1.5433
5
1.5201
5
1.5507
5
1.4893
56
1.5218
5
1.5205
5
1.5217
5
1.5213
5
1.5180
5
  1.5242
5
1.5327
5
1.5203
5
  1.5293
5
1.5188
5
  1.5053
4
1.5052
4
   
TPSSh   1.5246
4
1.5042
4
1.5301
4
1.4973
51
1.5053
4
1.4958
51
1.5060
4
      1.5090
4
1.5164
4
1.4974
51
  1.5154
4
1.5057
4
  1.5020
4
1.5020
4
   
Moller Plesset perturbation MP2 1.4717
21
1.5126
49
1.4916
49
1.5215
49
1.4925
63
1.4854
49
1.4796
89
1.4921
48
1.4861
49
1.4893
40
  1.4936
56
1.4999
49
1.4866
61
1.5036
14
1.5000
46
1.4920
44
1.4957
11
1.4761
36
1.4928
4
1.4949
5
1.4832
5
MP2=FULL 1.4718
21
1.5127
49
1.4995
23
1.5342
23
1.4922
63
1.4844
49
1.4829
49
1.4915
49
1.4975
21
1.4946
21
  1.5072
5
1.4993
49
1.4876
35
1.4907
14
1.5055
13
1.4990
15
1.4787
10
1.4713
36
1.4872
4
1.4946
5
1.4798
5
ROMP2 1.4700
15
1.5167
15
1.4995
15
1.5338
15
1.5040
15
1.4938
15
1.4916
15
1.5012
15
1.4953
15
1.4941
15
  1.5029
3
1.5102
15
1.4993
15
1.4993
10
1.5094
15
1.5024
10
1.4989
10
1.4734
2
1.4740
2
   
MP3         1.4996
49
  1.4877
51
        1.4977
4
1.5081
4
1.4986
4
        1.4956
4
1.4960
4
   
MP3=FULL         1.5003
51
  1.4884
51
        1.4968
4
1.5076
4
1.4956
4
        1.4917
4
1.4906
4
   
MP4   1.5310
33
    1.5017
47
    1.4911
25
1.5041
19
    1.5130
5
1.5240
5
1.5049
17
  1.5255
5
1.5132
5
  1.4986
4
1.4991
4
   
MP4=FULL   1.5476
5
    1.5214
5
      1.5075
5
      1.5232
5
1.5106
5
  1.5218
5
1.5081
5
  1.4949
4
1.4939
4
   
B2PLYP         1.4806
51
                1.4918
46
               
B2PLYP=FULLultrafine         1.4851
20
                                 
Configuration interaction CID   1.5367
21
1.5046
23
1.5424
23
1.4981
47
    1.4955
46
          1.4913
10
        1.4956
4
1.4959
4
   
CISD   1.5332
31
1.5055
23
1.5437
23
1.4987
47
    1.5079
23
          1.4919
10
        1.4965
4
1.4968
4
   
Quadratic configuration interaction QCISD 1.4491
2
1.5239
49
1.5160
31
1.5476
23
1.5038
49
1.4957
33
1.4887
41
1.4995
47
1.4903
47
1.5049
19
  1.5142
5
1.5039
46
1.5061
29
  1.5258
5
1.5133
5
  1.5037
5
1.4990
4
   
QCISD(T)   1.5087
2
    1.5070
44
1.4918
14
1.4909
14
1.4954
29
      1.5155
5
1.5193
27
1.5089
27
  1.5277
17
1.5151
17
  1.5005
4
1.5010
4
   
Coupled Cluster CCD 1.4489
2
1.5319
33
1.5073
23
1.5459
23
1.5018
47
1.4945
33
1.4933
29
1.4992
46
1.5053
19
1.5032
19
  1.5125
5
1.5028
46
1.5040
27
  1.5246
17
1.4990
12
  1.4974
4
1.4978
4
1.4977
5
1.4872
5
CCSD   1.5079
2
    1.5039
47
1.4908
14
1.4898
14
1.4939
29
      1.5140
5
1.5107
15
1.5009
15
1.5086
5
1.5257
5
1.5131
5
1.5085
5
1.4985
4
1.4988
4
   
CCSD=FULL         1.5228
5
            1.5131
5
1.5240
5
1.5107
5
1.4960
5
1.5220
5
1.5077
5
1.4930
5
1.4946
4
1.4934
4
   
CCSD(T)   1.5310
3
    1.5027
40
1.4829
28
1.4908
14
1.4953
29
1.5240
1
  1.5262
1
1.5154
5
1.5168
29
1.5030
35
1.4934
8
1.5232
19
1.5063
17
1.5107
5
1.4911
17
1.5009
4
1.4996
5
1.4889
5
CCSD(T)=FULL         1.5253
15
            1.5146
5
1.5128
10
1.5003
10
1.4813
8
1.5238
5
1.5100
5
1.4949
5
1.4967
4
1.4958
4
1.4994
5
1.4858
5

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 1.5152
49
1.4995
49
1.5107
49
1.5005
49
1.4865
49
1.4963
49
density functional B1B95 1.5202
29
1.5037
30
1.5152
2
1.5062
2
1.4924
2
1.4974
2
B3LYP 1.5267
47
1.5110
47
1.5269
47
1.5130
47
1.4996
47
1.5086
47
Moller Plesset perturbation MP2 1.5315
49
1.5097
49
1.5261
49
1.5090
49
1.5007
49
1.5085
49
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.