National Institute of Standards and Technology
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-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 1.4537
33
PM3 1.4926
33
PM6 1.4957
54
composite G2 1.4821
49
G3 1.4821
49
G3B3 1.4997
54
G3MP2 1.4779
8
G4 1.4983
54
CBS-Q 1.4821
49

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 aug-cc-pCVTZ
hartree fock HF 1.4357
46
1.4951
49
1.4811
49
1.5019
49
1.4846
53
1.4833
49
1.4817
45
1.4819
49
1.4841
49
1.4830
49
1.4767
28
1.4907
54
1.4941
49
1.4861
49
1.4842
43
1.4933
49
1.4852
49
1.4837
43
1.4748
39
1.4783
14
1.4939
5
1.4771
10
1.4765
3
ROHF 1.4610
10
1.5152
19
1.4955
19
1.5232
19
1.4979
19
1.4984
19
1.4960
19
1.4975
19
1.4994
19
1.4991
10
  1.5012
9
1.5108
19
1.5017
19
1.4969
19
1.5080
19
1.4992
19
1.4958
19
1.4843
7
1.4843
7
  1.4768
3
1.4767
3
density functional LSDA 1.4666
49
1.5174
49
1.5077
49
1.5277
49
1.5093
49
1.5084
49
1.5076
49
1.5064
49
1.5065
49
1.5051
49
  1.5106
19
1.5189
49
1.5053
49
1.5257
12
1.5156
49
1.5116
31
1.5244
12
1.4966
14
1.4966
14
  1.4915
7
1.4929
3
SVWN   1.5128
54
    1.4921
49
1.5100
19
1.4982
54
1.5080
19
1.5081
19
1.5067
19
  1.5137
51
1.5203
19
1.5066
19
  1.5175
19
1.5062
19
  1.4966
14
1.4966
14
  1.4915
7
1.4929
3
BLYP 1.4747
46
1.5202
49
1.5056
49
1.5272
49
1.5095
54
1.5067
49
1.5058
49
1.5046
49
1.5045
49
1.5031
49
  1.5086
19
1.5174
49
1.5032
49
  1.5077
26
1.4979
11
  1.4943
14
1.4942
14
  1.4896
7
1.4916
3
B1B95 1.4587
49
1.4997
49
1.4937
49
1.5121
49
1.4946
49
1.4946
49
1.4935
49
1.4930
49
1.4932
49
1.4918
49
  1.4967
19
1.5043
49
1.4925
49
1.5127
12
1.5031
46
1.4928
41
1.5113
12
1.4822
16
1.4841
14
  1.4802
7
1.4814
3
B3LYP 1.4612
49
1.5094
49
1.4953
49
1.5162
49
1.4949
47
1.4964
49
1.4954
49
1.4944
49
1.5006
33
1.4974
54
1.4841
25
1.5021
54
1.5069
49
1.4941
49
1.4919
43
1.5038
49
1.4935
50
1.4914
43
1.4818
39
1.4856
14
1.5038
5
1.4843
10
1.4831
3
B3LYPultrafine   1.5044
11
    1.4977
49
1.4919
11
1.4972
13
1.4894
11
      1.4950
18
1.5082
19
1.4895
32
  1.5055
19
1.4933
49
  1.4897
9
1.4897
9
  1.4816
7
1.4831
3
B3PW91 1.4681
33
1.5113
49
1.4976
49
1.5166
49
1.4986
49
1.4979
49
1.4969
49
1.4972
49
1.5028
33
1.4958
49
  1.5016
19
1.5081
49
1.4970
49
  1.5006
29
1.4891
17
  1.4887
14
1.4887
14
  1.4826
9
1.4858
3
mPW1PW91 1.4633
36
1.5088
49
1.5000
33
1.5142
49
1.4963
49
1.4956
49
1.4946
49
1.4952
49
1.4954
49
1.4938
49
  1.4997
19
1.5059
49
1.4954
49
  1.4997
35
1.4959
19
  1.4872
14
1.4872
14
  1.4834
7
1.4843
3
M06-2X 1.4521
19
1.5011
19
1.4938
54
1.5106
19
1.4783
54
1.4910
19
1.4902
19
1.4879
19
1.4888
19
1.4841
28
  1.4917
19
1.5001
19
1.4832
28
  1.4983
19
1.4829
28
  1.4775
16
1.4793
14
  1.4735
9
1.4762
3
PBEPBE 1.4808
33
1.5235
49
1.5147
33
1.5373
33
1.5112
49
1.5100
49
1.5091
49
1.5092
49
1.5087
49
1.5074
49
1.4983
25
1.5129
19
1.5210
48
1.5084
49
1.5290
12
1.5184
21
1.5031
37
1.5274
12
1.5005
17
1.4995
14
  1.4931
9
1.4962
3
PBEPBEultrafine   1.5182
11
    1.5064
37
1.5053
11
1.5048
11
1.5039
11
      1.5088
18
1.5216
19
1.5094
19
  1.5190
19
1.5088
19
  1.5035
9
1.5035
9
  1.4949
7
1.4962
3
PBE1PBE 1.4612
19
1.4985
19
1.4985
19
1.5193
19
1.4986
50
1.4998
19
1.4985
19
1.4986
19
1.4989
19
1.4973
19
  1.5021
19
1.5095
19
1.4989
19
  1.5078
19
1.4985
19
  1.4898
14
1.4898
14
  1.4859
7
1.4867
3
HSEh1PBE 1.4617
19
1.4986
54
1.4984
19
1.5198
19
1.4859
54
1.4994
19
1.4864
54
1.4985
19
1.4988
19
1.4972
19
  1.5020
19
1.5097
19
1.4816
50
  1.5079
19
1.4981
19
  1.4893
14
1.4893
14
  1.4853
7
1.4862
3
TPSSh 1.4658
3
1.5040
18
1.4895
18
1.5090
18
1.4961
54
1.4901
18
1.4946
54
1.4909
18
1.4861
3
1.4947
54
  1.4942
18
1.5007
18
1.4963
54
1.4838
3
1.4999
18
1.4910
18
1.4837
3
1.4857
14
1.4857
14
  1.4820
7
1.4838
3
wB97X-D 1.4493
7
1.4947
7
1.4967
54
1.5001
7
1.4970
54
1.4849
7
1.4959
54
1.4823
7
1.4962
54
1.4833
7
  1.4991
54
1.4973
54
1.4959
54
1.4808
7
1.4939
7
1.4955
54
1.4808
7
1.4789
4
1.4389
4
  1.4799
4
 
B97D3   1.5181
54
    1.5072
54
      1.5054
54
              1.5028
54
           
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 aug-cc-pCVTZ
Moller Plesset perturbation MP2 1.4556
33
1.5081
49
1.4885
49
1.5168
49
1.4959
54
1.4821
49
1.4808
49
1.4920
54
1.4828
49
1.4839
46
  1.4912
54
1.4964
49
1.4866
49
1.4890
22
1.4978
48
1.4872
47
1.4825
19
1.4757
39
1.4796
14
1.4949
5
1.4772
10
1.4758
3
MP2=FULL 1.4552
33
1.5082
49
1.4922
33
1.5235
33
1.4921
49
1.4812
49
1.4798
49
1.4881
49
1.4866
33
1.4821
40
  1.4869
19
1.4959
49
1.4837
43
1.4767
22
1.4937
21
1.4903
42
1.4683
19
1.4710
39
1.4747
14
1.4946
5
1.4736
10
1.4717
3
ROMP2 1.4663
19
1.5111
19
1.4975
19
1.5312
19
1.5019
19
1.4918
19
1.4899
19
1.4988
19
1.4932
19
1.4923
19
  1.4951
7
1.5077
19
1.4971
19
1.4993
10
1.5075
19
1.5024
10
1.4989
10
1.4734
8
1.4741
8
  1.4756
3
1.4761
3
MP3         1.4961
49
  1.4865
54
        1.4848
18
1.4948
18
1.4857
18
        1.4811
14
1.4816
14
  1.4771
7
1.4781
3
MP3=FULL   1.5038
7
1.4835
7
1.5131
7
1.4992
54
1.4735
7
1.4872
54
1.4827
7
1.4734
7
1.4745
7
  1.4837
18
1.4943
18
1.4824
18
  1.4876
7
1.4775
7
  1.4767
14
1.4771
14
  1.4737
7
1.4747
3
MP4   1.5240
33
    1.4993
49
    1.4911
25
1.4910
31
    1.4911
19
1.5012
19
1.4924
19
  1.5033
19
1.4952
16
  1.4861
11
1.4866
11
  1.4792
7
1.4803
3
MP4=FULL   1.5197
19
    1.5000
19
      1.4857
19
      1.5006
19
1.4890
19
  1.4998
19
1.4886
19
  1.4820
11
1.4823
11
  1.4761
7
1.4768
3
B2PLYP 1.4482
14
1.4982
14
1.4835
14
1.5055
14
1.4805
52
1.4824
14
1.4817
14
1.4824
14
1.4816
14
1.4795
23
  1.4851
14
1.4937
14
1.4908
49
  1.4932
14
1.4805
23
  1.4737
12
1.4754
10
  1.4751
9
1.4787
3
B2PLYP=FULL 1.4483
14
1.4987
14
1.4834
14
1.5055
14
1.4858
14
1.4821
14
1.4814
14
1.4825
14
1.4814
14
1.4809
14
  1.4848
14
1.4936
14
1.4817
14
  1.4922
14
1.4817
14
  1.4740
10
1.4742
10
  1.4765
7
1.4776
3
B2PLYP=FULLultrafine 1.4476
7
1.4958
7
1.4814
7
1.5033
7
1.4857
25
1.4802
7
1.4795
7
1.4799
7
1.4791
7
1.4790
7
  1.4826
7
1.4915
7
1.4796
7
  1.4903
7
1.4799
7
        1.4757
4
 
Configuration interaction CID   1.5213
33
1.4964
33
1.5307
33
1.4952
49
    1.4924
48
          1.4913
10
        1.4795
14
1.4798
14
  1.4767
7
1.4779
3
CISD   1.5223
33
1.4972
33
1.5317
33
1.4957
49
    1.4985
33
          1.4919
10
        1.4799
14
1.4802
14
  1.4771
7
1.4783
3
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 aug-cc-pCVTZ
Quadratic configuration interaction QCISD 1.4491
2
1.5190
49
1.5087
33
1.5360
33
1.5006
49
1.4905
33
1.4850
45
1.4968
49
1.4866
47
1.4888
38
  1.4916
19
1.5012
48
1.4941
38
  1.5033
19
1.4879
28
  1.4841
17
1.4841
14
  1.4768
9
1.4806
3
QCISD(T)   1.5087
2
    1.5020
46
1.4878
12
1.4869
12
1.4924
30
      1.4928
19
1.5101
29
1.5003
29
  1.5113
29
1.4998
29
  1.4851
14
1.4855
14
  1.4804
7
1.4817
3
QCISD(T)=FULL         1.4963
11
  1.4802
11
          1.4959
11
1.4843
11
1.4763
9
1.4954
11
1.4846
11
1.4746
9
1.4759
7
1.4770
7
  1.4774
7
1.4785
3
QCISD(TQ)         1.5001
9
  1.4846
9
          1.5006
9
1.4915
9
1.4883
9
1.5032
9
1.4920
9
1.4953
5
         
QCISD(TQ)=FULL         1.4998
9
  1.4837
9
          1.4999
9
1.4881
9
1.4722
8
1.4996
9
1.4885
9
1.4937
1
1.4775
3
       
Coupled Cluster CCD 1.4489
2
1.5249
33
1.4995
33
1.5347
33
1.4999
49
1.4894
33
1.4877
33
1.4965
48
1.4914
31
1.4912
31
  1.4905
19
1.5001
48
1.4973
31
  1.5086
29
1.4877
24
  1.4830
14
1.4834
14
1.4977
5
1.4843
8
1.4799
3
CCSD   1.5079
2
    1.5004
49
1.4868
12
1.4858
12
1.4914
27
  1.4790
20
  1.4914
19
1.5015
19
1.4877
28
1.4946
14
1.5033
19
1.4878
28
1.4947
14
1.4815
16
1.4840
14
  1.4767
9
1.4805
3
CCSD=FULL         1.4968
28
        1.4764
20
  1.4903
19
1.5008
19
1.4839
28
1.4827
14
1.4998
19
1.4849
25
1.4805
14
1.4770
16
1.4794
14
  1.4732
9
1.4768
3
CCSD(T)   1.5087
2
    1.5005
42
1.4817
30
1.4869
12
1.4923
30
    1.5262
1
1.4928
19
1.5083
31
1.4966
37
1.4906
17
1.5096
31
1.4946
29
1.4964
14
1.4828
18
1.4855
14
1.4996
5
1.4860
8
1.4816
3
CCSD(T)=FULL         1.5091
22
            1.4917
19
1.5022
19
1.4902
19
1.4786
17
1.5013
19
1.4925
16
1.4819
14
1.4808
14
1.4838
11
1.4994
5
1.4831
8
1.4785
3
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 aug-cc-pCVTZ

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 1.5103
49
1.4959
49
1.5061
49
1.4969
49
1.4823
49
1.4918
49
density functional B1B95 1.5160
27
1.5037
30
1.5152
2
1.5062
2
1.4924
2
1.4974
2
B3LYP 1.5232
49
1.5083
49
1.5233
49
1.5103
49
1.4965
49
1.5053
49
wB97X-D 1.5134
7
1.5017
7
1.5110
7
1.5029
7
1.4867
7
1.4898
7
Moller Plesset perturbation MP2 1.5264
49
1.5062
49
1.5213
49
1.5055
49
1.4965
49
1.5041
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.