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Comparison of levels of theory for Li-H


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 1.8424
5
PM3 1.8827
5
PM6 2.0406
6
composite G2 1.9223
5
G3 1.9223
5
G3B3 1.9078
5
G3MP2 1.9918
2
G4 1.8802
6
CBS-Q 1.9218
5

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 Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pCVDZ cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
hartree fock HF 1.7698
5
1.9478
5
1.9478
5
1.9696
5
1.8963
6
1.9159
5
1.9132
5
1.8686
5
1.8651
5
1.9026
5
1.6076
1
1.6077
1
1.8584
6
1.8717
6
1.8963
5
1.8674
5
1.8644
5
1.8933
5
1.8672
5
1.8648
5
1.9487
2
1.9095
2
1.6170
1
1.6074
1
ROHF   2.3585
1
2.3585
1
2.4637
1
2.0572
2
2.3281
1
2.3420
1
2.2286
1
2.2072
1
      2.2650
1
  2.2804
1
2.2156
1
2.2134
1
2.3103
1
2.2181
1
2.2150
1
       
density functional LSDA 1.7864
5
1.9232
5
1.9232
5
1.9421
5
1.9016
5
1.8969
5
1.8960
5
1.8499
5
1.8501
5
1.8788
5
1.5991
1
1.5972
1
1.8724
5
  1.8840
5
1.8498
5
1.5975
1
1.8766
5
1.8481
5
1.5973
1
    1.6027
1
1.5988
1
BLYP 1.8011
5
1.9260
5
1.9260
5
1.9445
5
1.8831
6
1.9029
5
1.9039
5
1.8641
5
1.8630
5
1.8865
5
1.5971
1
1.5959
1
1.8837
5
  1.8913
5
1.8631
5
1.5971
1
1.9492
2
1.9080
2
1.5956
1
    1.6069
1
1.5965
1
B1B95 1.7924
5
1.9394
5
1.9394
5
1.9597
5
1.9177
5
1.9129
5
1.9817
2
1.8646
5
1.8634
5
1.9847
2
1.5966
1
1.5961
1
1.8851
5
  1.9596
2
1.9232
2
1.9180
2
1.9671
2
1.9293
2
1.9196
2
    1.6069
1
1.5961
1
B3LYP 1.7882
5
1.9203
5
1.9203
5
1.9381
5
1.9011
5
1.8950
5
1.8945
5
1.8528
5
1.8516
5
1.8793
5
1.5905
1
1.5897
1
1.8449
6
1.8643
6
1.8817
5
1.8521
5
1.8463
5
1.8749
5
1.8509
5
1.8469
5
1.9295
2
1.8907
2
1.6003
1
1.5902
1
B3LYPultrafine 1.5260
1
1.9626
2
1.6297
1
1.6254
1
1.9010
5
1.9535
2
1.9506
2
1.8992
2
1.5923
1
1.6145
1
1.5906
1
1.5898
1
1.9183
2
  1.8815
5
1.8521
5
1.5894
1
1.8748
5
1.8469
6
1.5891
1
    1.6002
1
1.5903
1
B3PW91 1.7971
5
1.9466
5
1.9466
5
1.9646
5
1.9209
5
1.9152
5
1.9136
5
1.8692
5
1.8677
5
1.9015
5
1.5990
1
1.5985
1
1.8906
5
  1.9004
5
1.8694
5
1.5967
1
1.9678
2
1.9242
2
1.5970
1
    1.6093
1
1.5983
1
mPW1PW91 1.7934
5
1.9413
5
1.9413
5
1.9600
5
1.9166
5
1.9110
5
1.9095
5
1.8644
5
1.8626
5
1.8965
5
1.5985
1
1.5973
1
1.8849
5
  1.8951
5
1.9311
4
1.5962
1
1.8877
5
1.8636
5
1.5963
1
    1.6089
1
1.5976
1
M06-2X 1.7843
5
1.9427
5
1.9080
6
1.9677
5
1.8964
6
1.9215
5
1.9201
5
1.8787
5
1.7650
4
1.9115
5
1.5880
1
1.5875
1
1.7774
4
  1.9118
5
1.8809
5
1.5880
1
1.9079
5
1.7669
4
1.5881
1
    1.6009
1
1.5874
1
PBEPBE 1.8046
5
1.9413
5
2.0147
4
2.0382
4
1.9190
5
1.9137
5
1.9135
5
1.8717
5
1.8701
5
1.8980
5
1.6049
1
1.6036
1
1.8925
5
1.8713
6
1.9007
5
1.8713
5
1.9097
2
1.9627
4
1.8703
5
1.9118
2
    1.6151
1
1.6045
1
PBEPBEultrafine 1.5416
1
1.9868
2
1.6476
1
1.6435
1
1.9190
5
1.9781
2
1.9755
2
1.9259
2
1.6074
1
1.6311
1
1.6050
1
1.6037
1
1.9464
2
  1.9005
5
1.8714
5
1.6045
1
1.8934
5
1.8703
5
1.6037
1
    1.6150
1
1.6046
1
PBE1PBE 1.7908
5
1.9374
5
1.9374
5
1.9551
5
1.8863
6
1.9117
5
1.9060
5
1.8615
5
1.8598
5
1.8925
5
1.5990
1
1.5985
1
1.8811
5
  1.8920
5
1.8616
5
1.5971
1
1.8846
5
1.8605
5
1.5973
1
    1.6091
1
1.5985
1
HSEh1PBE 1.7912
5
1.9057
6
1.9366
5
1.9540
5
1.8860
6
1.9070
5
1.8704
6
1.8619
5
1.8604
5
1.8921
5
1.5989
1
1.5977
1
1.8813
5
  1.8920
5
1.8360
6
1.5970
1
1.8849
5
1.8611
5
1.5972
1
    1.6091
1
1.5982
1
TPSSh 2.0152
1
2.3245
1
2.3245
1
2.4179
1
1.9113
3
2.3098
1
1.8960
3
2.2096
1
2.1970
1
1.8769
6
    2.2505
1
  2.2736
1
1.8856
3
2.1955
1
2.2885
1
2.2014
1
2.1948
1
    1.6070
1
1.5956
1
wB97X-D 2.0593
1
2.4092
1
1.9051
6
2.5010
1
1.8989
6
2.4044
1
1.8896
6
2.3350
1
1.8817
6
2.4156
1
    1.8891
6
  1.8896
6
1.8819
6
2.3247
1
2.3894
1
1.8784
6
2.3268
1
    1.6266
1
1.6161
1
B97D3 2.1673
1
1.9214
6
2.4708
1
2.5669
1
1.9004
6
2.4859
1
1.9084
6
2.4044
1
1.8879
6
2.4737
1
1.8788
6
  2.4458
1
  2.4355
1
1.8887
6
2.3946
1
2.4588
1
1.8807
6
2.3952
1
    1.6269
1
1.6161
1
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 Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pCVDZ cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Moller Plesset perturbation MP2 1.7698
5
1.9510
5
1.9510
5
1.9755
5
1.8881
6
1.9106
5
1.9088
5
1.8694
6
1.8655
5
1.9042
5
1.6048
1
1.6016
1
1.8536
6
1.8693
6
1.9007
5
1.8705
5
1.8670
5
1.9004
5
1.8731
5
1.8682
5
1.9459
2
1.9070
2
1.6164
1
1.6048
1
MP2=FULL 1.7698
5
1.9462
5
1.9462
5
1.9700
5
1.9150
5
1.9016
5
1.8966
5
1.8660
5
1.8587
5
1.8843
5
1.5957
1
1.5925
1
1.8784
5
  1.8838
5
1.8527
5
1.8397
5
1.8814
5
1.8434
6
1.8248
5
1.9411
2
1.8953
2
1.5722
1
1.5832
1
ROMP2 1.9708
1
2.3582
1
2.3582
1
2.4634
1
2.3480
1
2.3282
1
2.3223
1
2.2286
1
2.2075
1
2.3324
1
    2.2655
1
  2.2806
1
2.2161
1
  2.3106
1
           
MP3 1.5370
1
1.6602
1
1.6602
1
1.6588
1
1.9236
5
1.6242
1
1.8849
6
1.6100
1
1.5964
1
1.6257
1
1.6062
1
1.6037
1
1.6008
1
  1.9477
2
1.9097
2
1.6026
1
1.6204
1
1.6062
1
1.6042
1
    1.6178
1
1.6065
1
MP3=FULL   2.3573
1
2.3573
1
2.4622
1
1.9179
3
2.3244
1
1.8925
3
2.2232
1
2.2002
1
2.3258
1
    2.2623
1
  2.2775
1
2.1944
1
  2.2970
1
2.1640
1
      1.5665
1
1.5831
1
MP4 1.5421
1
1.9565
5
1.6658
1
1.6641
1
1.9258
5
1.6262
1
1.6248
1
1.6128
1
1.8648
5
1.6275
1
1.6080
1
1.6059
1
1.8809
5
  1.9005
5
1.8450
6
1.6048
1
1.9019
5
1.8731
5
1.6061
1
    1.6199
1
1.6089
1
MP4=FULL 1.5423
1
1.9517
5
1.6658
1
1.6638
1
1.9165
5
1.6248
1
1.6231
1
1.6106
1
1.8573
5
1.6167
1
1.5981
1
1.5951
1
1.6012
1
  1.8822
5
1.8506
5
1.5818
1
1.8807
5
1.8408
5
1.5686
1
    1.5665
1
1.5847
1
B2PLYP 1.7538
2
1.9672
2
1.9672
2
2.0140
2
1.8762
6
1.9527
2
1.9495
2
1.8969
2
1.8874
2
1.9545
2
1.5934
1
1.5923
1
1.9137
2
  1.9297
2
1.8819
3
1.5910
1
1.9381
2
1.8967
2
1.5918
1
    1.6039
1
1.5933
1
B2PLYP=FULL 1.9842
1
1.9510
2
2.2996
1
2.3960
1
1.9472
2
2.2883
1
1.9414
2
2.1958
1
2.1807
1
2.2867
1
    2.2279
1
  2.2529
1
2.1833
1
  2.2664
1
2.1744
1
      1.5895
1
1.5867
1
B2PLYP=FULLultrafine 1.9842
1
2.2994
1
2.2994
1
2.3960
1
2.3025
1
2.2881
1
2.2832
1
2.1960
1
2.1809
1
2.2860
1
    2.2280
1
  2.2528
1
2.1836
1
  2.2659
1
2.1746
1
      1.5895
1
1.5867
1
Configuration interaction CID 1.5459
1
1.9565
5
1.9565
5
1.9805
5
1.9248
5
1.6275
1
1.6260
1
1.8717
5
1.5984
1
1.6283
1
1.6089
1
1.6068
1
1.6042
1
  1.6167
1
1.6067
1
1.6058
1
1.6234
1
1.6092
1
1.6072
1
    1.6208
1
1.6096
1
CISD 1.5474
1
1.9574
5
1.9574
5
1.9816
5
1.9257
5
  1.6290
1
1.8727
5
1.6000
1
1.6304
1
1.6102
1
1.6081
1
1.6070
1
  1.6191
1
1.6081
1
1.6069
1
1.6248
1
1.6103
1
1.6083
1
    1.6221
1
1.6106
1
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 Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pCVDZ cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Quadratic configuration interaction QCISD 1.5474
1
1.9584
5
1.9584
5
1.9830
5
1.9256
5
1.9110
5
1.9089
5
1.8740
5
1.8648
5
1.9053
5
1.6102
1
1.6081
1
1.8812
5
  1.9007
5
1.8729
5
1.6069
1
1.9012
5
1.8736
5
1.6083
1
    1.6221
1
1.6106
1
QCISD(T) 1.5472
1
1.6735
1
1.6735
1
1.6721
1
1.9273
5
1.6300
1
1.6286
1
1.9231
2
1.6000
1
1.6305
1
1.6100
1
1.6080
1
1.8819
5
  1.9012
5
1.8727
5
1.6068
1
1.9026
5
1.8737
5
1.6081
1
    1.6222
1
1.6110
1
QCISD(T)=FULL         1.9986
2
  1.9730
2
              1.9467
2
1.8949
2
1.8732
2
1.9407
2
1.8777
2
1.8517
2
    1.5679
1
1.5867
1
QCISD(TQ)=FULL         1.6531
1
  1.6275
1
              1.6157
1
1.5958
1
1.5840
1
1.5840
1
1.5920
1
1.5697
1
       
Coupled Cluster CCD 1.5459
1
1.9572
5
1.9573
5
1.9815
5
1.9247
5
1.9100
5
1.9078
5
1.8728
5
1.8641
5
1.9042
5
1.6089
1
1.6068
1
1.8803
5
  1.8999
5
1.8708
5
1.6058
1
1.9006
5
1.8717
5
1.6072
1
    1.6208
1
1.6096
1
CCSD 1.5474
1
1.6735
1
1.6735
1
1.6720
1
1.9255
5
1.6300
1
1.6286
1
1.6177
1
1.6000
1
1.9822
2
1.6102
1
1.6081
1
1.8812
5
  1.9006
5
1.8728
5
1.8681
5
1.9012
5
1.8736
5
1.9116
2
  1.6074
1
   
CCSD=FULL 1.5475
1
1.6735
1
1.6735
1
1.6718
1
1.9177
5
1.6291
1
1.6275
1
1.6158
1
1.5954
1
1.9746
2
1.6000
1
1.5975
1
1.8782
5
  1.8821
5
1.8524
5
1.8380
5
1.8802
5
1.8428
5
1.8521
2
       
CCSD(T) 1.5472
1
1.6731
1
1.6735
1
1.6721
1
1.9273
5
1.9791
2
1.9754
2
1.9231
2
1.9037
2
1.9814
2
1.6102
1
1.6080
1
1.8819
5
  1.9013
5
1.8728
5
1.8695
5
1.9025
5
1.8737
5
1.8703
5
1.9472
2
1.9099
2
1.6222
1
1.6110
1
CCSD(T)=FULL 1.5474
1
1.6735
1
1.6735
1
1.6718
1
1.9180
5
1.6291
1
1.6275
1
1.6155
1
1.5953
1
1.6201
1
1.6000
1
1.5973
1
1.8788
5
  1.8830
5
1.8512
5
1.8733
2
1.8813
5
1.8415
5
1.8518
2
1.9422
2
1.8969
2
1.5679
1
1.5867
1
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 Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pCVDZ cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ

average calculated bond lengths (Å)
Methods with effective core potentials (select basis sets)
daug-cc-pVDZ daug-cc-pVTZ daug-cc-pVQZ Sadlej_pVTZ CEP-31G CEP-31G* CEP-121G CEP-121G* LANL2DZ SDD
hartree fock HF 1.6170
1
1.6074
1
    2.0240
4
1.9798
4
2.0023
4
1.9529
4
2.0250
4
2.0220
4
density functional LSDA 1.6027
1
1.5988
1
    1.6904
1
1.6723
1
1.6420
1
1.6462
1
1.6340
1
1.6302
1
BLYP 1.6069
1
1.5965
1
    1.6671
1
1.6482
1
1.6168
1
1.6221
1
1.6252
1
1.6251
1
B1B95 1.6069
1
1.5961
1
    1.6648
1
1.6459
1
1.6085
1
1.6151
1
1.6252
1
1.6248
1
B3LYP 1.6003
1
1.5902
1
    2.0288
4
1.9898
4
2.0255
4
1.9760
4
1.9997
4
1.9946
4
B3LYPultrafine 1.6002
1
1.5903
1
    1.6645
1
1.6458
1
1.6112
1
1.6176
1
1.6186
1
1.6184
1
B3PW91 1.6093
1
1.5983
1
    1.6690
1
1.6501
1
1.6113
1
1.6178
1
1.6289
1
1.6284
1
mPW1PW91 1.6089
1
1.5976
1
    1.6709
1
1.6518
1
1.6127
1
1.6196
1
1.6283
1
1.6281
1
M06-2X 1.6009
1
1.5874
1
    1.6638
1
1.6479
1
1.6085
1
1.6158
1
1.6179
1
1.6172
1
PBEPBE 1.6151
1
1.6045
1
    1.6772
1
1.6579
1
1.6236
1
1.6290
1
1.6358
1
1.6351
1
PBEPBEultrafine 1.6150
1
1.6046
1
    1.6772
1
1.6580
1
1.6236
1
1.6290
1
1.6358
1
1.6351
1
PBE1PBE 1.6091
1
1.5985
1
    1.6735
1
1.6546
1
1.6164
1
1.6232
1
1.6287
1
1.6284
1
HSEh1PBE 1.6091
1
1.5982
1
    1.6721
1
1.6535
1
1.6166
1
1.6228
1
1.6280
1
1.6276
1
TPSSh 1.6070
1
1.5956
1
               
wB97X-D 1.6266
1
1.6161
1
    2.3743
1
2.3111
1
2.3755
1
2.2755
1
2.4336
1
2.4328
1
B97D3 1.6269
1
1.6161
1
               
Moller Plesset perturbation MP2 1.6164
1
1.6048
1
    2.0350
4
1.9841
4
2.0082
4
1.9529
4
2.0312
4
2.0233
4
MP2=FULL 1.5722
1
1.5832
1
    1.6810
1
1.6593
1
1.6167
1
1.6186
1
1.6441
1
1.6416
1
MP3 1.6178
1
1.6065
1
    1.6887
1
1.6641
1
1.6235
1
1.6222
1
1.6521
1
1.6482
1
MP3=FULL 1.5665
1
1.5831
1
               
MP4 1.6199
1
1.6089
1
    1.6947
1
1.6681
1
1.6284
1
1.6257
1
1.6575
1
1.6534
1
MP4=FULL 1.5665
1
1.5847
1
    1.6947
1
1.6681
1
1.6284
1
1.6257
1
1.6573
1
1.6542
1
B2PLYP 1.6039
1
1.5933
1
    1.6711
1
1.6496
1
1.6134
1
1.6175
1
1.6249
1
1.6240
1
B2PLYP=FULL 1.5895
1
1.5867
1
               
B2PLYP=FULLultrafine 1.5895
1
1.5867
1
               
Configuration interaction CID 1.6208
1
1.6096
1
    1.6989
1
1.6709
1
1.6315
1
1.6283
1
1.6610
1
1.6568
1
CISD 1.6221
1
1.6106
1
    1.7043
1
1.6748
1
1.6352
1
1.6310
1
1.6651
1
1.6609
1
Quadratic configuration interaction QCISD 1.6221
1
1.6106
1
    1.7043
1
1.6748
1
1.6352
1
1.6310
1
1.6651
1
1.6609
1
QCISD(T) 1.6222
1
1.6110
1
    1.7044
1
1.6748
1
1.6353
1
1.6311
1
1.6652
1
1.6611
1
QCISD(T)=FULL 1.5679
1
1.5867
1
               
Coupled Cluster CCD 1.6208
1
1.6096
1
    1.6989
1
1.6709
1
1.6315
1
1.6283
1
1.6610
1
1.6568
1
CCSD         1.7043
1
1.6748
1
1.6352
1
1.6310
1
1.6651
1
1.6609
1
CCSD=FULL         1.7043
1
1.6748
1
1.6352
1
1.6310
1
1.6649
1
1.6616
1
CCSD(T) 1.6222
1
1.6110
1
    1.7044
1
1.6748
1
1.6353
1
1.6311
1
1.6652
1
1.6611
1
CCSD(T)=FULL 1.5679
1
1.5867
1
    1.7044
1
1.6748
1
1.6353
1
1.6311
1
1.6650
1
1.6618
1
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.