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III.G.1.a.

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 1.7977
6
PM3 1.8365
6
PM6 2.0406
6
composite G2 1.8963
6
G3 1.8963
6
G3B3 1.8798
6
G4 1.8802
6
CBS-Q 1.8959
6

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 cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pCVDZ cc-pCVTZ
hartree fock HF 1.7313
6
1.9157
6
1.9157
6
1.9375
6
1.9031
9
1.8901
6
1.8766
6
1.8432
6
1.8401
6
1.8754
6
1.6076
1
1.6077
1
1.8547
9
1.8697
6
1.8425
6
1.8378
6
1.8602
6
1.8367
6
1.8340
6
1.8754
3
1.8454
3
ROHF         2.0572
2
                               
density functional LSDA 1.7478
6
1.8952
6
1.8952
6
1.9123
6
1.8766
6
1.8717
6
1.8627
6
1.8258
6
1.8256
6
1.8535
6
1.5991
1
1.5972
1
1.7835
4
1.8576
6
1.8252
6
1.6444
2
1.8433
6
1.7455
5
1.6335
2
   
SVWN 1.5339
1
1.8949
9
1.6458
1
1.6414
1
1.8705
9
1.7995
4
1.8605
9
1.7648
4
1.7666
4
1.7789
4
1.5991
1
1.5972
1
1.6093
1
1.7881
4
1.7656
4
1.5975
1
1.7755
4
1.7635
4
1.5973
1
   
BLYP 1.7624
6
1.8965
6
1.8965
6
1.9133
6
1.8822
6
1.8758
6
1.8678
6
1.8377
6
1.8364
6
1.8599
6
1.5971
1
1.5959
1
1.7900
4
1.8630
6
1.8362
6
1.5971
1
1.6078
1
1.5961
1
1.5956
1
   
B1B95 1.7539
6
1.9082
6
1.9082
6
1.9268
6
1.8902
6
1.8854
6
1.8849
3
1.8389
6
1.8374
6
1.9000
3
1.5966
1
1.5961
1
1.7822
4
1.8821
3
1.8516
3
1.8444
3
1.6485
2
1.8401
3
1.8358
3
   
B3LYP 1.7497
6
1.8904
6
1.8904
6
1.9070
6
1.8743
6
1.8682
6
1.8591
6
1.8270
6
1.8257
6
1.8526
6
1.5905
1
1.5897
1
1.8434
9
1.8538
6
1.8259
6
1.8196
6
1.8422
6
1.8199
6
1.8160
6
1.8551
3
1.8255
3
B3LYPultrafine 1.5260
1
1.6297
1
1.6297
1
1.6254
1
1.8742
6
1.6149
1
1.6139
1
1.5948
1
1.5923
1
1.6145
1
1.5906
1
1.5898
1
1.6000
1
1.7863
4
1.7658
4
1.5894
1
1.7749
4
1.8469
6
1.5891
1
   
B3PW91 1.7579
6
1.9147
6
1.9147
6
1.9315
6
1.8933
6
1.8877
6
1.8773
6
1.8424
6
1.8408
6
1.8735
6
1.5990
1
1.5985
1
1.7909
4
1.8716
6
1.8424
6
1.5967
1
1.6115
1
1.5986
1
1.5970
1
   
mPW1PW91 1.7543
6
1.9098
6
1.9098
6
1.9274
6
1.8894
6
1.8839
6
1.8737
6
1.8379
6
1.8362
6
1.8690
6
1.5985
1
1.5973
1
1.7875
4
1.8669
6
1.8860
5
1.5962
1
1.7822
4
1.7726
4
1.5963
1
   
M06-2X 1.7241
4
1.8258
4
1.8258
4
1.8278
4
1.8843
9
1.7969
4
1.7962
4
1.7643
4
1.7650
4
1.7789
4
1.5880
1
1.5875
1
1.7774
4
1.7865
4
1.7650
4
1.5880
1
1.7743
4
1.7638
4
1.5881
1
   
PBEPBE 1.7657
6
1.9113
6
1.9640
5
1.9847
5
1.8924
6
1.8871
6
1.8783
6
1.8454
6
1.8437
6
1.8714
6
1.6049
1
1.6036
1
1.7960
4
1.8726
6
1.8448
6
1.8405
3
1.8471
3
1.7787
4
1.8333
3
   
PBEPBEultrafine 1.5416
1
1.6476
1
1.6476
1
1.6435
1
1.8147
4
1.6321
1
1.6311
1
1.6105
1
1.6074
1
1.6311
1
1.6050
1
1.6037
1
1.6153
1
1.8014
4
1.7803
4
1.6045
1
1.7895
4
1.7787
4
1.6037
1
   
PBE1PBE 1.7366
4
1.8406
4
1.8406
4
1.8402
4
1.8806
9
1.8078
4
1.8052
4
1.7709
4
1.7724
4
1.7877
4
1.5990
1
1.5985
1
1.7860
4
1.7943
4
1.7725
4
1.5971
1
1.7811
4
1.7711
4
1.5973
1
   
HSEh1PBE 1.7369
4
1.8405
4
1.8405
4
1.8401
4
1.8860
6
1.8057
4
1.8052
4
1.7714
4
1.7729
4
1.7875
4
1.5989
1
1.5977
1
1.7865
4
1.7946
4
1.7729
4
1.5970
1
1.7819
4
1.7716
4
1.5972
1
   
TPSSh         1.9113
3
  1.8960
3
              1.8856
3
           
Moller Plesset perturbation MP2 1.7339
6
1.9202
6
1.9202
6
1.9440
6
1.8590
7
1.8829
6
1.8714
6
1.8433
6
1.8375
6
1.8739
6
1.6048
1
1.6016
1
1.8514
9
1.8714
6
1.8431
6
1.8383
6
1.8663
6
1.8398
6
1.8363
6
1.8688
3
1.8398
3
MP2=FULL 1.7340
6
1.9162
6
1.9162
6
1.9394
6
1.8536
7
1.8752
6
1.8610
6
1.8388
6
1.8309
6
1.8551
6
1.5957
1
1.5925
1
1.7825
4
1.8569
6
1.7924
7
1.8119
6
1.8424
6
1.8118
6
1.7939
6
1.8642
3
1.8290
3
MP3 1.5370
1
1.6602
1
1.6602
1
1.6588
1
1.8066
5
1.6242
1
1.7930
5
1.6100
1
1.5964
1
1.6257
1
1.6062
1
1.6037
1
1.6008
1
1.6150
1
1.6038
1
1.6026
1
1.6204
1
1.6062
1
1.6042
1
   
MP3=FULL         1.9179
3
  1.8925
3
                           
MP4 1.5421
1
1.9272
6
1.6658
1
1.6641
1
1.8994
6
1.6262
1
1.6248
1
1.6128
1
1.8363
6
1.6275
1
1.6080
1
1.6059
1
1.7848
4
1.8055
4
1.8450
6
1.6048
1
1.7997
4
1.7867
4
1.6061
1
   
MP4=FULL   1.9118
3
    1.8636
3
      1.8315
3
        1.8404
3
1.8217
3
  1.8414
3
1.8169
3
     
B2PLYP         1.8758
6
                  2.0209
2
           
Configuration interaction CID 1.5459
1
1.9277
6
1.9277
6
1.9504
6
1.8989
6
1.6275
1
1.6260
1
1.8453
6
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
   
CISD 1.5474
1
1.9291
6
1.9291
6
1.9521
6
1.9003
6
  1.6290
1
1.8466
6
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
   
Quadratic configuration interaction QCISD 1.5474
1
1.9299
6
1.8931
7
1.9533
6
1.9010
6
1.8839
6
1.8724
6
1.8477
6
1.8369
6
1.8750
6
1.6102
1
1.6081
1
1.7853
4
1.8717
6
1.8447
6
1.6069
1
1.7990
4
1.7857
4
1.6083
1
   
QCISD(T) 1.5472
1
1.6735
1
1.6735
1
1.6721
1
1.9017
6
1.6300
1
1.6286
1
1.6177
1
1.6000
1
1.6305
1
1.6100
1
1.6080
1
1.7861
4
1.8723
6
1.8459
6
1.6068
1
1.8694
6
1.8429
6
1.6081
1
   
Coupled Cluster CCD 1.5459
1
1.9283
6
1.9283
6
1.9513
6
1.8994
6
1.8825
6
1.8709
6
1.8462
6
1.8358
6
1.8738
6
1.6089
1
1.6068
1
1.7842
4
1.8705
6
1.8440
6
1.6058
1
1.8675
6
1.8410
6
1.6072
1
   
CCSD 1.5474
1
1.6735
1
1.6735
1
1.6720
1
1.9265
5
1.6300
1
1.6286
1
1.6177
1
1.6000
1
1.6304
1
1.6102
1
1.6081
1
1.7852
4
1.8057
4
1.7853
4
1.7818
4
1.7989
4
1.7857
4
1.6083
1
   
CCSD=FULL 1.5475
1
1.6735
1
1.6735
1
1.6718
1
1.8113
4
1.6291
1
1.6275
1
1.6158
1
1.5954
1
1.6202
1
1.6000
1
1.5975
1
1.7822
4
1.7833
4
1.7643
4
1.7568
4
1.7761
4
1.7596
4
1.5705
1
   
CCSD(T) 1.5472
1
1.6731
1
1.6735
1
1.6721
1
1.9016
6
1.6300
1
1.6286
1
1.6177
1
1.5999
1
1.6305
1
1.6102
1
1.6080
1
1.7861
4
1.8723
6
1.8460
6
1.8417
6
1.8694
6
1.8429
6
1.8394
6
1.8696
3
1.8436
3
CCSD(T)=FULL 1.5474
1
1.6735
1
1.6735
1
1.6718
1
1.8938
6
1.6291
1
1.6275
1
1.6155
1
1.5953
1
1.6201
1
1.6000
1
1.5973
1
1.7828
4
1.8567
6
1.8254
6
1.8085
3
1.8813
5
1.8415
5
1.7818
3
1.8651
3
1.8319
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 1.9765
5
1.9331
5
1.9436
5
1.9049
5
1.9670
5
1.9630
5
density functional LSDA 1.6904
1
1.6723
1
1.6420
1
1.6462
1
1.6340
1
1.6302
1
SVWN 1.6904
1
1.6723
1
1.6420
1
1.6462
1
1.6340
1
1.6302
1
BLYP 1.6671
1
1.6482
1
1.6168
1
1.6221
1
1.6252
1
1.6251
1
B1B95 1.6648
1
1.6459
1
1.6085
1
1.6151
1
1.6252
1
1.6248
1
B3LYP 1.9788
5
1.9391
5
1.9626
5
1.9231
5
1.9437
5
1.9386
5
B3LYPultrafine 1.6645
1
1.6458
1
1.6112
1
1.6176
1
1.6186
1
1.6184
1
B3PW91 1.6690
1
1.6501
1
1.6113
1
1.6178
1
1.6289
1
1.6284
1
mPW1PW91 1.6709
1
1.6518
1
1.6127
1
1.6196
1
1.6283
1
1.6281
1
M06-2X 1.6638
1
1.6479
1
1.6085
1
1.6158
1
1.6179
1
1.6172
1
PBEPBE 1.6772
1
1.6579
1
1.6236
1
1.6290
1
1.6358
1
1.6351
1
PBEPBEultrafine 1.6772
1
1.6580
1
1.6236
1
1.6290
1
1.6358
1
1.6351
1
PBE1PBE 1.6735
1
1.6546
1
1.6164
1
1.6232
1
1.6287
1
1.6284
1
HSEh1PBE 1.6721
1
1.6535
1
1.6166
1
1.6228
1
1.6280
1
1.6276
1
Moller Plesset perturbation MP2 1.9882
5
1.9376
5
1.9496
5
1.9037
5
1.9750
5
1.9663
5
MP2=FULL 1.6810
1
1.6593
1
1.6167
1
1.6186
1
1.6441
1
1.6416
1
MP3 1.6887
1
1.6641
1
1.6235
1
1.6222
1
1.6521
1
1.6482
1
MP4 1.6947
1
1.6681
1
1.6284
1
1.6257
1
1.6575
1
1.6534
1
Configuration interaction CID 1.6989
1
1.6709
1
1.6315
1
1.6283
1
1.6610
1
1.6568
1
CISD 1.7043
1
1.6748
1
1.6352
1
1.6310
1
1.6651
1
1.6609
1
Quadratic configuration interaction QCISD 1.7043
1
1.6748
1
1.6352
1
1.6310
1
1.6651
1
1.6609
1
QCISD(T) 1.7044
1
1.6748
1
1.6353
1
1.6311
1
1.6652
1
1.6611
1
Coupled Cluster CCD 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) 1.7044
1
1.6748
1
1.6353
1
1.6311
1
1.6652
1
1.6611
1
CCSD(T)=FULL 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.