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Comparison of levels of theory for Na-O


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 1.8273
5
PM3 1.8665
10
PM6 2.0978
13
composite G2 1.9568
6
G3 1.9250
3
G3B3 1.9693
3
G3MP2 1.9984
1
G4 2.0825
7
CBS-Q 1.9245
3

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-pCVTZ daug-cc-pVTZ
hartree fock HF 1.8603
12
1.9891
12
1.9641
12
2.0267
12
2.0847
13
2.0159
12
2.0360
11
2.0249
12
2.0251
12
2.0184
12
1.9605
6
2.0396
12
2.0232
12
2.0539
11
1.9784
7
2.0544
11
2.0372
12
1.9936
7
1.9717
4
2.1491
11
ROHF   2.0103
1
1.9757
1
2.0510
1
2.0318
1
2.0318
1
2.0569
1
2.0429
1
2.0436
1
    2.0603
1
2.0301
1
2.0529
1
2.0521
1
2.0549
1
2.0580
1
2.0536
1
2.0424
1
 
density functional LSDA 1.9895
10
1.9512
12
1.9550
11
2.0207
11
2.0031
12
2.0031
12
2.0188
11
2.0130
12
2.0135
12
2.0021
12
1.9529
2
2.0494
9
2.0107
12
2.0225
12
1.9714
1
2.0204
12
2.0264
11
1.9763
1
1.9741
5
 
BLYP 1.8902
12
2.0238
12
1.9787
12
2.0603
12
2.0479
13
2.0425
12
2.0575
12
2.0636
12
2.0543
12
2.0500
12
2.0047
4
2.0892
10
2.0636
11
2.0809
11
  2.0145
6
2.0335
5
  2.0253
5
 
B1B95 1.8718
12
1.9296
2
1.9687
12
2.0334
12
2.0283
12
2.0375
11
1.9973
7
2.0439
11
2.0356
12
2.0270
12
1.9790
2
2.0636
10
2.0332
12
2.0566
11
1.9978
1
2.0735
8
1.9951
3
  1.9970
5
 
B3LYP 1.8764
12
1.9859
12
1.9609
12
2.0331
12
2.0188
12
2.0187
12
2.0388
12
2.0378
12
2.0351
11
2.0181
12
1.9865
6
2.0422
12
2.0327
12
2.0585
11
1.9956
7
2.0593
11
2.0479
12
1.9953
6
2.0010
5
 
B3LYPultrafine   1.9653
5
    2.0290
12
1.9833
5
2.0056
5
1.9945
5
    1.9802
4
2.0077
5
2.0505
10
2.0644
10
  2.0795
8
2.1009
13
  2.0010
5
 
B3PW91 1.8751
11
1.9920
12
1.9679
12
2.0355
12
2.0309
12
2.0309
12
2.0400
12
2.0375
12
2.0373
11
2.0210
12
1.9806
4
2.0671
10
2.0464
11
2.0603
11
  1.9864
6
1.9924
4
  2.0009
5
 
mPW1PW91 1.8647
11
1.9853
12
1.9835
11
2.0202
12
2.0256
12
2.0117
12
2.0356
12
2.0325
12
2.0232
12
2.0247
12
1.9761
4
2.0617
10
2.0414
11
2.0551
11
  2.0414
11
2.0579
10
  1.9959
5
 
M06-2X 1.8717
10
1.9946
10
1.9870
13
2.0323
10
2.0366
13
2.0234
10
2.0426
10
2.0340
10
2.0341
10
2.0278
10
1.9647
4
2.0473
10
2.0346
10
2.0471
10
  2.0442
10
2.0448
10
  1.9828
5
 
PBEPBE 1.9991
11
2.0180
12
1.9991
11
2.0654
11
2.0493
12
2.0493
12
2.0648
11
2.0580
12
2.0487
12
2.0463
12
2.0035
6
2.0823
10
2.0446
12
2.0700
12
2.0204
1
2.0799
10
2.0779
10
  2.0190
5
 
PBEPBEultrafine   1.9905
5
    2.0531
11
2.0059
5
2.0227
5
2.0160
5
    1.9992
4
2.0284
5
2.0661
10
2.0805
10
  2.0790
10
2.0776
10
  2.0190
5
 
PBE1PBE 1.8784
10
1.9271
2
1.9883
10
2.0459
10
2.0616
13
2.0362
10
2.0561
10
2.0468
10
2.0468
10
2.0406
10
1.9752
4
2.0595
10
2.0475
10
2.0595
10
  2.0582
10
2.0566
10
  1.9949
5
 
HSEh1PBE 1.8784
10
2.0225
13
1.9880
10
2.0461
10
2.0581
13
2.0363
10
2.0721
13
2.0472
10
2.0472
10
2.0407
10
1.9757
4
2.0602
10
2.0476
10
2.0942
13
  2.0586
10
2.0572
10
  1.9952
5
 
TPSSh 1.8219
4
1.9786
5
1.9510
5
2.0009
5
1.9934
9
1.9919
5
2.0058
9
2.0006
5
1.9849
4
2.0415
13
1.9843
4
2.0130
5
2.0029
5
2.0069
9
1.9939
4
2.0174
5
2.0119
5
1.9931
4
2.0047
5
 
wB97X-D 1.8145
4
1.9546
4
2.0199
13
1.9722
4
2.0389
13
1.9656
4
2.0489
13
1.9792
4
2.0439
13
1.9832
4
1.9831
4
2.0505
13
2.0489
13
2.0508
13
1.9915
4
1.9972
4
2.0526
13
1.9917
2
   
B97D3 1.8346
4
2.0458
13
1.9699
4
2.0179
4
2.0560
13
2.0084
4
2.0843
13
2.0196
4
2.0806
13
2.0141
4
2.1526
13
2.1711
12
2.0178
4
2.0377
12
2.0241
4
2.0339
4
2.3998
13
2.0230
4
   
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-pCVTZ daug-cc-pVTZ
Moller Plesset perturbation MP2 1.8591
11
2.0189
12
1.9919
12
2.0582
12
2.0560
13
2.0457
12
2.0783
12
2.0575
13
2.0482
12
2.0510
12
2.0237
5
2.0666
12
2.0499
12
2.0820
11
2.0544
5
2.1013
11
2.0893
12
2.0554
5
2.0426
5
 
MP2=FULL 1.8586
11
2.0117
12
2.0061
11
2.0773
11
2.0320
12
2.0320
12
2.0492
12
2.0381
12
2.0482
11
2.0342
11
2.0121
4
2.0886
10
2.0606
11
2.0720
11
1.9583
5
2.0593
11
2.0214
10
1.7676
5
2.0202
5
 
ROMP2 1.8654
1
  1.9998
1
2.0823
1
2.0614
1
2.0614
1
2.1022
1
2.0643
1
2.0644
1
2.0508
1
  2.0914
1
2.0546
1
2.0841
1
  2.0987
1
    2.0725
1
 
MP3         2.0311
12
  2.0581
13
      1.9859
4
2.0047
5
1.9967
5
2.0113
5
        2.0005
5
 
MP3=FULL   1.9287
4
1.9221
4
1.9620
4
1.9837
9
1.9519
4
2.0189
9
1.9658
4
1.9658
4
1.9597
4
1.9664
4
1.9987
5
1.9913
5
1.9937
5
  1.9720
4
1.9409
4
  1.9821
5
 
MP4   2.1086
9
    2.0789
10
    1.9454
2
2.0955
9
  2.0765
2
2.1345
8
2.1251
8
2.1639
11
  2.1443
8
2.1418
8
  2.0765
3
 
MP4=FULL   2.1312
8
    2.1305
8
      2.1152
8
  2.0449
2
  2.1126
8
2.1129
8
  2.0890
8
2.0325
8
  2.0504
3
 
B2PLYP 1.8272
5
1.9971
5
1.9592
5
2.0248
5
2.0383
8
2.0090
5
2.0055
5
2.0159
5
1.9926
5
2.0085
5
2.0009
4
2.0251
5
2.0122
5
2.0211
8
  2.0343
5
2.0261
5
  2.0157
5
 
B2PLYP=FULL 1.8280
5
1.9904
5
1.9577
5
2.0236
5
1.9979
5
2.0054
5
2.0044
5
2.0139
5
2.0139
5
1.9984
5
1.9930
4
2.0224
5
2.0101
5
2.0197
5
  2.0200
5
2.0076
5
  2.0085
5
 
B2PLYP=FULLultrafine 1.8156
4
1.9859
4
1.9501
4
2.0116
4
1.9945
4
1.9945
4
2.0042
4
2.0029
4
2.0029
4
1.9913
4
1.9924
4
2.0086
4
2.0016
4
2.0080
4
  2.0089
4
1.9930
4
     
Configuration interaction CID   2.0161
11
1.9985
11
2.0589
11
2.0284
12
    2.0333
12
    1.9944
4
              2.0079
5
 
CISD   2.0345
10
2.0059
11
2.0714
10
2.0335
12
    2.0575
11
    1.9960
4
              2.0098
5
 
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-pCVTZ daug-cc-pVTZ
Quadratic configuration interaction QCISD   2.0391
7
2.0691
6
2.1343
6
2.0771
7
2.1213
6
2.1071
7
2.0787
7
2.0961
7
2.1208
6
  2.1418
6
2.0976
7
2.1169
7
  2.1485
6
2.1479
6
  2.0704
1
 
QCISD(T)         2.0783
7
    1.9439
2
      2.1450
6
2.1270
6
2.1464
6
  2.1528
6
2.1531
6
  2.0748
1
 
QCISD(T)=FULL         2.0600
1
  2.0853
1
          2.0573
1
2.0775
1
1.9574
3
2.0660
1
2.0556
1
1.7787
3
2.0538
1
 
QCISD(TQ)         1.9572
3
  2.1039
1
          2.0588
1
2.0841
1
2.0886
1
2.0995
1
2.0995
1
2.0939
1
   
QCISD(TQ)=FULL         2.0571
1
  2.0828
1
          2.0541
1
2.0757
1
2.0434
1
2.0621
1
2.0536
1
     
Coupled Cluster CCD   2.0201
11
2.0024
11
2.0639
11
2.0353
12
2.0559
11
2.0907
11
2.0394
12
2.0598
11
2.0659
11
2.0023
4
2.0838
10
2.0539
12
2.0843
11
  2.0924
11
2.0928
10
  2.0144
5
 
CCSD         2.0443
11
    1.9415
2
  2.0126
5
2.0039
4
2.0864
10
2.0754
10
2.0905
10
2.0255
5
2.0964
10
2.0943
10
2.0366
3
2.0166
5
 
CCSD=FULL         2.0529
10
        1.9835
5
1.9820
2
2.0748
10
2.0641
10
2.0685
10
1.9346
5
2.0508
10
2.0013
10
1.8516
1
1.9970
5
 
CCSD(T)         2.0749
9
2.0019
4
2.0141
3
1.9762
4
2.0092
2
2.0148
2
2.0061
3
2.1129
8
2.0949
9
2.1087
9
2.0456
3
2.1157
9
2.1214
8
2.0474
3
2.0344
3
 
CCSD(T)=FULL         2.0767
9
          1.9917
2
2.0996
8
2.0869
8
2.0670
10
1.9572
3
2.0722
8
2.0171
8
1.7785
3
2.0133
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-pCVTZ daug-cc-pVTZ

average calculated bond lengths (Å)
Methods with effective core potentials (select basis sets)
CEP-31G CEP-31G* CEP-121G CEP-121G* LANL2DZ SDD cc-pVTZ-PP aug-cc-pVTZ-PP Def2TZVPP
hartree fock HF 2.0979
12
2.0643
12
2.0345
12
2.0240
12
2.0677
12
2.0392
12
    2.0372
13
density functional B1B95 2.0593
2
2.0460
2
             
B3LYP 2.0968
12
2.0715
12
2.0512
12
2.0428
12
2.0691
12
2.0400
12
    2.0525
11
PBEPBE                 2.0658
13
wB97X-D 2.0118
4
1.9942
4
1.9760
4
1.9756
4
1.9959
4
1.9776
4
     
Moller Plesset perturbation MP2 2.1154
12
2.0840
12
2.0581
12
2.0457
12
2.0868
12
2.0776
12
    2.0627
13
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.