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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 1.8130
3
PM3 1.8681
11
PM6 2.0978
13
composite G2 1.9568
6
G3 1.9366
5
G3B3 1.9671
7
G3MP2 1.9666
3
G4 2.0825
7
CBS-Q 1.9368
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) TZVP Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pCVTZ
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
2.7659
13
2.0372
13
2.0232
12
2.0539
11
1.9784
7
2.0544
11
2.0372
12
1.9936
7
1.9717
4
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
2.0149
10
2.0149
10
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 1.9083
10
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
2.0581
9
2.0468
10
2.0270
12
1.9790
2
2.0636
10
  2.0332
12
2.0566
11
1.9978
1
2.0735
8
2.0080
1
  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
2.7604
13
2.0421
13
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
2.1223
11
  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
2.0658
13
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
2.0314
4
  2.0178
4
2.0876
13
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 Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pCVTZ
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
2.7908
13
2.0627
13
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 Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pCVTZ
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
  2.1143
8
  2.0976
7
2.1169
7
  2.1485
6
2.1479
6
  2.0704
1
QCISD(T)         2.0783
7
    1.9678
4
    2.0135
2
2.1111
8
  2.0924
8
2.1154
8
  2.1528
6
2.1211
8
  2.0342
3
QCISD(T)=FULL         2.0600
1
  2.0853
1
      1.9892
2
    2.0073
3
2.0266
3
1.9574
3
2.0660
1
1.9918
3
1.7787
3
2.0127
3
QCISD(TQ)         1.9572
3
  2.1039
1
      1.9889
2
    2.0588
1
2.0226
3
2.0291
3
2.0135
3
2.0995
1
2.0939
1
1.9875
2
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
2.0263
5
2.0166
5
CCSD=FULL         2.0529
10
        1.9835
5
1.9820
4
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
2.0932
8
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 Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pCVTZ

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         2.0979
12
2.0643
12
2.0345
12
2.0240
12
2.0677
12
2.0392
12
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
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
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.