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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 1.9317
16
PM6 2.1245
19
composite G2 2.0211
10
G3 2.0211
10
G3B3 2.0210
13
G3MP2 1.9666
3
G4 2.0825
13
CBS-Q 2.0246
10

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-pVDZ daug-cc-pVTZ
hartree fock HF 1.8750
18
2.0070
18
1.9863
18
2.0471
18
2.0817
19
2.0356
18
2.0551
17
2.0443
18
2.0444
18
2.0372
18
2.0201
12
2.0573
18
2.0431
18
2.0669
17
2.0281
13
2.0664
17
2.0545
18
2.0356
13
1.9717
4
2.0874
6
2.1276
17
ROHF   2.0570
3
2.0367
3
2.1082
3
2.0872
3
2.0872
3
2.1050
3
2.0979
3
2.0981
3
  2.1159
2
2.1100
3
2.0937
3
2.1034
3
2.0989
3
2.1008
3
2.1034
3
2.0989
3
2.0424
1
2.1228
2
2.1254
2
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 1.9043
18
2.0347
16
1.9933
16
2.0804
18
2.0659
19
2.0633
18
2.0788
18
2.0819
18
2.0756
18
2.0672
18
2.0715
10
2.1058
16
2.0808
17
2.0975
17
  2.0685
12
2.0837
11
  2.0253
5
2.1238
6
2.1240
6
B1B95 1.8856
18
2.0079
8
1.9836
14
2.0530
18
2.0453
18
2.0522
17
2.0424
13
2.0572
13
2.0492
14
2.0441
18
2.0600
8
2.0778
16
2.0514
18
2.0712
17
1.9978
1
2.0750
12
2.0615
9
  1.9970
5
2.0778
4
2.0939
6
B3LYP 1.8906
18
2.0108
18
1.9864
18
2.0546
18
2.0405
18
2.0404
18
2.0594
18
2.0575
18
2.0569
17
2.0395
18
2.0400
12
2.0647
18
2.0526
18
2.0752
17
2.0443
13
2.0739
17
2.0663
18
2.0481
12
2.0010
5
2.1014
6
2.1021
6
B3LYPultrafine   2.0173
11
    2.0473
18
2.0382
11
2.0574
11
2.0504
11
  2.0823
6
2.0482
10
2.0634
11
2.0661
16
2.0799
16
  2.0886
14
2.1016
19
  2.0010
5
2.1014
6
2.1021
6
B3PW91 1.8901
17
2.0167
18
1.9933
18
2.0567
18
2.0491
18
2.0491
18
2.0605
18
2.0577
18
2.0588
17
2.0421
18
2.0484
10
2.0835
16
2.0636
17
2.0768
17
  2.0439
12
2.0591
10
  2.0009
5
2.1021
6
2.1026
6
mPW1PW91 1.8822
17
2.0097
18
2.0025
17
2.0448
18
2.0439
18
2.0346
18
2.0558
18
2.0527
18
2.0465
18
2.0429
18
2.0434
10
2.0779
16
2.0584
17
2.0715
17
  2.0606
17
2.0728
16
  1.9959
5
2.0963
6
2.0969
6
M06-2X 1.8842
16
2.0107
16
1.9979
19
2.0494
16
2.0458
19
2.0393
16
2.0564
16
2.0497
16
2.0498
16
2.0415
16
2.0672
19
2.0624
16
2.0493
16
2.0608
16
  2.0569
16
2.0584
16
  1.9828
5
2.0782
6
2.0801
6
PBEPBE 1.9735
17
2.0331
14
2.0184
17
2.0830
17
2.0624
14
2.0685
18
2.0827
17
2.0761
18
2.0700
18
2.0631
18
2.0559
12
2.0986
16
2.0660
18
2.0872
18
2.0204
1
2.0933
16
2.0931
16
  2.0190
5
2.1172
6
2.1173
6
PBEPBEultrafine   2.0226
9
    2.0695
17
2.0571
11
2.0733
11
2.0685
11
  2.0967
6
2.0647
10
2.0814
11
2.0820
16
2.0959
16
  2.0927
16
2.0929
16
  2.0190
5
2.1172
6
2.1173
6
PBE1PBE 1.8913
16
2.0078
8
2.0057
16
2.0635
16
2.0670
19
2.0522
16
2.0706
16
2.0633
16
2.0633
16
2.0545
16
2.0419
10
2.0756
16
2.0628
16
2.0744
16
  2.0718
16
2.0714
16
  1.9949
5
2.0947
6
2.0953
6
HSEh1PBE 1.8913
16
2.0329
19
2.0054
16
2.0636
16
2.0648
19
2.0524
16
2.0794
19
2.0638
16
2.0638
16
2.0547
16
2.0424
10
2.0762
16
2.0629
16
2.0960
19
  2.0722
16
2.0720
16
  1.9952
5
2.0952
6
2.0959
6
TPSSh 1.8800
10
2.0273
11
2.0014
11
2.0558
11
2.0312
15
2.0442
11
2.0452
15
2.0550
11
2.0542
10
2.0556
19
2.0507
10
2.0672
11
2.0541
11
2.0476
15
2.0593
10
2.0644
11
2.0624
11
2.0581
10
2.0047
5
2.1041
6
2.1037
6
wB97X-D 1.8750
10
2.0253
10
2.0303
19
2.0495
10
2.0546
19
2.0395
10
2.0675
19
2.0529
10
2.0622
19
2.0465
10
2.0533
10
2.0716
19
2.0649
19
2.0707
19
2.0618
10
2.0637
10
2.0711
19
2.0785
8
  2.1087
6
2.1103
6
B97D3 1.8953
10
2.0556
17
2.0352
10
2.0865
10
2.0754
19
2.0735
10
2.1000
19
2.0859
10
2.0962
19
2.0752
10
2.1452
19
2.1630
18
2.0828
10
2.0720
18
2.0912
10
2.0946
10
2.3170
19
2.0901
10
  2.1367
6
2.3465
19
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-pVDZ daug-cc-pVTZ
Moller Plesset perturbation MP2 1.8742
17
2.0427
18
2.0195
18
2.0840
18
2.0773
19
2.0716
18
2.1035
18
2.0793
19
2.0743
18
2.0775
18
2.0899
11
2.0921
18
2.0769
18
2.1060
17
2.1078
11
2.1201
17
2.1119
18
2.1092
11
2.0426
5
2.1541
6
2.1329
4
MP2=FULL 1.8737
17
2.0354
18
2.0269
17
2.0958
17
2.0570
18
2.0570
18
2.0723
18
2.0627
18
2.0708
17
2.0539
17
2.0687
10
2.1036
16
2.0805
17
2.0918
17
2.0098
11
2.0758
17
2.0410
16
1.8574
11
2.0202
5
2.1138
6
2.0261
6
ROMP2 1.9079
3
2.1151
2
2.0766
3
2.1522
3
2.1337
3
2.1337
3
2.1685
3
2.1383
3
2.1383
3
2.1312
3
2.1934
2
2.0914
1
2.1360
3
2.1590
3
  2.1651
3
    2.0725
1
2.1986
2
2.2055
2
MP3         2.0500
14
  2.0756
15
      2.0538
6
2.0565
7
2.0473
7
2.0630
7
        2.0005
5
2.1896
2
2.1996
2
MP3=FULL   1.9860
6
1.9764
6
2.0283
6
2.0110
11
2.0126
6
2.0417
11
2.0232
6
2.0232
6
2.0086
6
2.0187
6
2.0432
7
2.0348
7
2.0375
7
  2.0221
6
1.9952
6
  1.9821
5
2.1271
2
2.0680
2
MP4   2.1128
11
    2.0944
12
    1.9454
2
2.1106
11
  2.1370
4
2.1469
10
2.1362
10
2.1693
13
  2.1556
10
2.1553
10
  2.0765
3
2.2011
2
2.2098
2
MP4=FULL   2.1288
10
    2.1340
10
      2.1225
10
  2.0926
4
  2.1212
10
2.1230
10
  2.0992
10
2.0503
10
  2.0504
3
2.1437
2
2.0828
2
B2PLYP 1.8726
11
2.0360
11
2.0075
11
2.0706
11
2.0628
14
2.0561
11
2.0666
11
2.0649
11
2.0543
11
2.0570
11
2.0668
10
2.0766
11
2.0622
11
2.0631
14
  2.0801
11
2.0778
11
  2.0157
5
2.1182
6
2.1203
6
B2PLYP=FULL 1.8729
11
2.0312
11
2.0046
11
2.0688
11
2.0477
11
2.0511
11
2.0594
11
2.0610
11
2.0610
11
2.0446
11
2.0554
10
2.0724
11
2.0583
11
2.0696
11
  2.0646
11
2.0549
11
  2.0085
5
2.1043
6
2.0811
6
B2PLYP=FULLultrafine 1.8724
10
2.0335
10
2.0062
10
2.0685
10
2.0758
19
2.0513
10
2.0648
10
2.0614
10
2.0614
10
2.0464
10
2.0552
10
2.0718
10
2.0849
19
2.1022
19
  2.0646
10
2.0882
19
    2.1043
6
2.0811
6
Configuration interaction CID   2.0357
17
2.0198
17
2.0791
17
2.0546
18
    2.0594
18
    2.0712
10
  2.1148
6
2.1287
6
        2.0079
5
2.1301
6
2.1323
6
CISD   2.0495
16
2.0253
17
2.0891
16
2.0583
18
    2.0769
17
    2.0723
10
  2.1158
6
2.1294
6
        2.0098
5
2.1316
6
2.1330
6
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-pVDZ daug-cc-pVTZ
Quadratic configuration interaction QCISD   2.0624
13
2.0706
12
2.1345
12
2.0971
13
2.1209
12
2.1262
13
2.0995
13
2.1089
13
2.1233
12
2.1376
6
2.1404
12
2.1117
13
2.1287
13
  2.1488
12
2.1480
12
  2.0704
1
2.1485
6
2.1479
6
QCISD(T)         2.0984
13
    2.0804
8
    2.1427
6
2.1433
12
2.1287
12
2.1462
12
  2.1525
12
2.1537
12
  2.0748
1
2.1513
6
2.1542
6
QCISD(T)=FULL         2.0976
7
  2.1084
7
      2.1012
6
  2.1065
7
2.1154
7
2.0128
9
2.0944
7
2.0624
7
1.8809
9
2.0538
1
2.1081
6
2.0164
6
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   2.0402
17
2.0242
17
2.0846
17
2.0616
18
2.0764
17
2.1083
17
2.0655
18
2.0803
17
2.0855
17
2.0802
10
2.1020
16
2.0765
18
2.1031
17
  2.1097
17
2.1117
16
  2.0144
5
2.1405
6
2.1430
6
CCSD         2.0701
17
2.1173
6
2.1441
6
2.0762
8
2.1211
6
2.0732
11
2.0826
10
2.1051
16
2.0940
16
2.1091
16
2.0885
11
2.1146
16
2.1135
16
2.1069
9
2.0166
5
2.1442
6
2.2029
2
CCSD=FULL         2.0701
16
        2.0352
11
2.0661
8
2.0913
16
2.0808
16
2.0855
16
1.9876
11
2.0665
16
2.0219
16
1.8516
1
1.9970
5
2.1003
6
2.0115
6
CCSD(T)         2.0936
15
2.0737
10
2.1050
9
2.0656
10
2.0962
8
2.1002
8
2.0966
9
2.1250
14
2.1089
15
2.1234
15
2.1141
9
2.1300
15
2.1351
14
2.1156
9
2.0344
3
2.1512
6
2.1532
6
CCSD(T)=FULL         2.0874
15
          2.0732
8
2.1105
14
2.0986
14
2.0872
16
2.0122
9
2.0835
14
2.0367
14
1.8806
9
2.0133
3
2.1075
6
2.0160
6
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-pVDZ 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 2.1158
18
2.0782
18
2.0522
18
2.0380
18
2.0883
18
2.0596
18
    2.0494
19
ROHF                 2.1127
2
density functional BLYP                 2.1134
6
B1B95 2.0593
2
2.0460
2
            2.0836
6
B3LYP 2.1184
18
2.0910
18
2.0728
18
2.0615
18
2.0923
18
2.0623
18
    2.0660
17
B3LYPultrafine                 2.0907
6
B3PW91                 2.0912
6
mPW1PW91                 2.0853
6
M06-2X                 2.0692
6
PBEPBE                 2.0783
19
PBEPBEultrafine                 2.1054
6
PBE1PBE                 2.0829
6
HSEh1PBE                 2.0837
6
TPSSh                 2.0919
6
wB97X-D 2.1001
10
2.0719
10
2.0549
10
2.0438
10
2.0806
10
2.0584
10
    2.0975
6
B97D3                 2.1273
6
Moller Plesset perturbation MP2 2.1408
18
2.1072
18
2.0832
18
2.0668
18
2.1128
18
2.1014
18
    2.0852
19
MP2=FULL                 2.0908
6
ROMP2                 2.1833
2
MP3                 2.1796
2
MP3=FULL                 2.1111
2
MP4                 2.1858
2
MP4=FULL                 2.1263
2
B2PLYP                 2.1043
6
B2PLYP=FULL                 2.0896
6
B2PLYP=FULLultrafine                 2.0896
6
Configuration interaction CID                 2.1141
6
CISD                 2.1147
6
Quadratic configuration interaction QCISD                 2.1272
6
QCISD(T)                 2.1307
6
QCISD(T)=FULL                 2.0856
6
Coupled Cluster CCD                 2.1228
6
CCSD                 2.1252
6
CCSD=FULL                 2.0800
6
CCSD(T)                 2.1302
6
CCSD(T)=FULL                 2.0850
6
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.