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III.G.1.a.

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 2.2069
9
PM6 2.1244
11
composite G2 2.0742
5
G3 2.0782
4
G3B3 2.1122
4
G4 2.0825
7
CBS-Q 2.0799
4

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
hartree fock HF 1.8596
11
2.0282
13
2.0064
13
2.0685
13
2.1098
17
2.0561
13
2.0781
12
2.0651
13
2.0653
13
2.0554
13
1.9463
2
2.9100
11
2.0658
13
2.0987
11
2.1161
4
2.0956
11
2.0745
13
2.1428
4
 
ROHF   2.0103
1
1.9757
1
  2.0318
1
2.0318
1
2.0569
1
2.0429
1
                     
density functional LSDA 1.8662
11
1.9908
13
1.9861
13
2.0457
13
2.0366
13
2.0365
13
2.0545
12
2.0458
13
2.0462
13
2.0325
13
  2.0906
5
2.0470
13
2.0558
13
2.1985
2
2.0514
13
2.1156
7
2.1923
2
 
SVWN   2.0121
11
    2.0570
10
2.0668
5
2.0540
11
2.0769
5
2.0769
5
2.0634
5
    2.0779
5
2.0875
5
  2.0831
5
2.0808
5
   
BLYP 1.8890
11
2.0619
13
2.0201
13
2.0984
13
2.0794
13
2.0795
13
2.0956
13
2.0999
13
2.0913
13
2.0842
13
  2.1427
5
2.1106
11
2.1226
11
  1.9978
2
     
B1B95 1.8722
12
1.9824
10
1.9769
10
2.0340
12
2.0288
12
2.0381
11
2.0695
7
2.0586
9
2.0472
10
2.0274
12
  2.1233
5
2.0931
11
2.0570
11
1.9978
1
2.1006
6
1.9951
3
   
B3LYP 1.8764
12
2.0248
13
2.0020
13
2.0714
13
2.0559
13
2.0558
13
2.0758
13
2.0743
13
2.0872
11
2.0530
13
1.9991
2
2.9002
11
2.0724
13
2.1000
11
2.1275
4
2.0991
11
2.1147
10
2.0081
2
 
B3LYPultrafine         2.0654
13
              2.1050
5
2.1193
5
  2.1162
5
2.1009
13
   
B3PW91 1.8738
10
2.0351
13
2.0129
13
2.0776
13
2.0707
13
2.0707
13
2.0807
13
2.0776
13
2.0932
11
2.0590
13
  2.1247
5
2.0974
11
2.1058
11
  1.9650
2
     
mPW1PW91 1.8647
11
2.0412
11
2.0327
11
2.0618
13
2.0642
13
2.0514
13
2.0747
13
2.0714
13
2.0628
13
2.0608
13
  2.1194
5
2.0906
11
2.0992
11
  2.0694
7
2.1123
5
   
M06-2X 1.9206
5
2.0426
5
2.0223
5
2.0911
5
2.0519
11
2.0811
5
2.0974
5
2.0905
5
2.0907
5
2.0789
5
  2.1060
5
2.0890
5
2.1028
5
  2.0969
5
2.0992
5
   
PBEPBE 1.9044
11
2.0573
13
2.0468
11
2.1080
11
2.0858
13
2.0857
13
2.1050
12
2.0943
13
2.0857
13
2.0805
13
2.0120
2
2.1353
5
2.0855
13
2.1063
13
2.2713
2
2.1290
5
2.1282
5
2.5103
1
 
PBEPBEultrafine         2.0882
7
              2.1191
5
2.1321
5
  2.1284
5
2.1279
5
   
PBE1PBE 1.9282
5
2.0381
5
2.0381
5
2.1030
5
2.0791
11
2.0934
5
2.1100
5
2.1036
5
2.1036
5
2.0920
5
  2.1164
5
2.1019
5
2.1138
5
  2.1107
5
2.1104
5
   
HSEh1PBE 1.9280
5
2.0598
5
2.0375
5
2.1032
5
2.0640
11
2.0936
5
2.1106
5
2.1041
5
2.1041
5
2.0924
5
  2.1173
5
2.1022
5
2.1145
5
  2.1115
5
2.1111
5
   
TPSSh         2.0091
9
  2.0203
9
            2.0090
9
         
Moller Plesset perturbation MP2 1.8584
10
2.0565
13
2.0319
13
2.0991
13
2.0843
13
2.0844
13
2.1157
13
2.0862
13
2.0866
13
2.0874
13
1.9734
1
2.9282
11
2.0922
13
2.1355
11
2.0891
1
2.1386
12
2.1582
9
2.0944
1
2.0351
2
MP2=FULL 1.8592
10
2.0497
13
2.0523
11
2.1233
11
2.0711
13
2.0711
13
2.0876
13
2.0762
13
2.1017
11
2.0769
11
  2.1393
5
2.1286
9
2.1134
11
2.0476
1
2.0594
11
2.0411
5
   
MP3         2.0709
13
  2.0525
13
                       
MP3=FULL         1.9820
9
  2.0453
9
                       
MP4   2.1586
9
    2.1216
11
    1.9454
2
2.1487
9
    2.1572
5
2.1419
5
2.1683
9
  2.1672
5
2.1676
5
   
MP4=FULL   2.0877
5
    2.1168
5
      2.1192
5
      2.1261
5
2.1356
5
  2.1093
5
2.0345
5
   
B2PLYP         2.0475
6
                2.0178
8
         
Configuration interaction CID   2.0587
11
2.0449
11
2.1054
11
2.0684
13
    2.0729
13
                     
CISD   2.0807
10
2.0519
11
2.1222
10
2.0732
13
    2.1019
11
                     
Quadratic configuration interaction QCISD   2.0976
8
2.1521
6
2.2176
6
2.1364
8
2.2021
6
2.1647
8
2.1378
8
2.1529
8
2.2000
6
  2.1515
5
2.1609
8
2.1740
8
  2.1585
5
2.1584
5
   
QCISD(T)         2.1374
8
    1.9439
2
      2.1546
5
2.2172
6
2.2280
6
  2.2287
6
2.1634
5
   
QCISD(TQ)         1.9026
2
                           
Coupled Cluster CCD   2.0625
11
2.0487
11
2.1103
11
2.0749
13
2.1004
11
2.1590
9
2.0787
13
2.1695
7
2.1706
7
  2.1479
5
2.0959
13
2.1959
7
  2.1991
7
2.2218
6
   
CCSD         2.1347
8
    1.9415
2
      2.1501
5
2.1365
5
2.1533
5
  2.1564
5
2.1570
5
   
CCSD=FULL         2.1118
5
            2.1334
5
2.1200
5
2.1278
5
  2.1010
5
2.0295
5
   
CCSD(T)         2.0954
7
2.0008
2
1.9783
1
1.9433
2
    1.9867
1
2.1539
5
2.1780
8
2.1559
10
  2.1914
8
2.1522
6
   
CCSD(T)=FULL         2.1701
7
            2.1369
5
2.1235
5
2.0834
7
  2.1049
5
2.0316
5
   

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 2.1411
13
2.1061
13
2.0793
13
2.0650
13
2.1085
13
2.0833
13
density functional B1B95 2.0593
2
2.0460
2
       
B3LYP 2.1409
13
2.1135
12
2.0985
12
2.1077
10
2.1106
13
2.0815
12
Moller Plesset perturbation MP2 2.1587
13
2.1253
13
2.1170
11
2.0867
13
2.1275
13
2.1204
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.