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Comparison of levels of theory for K-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 PM3 2.5657
3
PM6 2.3786
3
composite G2 2.6558
3
G3 2.6408
3
G3B3 2.6002
3
G4 2.6114
3
CBS-Q 2.7027
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 Def2TZVPP cc-pVDZ
hartree fock HF 2.3301
3
2.5078
3
2.4559
3
2.5603
3
2.4999
3
2.4998
3
2.5452
3
2.4801
3
2.4811
3
2.4803
3
2.2381
1
2.5881
3
2.6830
3
 
ROHF   2.6465
2
2.5989
2
2.7088
2
2.6314
2
2.6314
2
2.6742
2
2.6184
2
2.6184
2
    2.7278
2
   
density functional LSDA 2.5105
2
2.3811
3
2.3811
3
2.4736
3
2.4357
3
2.4359
3
2.4198
3
2.3809
3
2.3816
3
2.3968
3
2.1416
1
2.5414
3
2.1697
1
 
BLYP 2.4412
3
2.5680
3
2.4645
3
2.5954
3
2.6612
3
2.4904
3
2.5440
3
2.4436
3
2.4443
3
2.4561
3
2.2149
1
2.6008
3
2.2350
1
 
B1B95 2.4296
3
  2.1490
2
2.2610
2
2.2150
1
2.2150
1
2.6620
2
2.1515
2
2.1527
2
2.1679
2
2.1981
1
2.5675
3
2.2162
1
 
B3LYP 2.4236
3
2.5238
3
2.4404
3
2.5559
3
2.4647
3
2.4648
3
2.5167
3
2.4265
3
2.4272
3
2.4350
3
2.2053
1
2.5717
3
2.6673
3
 
B3LYPultrafine   2.5227
3
    2.4635
3
2.4636
3
2.5153
3
2.4249
3
  2.1859
1
2.2053
1
2.5695
3
2.2240
1
 
B3PW91 2.4295
3
2.5432
3
2.4563
3
2.5763
3
2.4767
3
2.4768
3
2.5273
3
2.4333
3
2.4341
3
2.4439
3
2.1938
1
2.5878
3
2.2157
1
 
mPW1PW91 2.4270
3
2.5232
3
2.4429
3
2.5545
3
2.4651
3
2.4652
3
2.5134
3
2.4243
3
2.4251
3
2.4321
3
2.1908
1
2.5718
3
2.2121
1
 
M06-2X 2.3159
3
2.4980
3
2.4232
3
2.5217
3
2.4403
3
2.4404
3
2.4894
3
2.4175
3
2.4183
3
2.4164
3
2.2083
1
2.5559
3
2.2255
1
 
PBEPBE 2.4358
3
2.5488
3
2.4530
3
2.5725
3
2.4726
3
2.4728
3
2.5198
3
2.4198
3
2.4206
3
2.4347
3
2.1957
1
2.5786
3
2.6625
3
 
PBEPBEultrafine   2.5476
3
    2.4709
3
2.4710
3
2.5185
3
2.4177
3
  2.1857
1
2.1957
1
2.5781
3
2.2180
1
 
PBE1PBE 2.3233
3
  2.4349
3
2.5395
3
2.4548
3
2.4548
3
2.5022
3
2.4138
3
2.4146
3
2.4225
3
2.1900
1
2.5579
3
2.2104
1
 
HSEh1PBE 2.4231
3
2.5105
3
2.4337
3
2.5385
3
2.4512
3
2.4513
3
2.4986
3
2.4111
3
2.4119
3
2.4192
3
2.1906
1
2.5570
3
2.2105
1
 
TPSSh 2.1602
1
2.5351
3
2.4499
3
2.5621
3
2.4719
3
2.4721
3
2.5171
3
2.4250
3
2.1653
1
2.6446
3
2.1912
1
2.5748
3
2.2139
1
 
wB97X-D 2.1499
1
2.2305
1
2.6208
3
2.2479
1
2.6584
3
2.2167
1
2.6936
3
2.1685
1
2.6429
3
2.1824
1
2.2053
1
2.7207
3
2.2240
1
2.9053
2
B97D3   2.7328
3
2.1821
1
2.2918
1
2.6632
3
2.2474
1
2.7023
3
2.1827
1
2.6402
3
2.1985
1
2.6576
3
2.3304
1
2.2349
1
 
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
Moller Plesset perturbation MP2 2.3164
3
2.5752
3
2.6266
2
2.5804
3
2.6922
3
2.4760
3
2.5313
3
2.6669
3
2.4457
3
2.4328
3
2.2167
1
2.7218
3
2.8160
3
 
MP2=FULL 2.3166
3
2.5262
3
2.4535
3
2.5802
3
2.4748
3
2.4749
3
2.5300
3
2.4413
3
2.4428
3
2.4308
3
2.2127
1
2.6013
3
2.2332
1
 
ROMP2 2.1636
1
  3.0388
1
3.1576
1
2.6003
2
2.6003
2
2.6491
2
2.5730
2
2.5730
2
2.5583
2
  3.2196
1
   
MP3         2.4729
3
  2.5244
3
      2.2151
1
2.7229
3
2.3194
1
 
MP3=FULL   2.2381
1
2.1693
1
2.2721
1
2.4718
3
2.2208
1
2.5232
3
2.1847
1
2.1893
1
2.1748
1
2.2120
1
2.5967
3
2.2324
1
 
MP4   2.6026
3
    2.4759
3
      2.4473
3
  2.2227
1
2.7344
3
2.3335
1
 
MP4=FULL   2.5454
3
    2.4748
3
      2.4445
3
  2.2190
1
  2.2372
1
 
B2PLYP 2.3962
2
2.5326
3
2.4526
3
2.5536
3
2.4624
3
2.4625
3
2.5151
3
2.4284
3
2.4294
3
2.4295
3
2.2101
1
2.6052
3
2.2619
1
 
B2PLYP=FULL 2.3209
3
2.5170
3
2.4381
3
2.5536
3
2.4621
3
2.4622
3
2.5147
3
2.4276
3
2.4286
3
2.4289
3
2.2090
1
2.5728
3
2.2270
1
 
B2PLYP=FULLultrafine 2.1516
1
2.2544
1
2.1637
1
2.2675
1
2.2228
1
2.2231
1
2.2767
1
2.1768
1
2.1797
1
2.1826
1
2.2087
1
2.3084
1
2.2267
1
 
Configuration interaction CID   2.5652
3
2.6218
2
2.5768
3
2.4750
3
    2.4503
3
    2.2169
1
  2.3157
1
 
CISD   2.5725
3
2.6236
2
2.5798
3
2.4750
3
    2.4497
3
    2.2171
1
  2.3165
1
 
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
Quadratic configuration interaction QCISD   2.5940
3
2.6289
2
2.5859
3
2.4765
3
2.4765
3
2.5298
3
2.4503
3
2.4516
3
2.4369
3
2.2213
1
2.7308
3
2.3258
1
 
QCISD(T)         2.4743
3
    2.1887
1
    2.2200
1
2.7341
3
2.3294
1
 
QCISD(T)=FULL         2.4732
3
  2.5283
3
      2.2165
1
  2.2364
1
 
QCISD(TQ)         2.5980
2
  2.6498
2
             
QCISD(TQ)=FULL         2.5966
2
  2.2703
1
             
Coupled Cluster CCD   2.5683
3
2.6230
2
2.5781
3
2.4740
3
2.4740
3
2.5267
3
2.4490
3
2.4505
3
2.4362
3
2.2187
1
2.7269
3
2.3232
1
 
CCSD         2.4748
3
        2.1790
1
2.2197
1
2.7291
3
2.3244
1
 
CCSD=FULL         2.4736
3
        2.1773
1
2.2162
1
2.6002
3
2.2363
1
 
CCSD(T)         2.4742
3
2.2248
1
2.2862
1
2.1883
1
2.1924
1
2.1775
1
2.2195
1
2.7336
3
2.3291
1
 
CCSD(T)=FULL         2.4731
3
          2.2159
1
2.6021
3
2.2362
1
 
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

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         2.5564
3
  2.5527
3
  2.5798
3
2.5634
3
density functional B3LYP         2.5764
3
  2.5758
3
  2.5591
3
2.5380
3
wB97X-D         2.2440
1
  2.2431
1
  2.2571
1
2.2631
1
Moller Plesset perturbation MP2         2.5796
3
  2.5761
3
  2.6514
3
2.6343
3
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.