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Comparison of levels of theory for N-K


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 2.7933
2
PM6 2.9841
3
composite G2 3.1938
2
G3 3.1619
2
G3B3 2.8999
3
G4 2.8971
3
CBS-Q 3.1969
2

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
hartree fock HF 2.8753
3
2.9143
3
2.9020
3
3.1538
2
2.9581
3
2.9571
3
2.9718
3
2.9333
3
2.9333
3
2.9351
3
2.9400
3
3.1976
2
ROHF                     3.8041
1
 
density functional LSDA 2.5123
1
2.8527
3
2.4810
1
2.5682
1
2.8856
3
2.8856
3
2.9062
3
2.8376
3
2.8376
3
2.8444
3
2.8404
3
2.5962
1
BLYP 2.9351
3
2.9599
3
2.9239
3
2.9840
3
2.9563
3
2.9563
3
2.9802
3
2.9130
3
2.9130
3
2.9175
3
2.9202
3
3.0253
3
B1B95 2.8986
3
2.5225
1
2.9014
3
2.9464
3
2.9328
3
2.9326
3
  2.8996
3
2.9001
3
2.9009
3
2.5326
1
2.9987
3
B3LYP 2.9042
3
2.9324
3
2.9015
3
2.9559
3
2.9379
3
2.9379
3
2.9600
3
2.9000
3
2.9000
3
2.9029
3
2.9047
3
3.0016
3
B3LYPultrafine   2.9327
3
    2.9385
3
2.9385
3
2.9605
3
2.9001
3
    2.9047
3
3.0027
3
B3PW91 2.9053
3
2.9293
3
2.9006
3
2.9523
3
2.9360
3
2.9360
3
2.9565
3
2.8972
3
2.8972
3
2.9004
3
2.9008
3
3.0016
3
mPW1PW91 2.8975
3
2.9193
3
2.8923
3
2.9438
3
2.9309
3
2.9309
3
2.9506
3
2.8935
3
2.8935
3
2.8958
3
2.8971
3
2.9945
3
M06-2X 2.8775
3
2.9127
3
2.8928
3
2.9320
3
2.9243
3
2.9243
3
2.9429
3
2.8999
3
2.8999
3
2.9006
3
2.9066
3
2.9798
3
PBEPBE 2.9275
3
2.9452
3
2.9135
3
2.9742
3
2.9459
3
2.9459
3
2.9682
3
2.9009
3
2.9009
3
2.9076
3
2.9059
3
3.0143
3
PBEPBEultrafine   2.9450
3
    2.9468
3
2.9468
3
2.9686
3
2.9017
3
    2.9059
3
3.0142
3
PBE1PBE 2.8963
3
2.5045
1
2.8918
3
2.9454
3
2.9298
3
2.9298
3
2.9510
3
2.8925
3
2.8925
3
2.8958
3
2.8965
3
2.9929
3
HSEh1PBE 2.8965
3
2.9184
3
2.8906
3
2.9438
3
2.9281
3
2.9281
3
2.9488
3
2.8910
3
2.8910
3
2.8939
3
2.8950
3
2.9916
3
TPSSh 2.9114
3
2.9333
3
2.9033
3
2.9576
3
2.9390
3
2.9390
3
2.9583
3
2.8977
3
2.8977
3
2.9026
3
2.9007
3
3.0036
3
wB97X-D 2.8944
3
2.9287
3
2.9014
3
2.9445
3
2.9355
3
2.9355
3
2.9570
3
2.9049
3
2.9049
3
2.9051
3
2.9123
3
3.0020
3
B97D3 2.9404
3
2.9649
3
2.9345
3
2.9869
3
2.9638
3
2.9638
3
2.9854
3
2.9207
3
2.9207
3
2.9241
3
2.9244
3
3.0358
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
Moller Plesset perturbation MP2 2.9214
3
3.0283
3
3.0001
3
3.0360
3
2.9646
3
2.9646
3
2.9920
3
2.9357
3
2.9357
3
2.9107
3
2.9338
3
3.0921
3
MP2=FULL 2.9175
3
2.9995
3
2.9709
3
3.0366
3
2.9630
3
2.9630
3
2.9903
3
2.9321
3
2.9321
3
2.9055
3
2.9276
3
3.0474
3
ROMP2 2.5886
1
  2.6304
1
2.7094
1
2.6066
1
2.6066
1
2.6201
1
2.5632
1
2.5632
1
2.5489
1
3.7853
1
2.7574
1
MP3         2.9529
3
  2.9742
3
      2.9281
3
3.0654
3
MP3=FULL   2.9759
3
2.9491
3
3.0025
3
2.9521
3
2.9521
3
2.9729
3
2.9263
3
2.9263
3
2.8988
3
2.9225
3
3.0272
3
MP4   3.0184
3
    2.9609
3
      2.9364
3
  2.9375
3
3.0898
3
MP4=FULL   2.9901
3
    2.9597
3
      2.9340
3
  2.9325
3
 
B2PLYP 3.1317
2
2.9623
3
2.9329
3
2.9783
3
2.9448
3
2.9448
3
2.9689
3
2.9122
3
2.9122
3
2.9046
3
2.9162
3
3.0319
3
B2PLYP=FULL 2.9029
3
2.9504
3
2.9223
3
2.9782
3
2.9444
3
2.9444
3
2.9684
3
2.9115
3
2.9115
3
2.9031
3
2.9154
3
3.0141
3
B2PLYP=FULLultrafine 2.9028
3
2.9505
3
2.9218
3
2.9789
3
2.9444
3
2.9444
3
2.9691
3
2.9122
3
2.9122
3
2.9028
3
2.9154
3
3.0141
3
Configuration interaction CID   2.9975
3
2.9716
3
2.9976
3
2.9531
3
    2.9265
3
    2.9223
3
 
CISD   2.9967
3
2.9700
3
2.9986
3
2.9536
3
    2.9274
3
    2.9230
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
Quadratic configuration interaction QCISD   3.0111
3
2.9833
3
3.0142
3
2.9563
3
2.9563
3
2.9787
3
2.9338
3
2.9338
3
2.9056
3
2.9328
3
3.0740
3
QCISD(T)         2.9594
3
    2.9349
3
    2.9348
3
3.0829
3
QCISD(T)=FULL         2.9581
3
  2.9810
3
      2.9295
3
 
QCISD(TQ)         2.9602
3
  2.9837
3
      3.1211
2
 
QCISD(TQ)=FULL         2.9590
3
  2.9822
3
         
Coupled Cluster CCD   3.0092
3
2.9824
3
3.0137
3
2.9552
3
2.9552
3
2.9776
3
2.9321
3
2.9321
3
2.9052
3
2.9304
3
3.0707
3
CCSD         2.9563
3
        2.9061
3
2.9324
3
3.0732
3
CCSD=FULL         2.9551
3
        2.9012
3
2.9275
3
3.0331
3
CCSD(T)         2.9594
3
2.9594
3
2.9826
3
2.9347
3
2.9346
3
2.9065
3
2.9344
3
3.0824
3
CCSD(T)=FULL         2.9581
3
          2.9294
3
3.0392
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

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 3.2333
2
  2.9997
3
  3.1752
2
3.1619
2
    3.7882
1
density functional B3LYP 3.0432
3
  3.0437
3
  2.9629
3
2.9670
3
    3.7387
1
PBEPBE                 3.7299
1
wB97X-D 3.0102
3
  3.0365
3
  3.1486
2
2.9560
3
     
Moller Plesset perturbation MP2 3.2953
2
  3.1025
3
  3.0869
3
3.0764
3
    3.7968
1
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.