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Comparison of levels of theory for K-H


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 2.7148
2
PM6 3.5352
2
composite G2 2.9112
2
G3 2.9072
2
G3B3 2.8626
2
G3MP2 2.3122
1
G4 2.2538
1
CBS-Q 2.9117
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 Def2TZVPP cc-pVDZ
hartree fock HF 2.3626
2
2.8713
2
2.8217
2
2.9654
2
2.9111
2
2.8898
2
2.8880
2
2.9628
2
2.8952
2
2.8604
2
2.3077
1
3.0487
2
2.9050
2
 
ROHF   2.8713
2
2.8217
2
2.9653
2
2.9112
2
2.8898
2
2.9112
2
2.9627
2
2.8954
2
  2.3077
1
3.0486
2
2.3223
1
 
density functional LSDA 2.2795
2
2.6597
2
2.6534
2
2.7160
2
2.6310
2
2.6220
2
2.6213
2
2.5760
2
2.5562
2
2.6131
2
2.1948
1
2.7378
2
2.2249
1
 
BLYP 2.3387
2
2.8051
2
2.7446
2
2.8497
2
2.8837
2
2.7578
2
2.7568
2
2.7728
2
2.7352
2
2.7309
2
2.2472
1
2.9007
2
2.2723
1
 
B1B95 2.3376
2
  2.3185
1
2.9058
2
2.2826
1
2.2826
1
2.8443
2
2.2464
1
2.8389
2
2.2657
1
2.2437
1
2.9364
2
2.2669
1
 
B3LYP 2.3243
2
2.7879
2
2.7302
2
2.8325
2
2.7567
2
2.7421
2
2.7410
2
2.7534
2
2.7122
2
2.7167
2
2.2400
1
2.8831
2
2.8663
2
 
B3LYPultrafine   2.3266
1
    2.7495
2
2.2823
1
2.2823
1
2.2430
1
  2.2631
1
2.2400
1
2.3363
1
2.2637
1
 
B3PW91 2.3356
2
2.8424
2
2.7885
2
2.9176
2
2.8245
2
2.8095
2
2.8083
2
2.8478
2
2.7937
2
2.7757
2
2.2376
1
2.9859
2
2.2643
1
 
mPW1PW91 2.3341
2
2.8096
2
2.7691
2
2.8713
2
2.8015
2
2.7891
2
2.7882
2
2.8056
2
2.7691
2
2.7608
2
2.2360
1
2.9464
2
2.2618
1
 
M06-2X 2.3197
2
2.8895
2
2.8752
2
3.0649
2
3.0250
2
3.0163
2
3.0165
2
3.1656
2
3.1396
2
2.8831
2
2.2477
1
3.2082
2
2.2671
1
 
PBEPBE 2.3384
2
2.7933
2
2.7479
2
2.8307
2
2.7657
2
2.7539
2
2.7530
2
2.7606
2
2.7292
2
2.7296
2
2.2379
1
2.8791
2
2.8676
2
 
PBEPBEultrafine   2.3377
1
    2.2919
1
2.2889
1
2.2889
1
2.2419
1
  2.2689
1
2.2379
1
2.3435
1
2.2655
1
 
PBE1PBE 2.3288
2
  2.7517
2
2.8369
2
2.7741
2
2.7745
2
2.7612
2
2.7722
2
2.7386
2
2.7369
2
2.2368
1
2.8953
2
2.2616
1
 
HSEh1PBE 2.3283
2
2.7912
2
2.7464
2
2.8347
2
2.7680
2
2.7551
2
2.7538
2
2.7684
2
2.7314
2
2.7298
2
2.2361
1
2.8958
2
2.2608
1
 
TPSSh 2.1103
1
2.3296
1
2.3189
1
2.3223
1
2.8832
2
2.2816
1
2.8803
2
2.2367
1
2.2358
1
2.8689
2
2.2341
1
2.3378
1
2.2612
1
 
wB97X-D 2.0986
1
2.3340
1
2.8995
2
2.3280
1
2.8960
2
2.2844
1
2.8930
2
2.2559
1
2.8817
2
2.2687
1
2.2527
1
2.9326
2
2.2750
1
2.8930
2
B97D3 2.1335
1
2.9123
2
2.3448
1
2.3520
1
2.9042
2
2.3087
1
2.9055
2
2.2629
1
2.8784
2
2.2858
1
2.8730
2
2.3686
1
2.2883
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 2.3739
2
2.8821
2
2.8290
2
2.9691
2
2.9061
2
2.8531
2
2.8502
2
2.8808
2
2.7909
2
2.8071
2
2.2379
1
3.0438
2
2.9040
2
 
MP2=FULL 2.4027
2
2.8794
2
2.8208
2
2.9690
2
2.8867
2
2.8530
2
2.8500
2
2.8809
2
2.7869
2
2.8066
2
2.2356
1
3.0319
2
2.2553
1
 
ROMP2 2.3749
2
  2.8289
2
2.9693
2
2.8866
2
2.8530
2
2.8501
2
2.8815
2
2.7915
2
2.8077
2
2.2378
1
3.0441
2
2.3171
1
 
MP3         2.8891
2
  2.8948
2
      2.2465
1
2.3759
1
2.3192
1
 
MP3=FULL   2.3938
1
2.3724
1
2.3877
1
2.9087
2
2.2995
1
2.8947
2
2.2715
1
2.2446
1
2.2881
1
2.2451
1
2.3615
1
2.2614
1
 
MP4   2.8929
2
    2.8914
2
      2.7906
2
  2.2470
1
2.3791
1
2.3223
1
 
MP4=FULL   2.4021
1
    2.3323
1
      2.2453
1
  2.2449
1
  2.2621
1
 
B2PLYP 2.1054
1
2.3431
1
2.3289
1
2.3381
1
2.2928
1
2.2848
1
2.2845
1
2.2504
1
2.2439
1
2.2684
1
2.2396
1
2.3485
1
2.2814
1
 
B2PLYP=FULL 2.1054
1
2.3452
1
2.3277
1
2.3381
1
2.2954
1
2.2848
1
2.2878
1
2.2501
1
2.2434
1
2.2683
1
2.2389
1
2.3437
1
2.2604
1
 
B2PLYP=FULLultrafine 2.1057
1
2.3423
1
2.3274
1
2.3378
1
2.2926
1
2.2846
1
2.2847
1
2.2496
1
2.2428
1
2.2679
1
2.2383
1
2.3434
1
2.2599
1
 
Configuration interaction CID   2.8935
2
2.8388
2
2.9777
2
2.8928
2
    2.8880
2
    2.2523
1
  2.3223
1
 
CISD   2.9004
2
2.8436
2
2.9847
2
2.8954
2
    2.8885
2
    2.2529
1
  2.3263
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   2.9004
2
2.8436
2
2.9845
2
2.8990
2
2.8599
2
2.8567
2
2.8960
2
2.7981
2
2.8178
2
2.2587
1
3.0497
2
2.3263
1
 
QCISD(T)         2.8990
2
    2.2907
1
    2.2548
1
3.0497
2
2.3263
1
 
QCISD(T)=FULL         2.3472
1
  2.3160
1
      2.2528
1
  2.2686
1
 
QCISD(TQ)         2.3478
1
  2.3166
1
      2.2548
1
     
QCISD(TQ)=FULL         2.3478
1
  2.3165
1
      2.2538
1
  2.2687
1
 
Coupled Cluster CCD   2.8935
2
2.8388
2
2.9778
2
2.8938
2
2.8552
2
2.8521
2
2.8910
2
2.7955
2
2.8140
2
2.2542
1
3.0453
2
2.3223
1
 
CCSD         2.8993
2
        2.3060
1
2.2586
1
2.3883
1
2.3263
1
 
CCSD=FULL         2.3475
1
        2.3058
1
2.2568
1
2.3741
1
2.2715
1
 
CCSD(T)         2.8988
2
2.3159
1
2.3163
1
2.2909
1
2.2574
1
2.3058
1
2.2548
1
3.0497
2
2.3263
1
 
CCSD(T)=FULL         2.8986
2
          2.2528
1
3.0375
2
2.2687
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         2.8845
2
  3.1929
2
  2.8854
2
2.8549
2
density functional B1B95         2.3546
1
         
B3LYP         2.8616
2
  3.1466
2
  2.7742
2
2.7235
2
wB97X-D         2.3580
1
  2.4561
1
  2.3239
1
2.3167
1
Moller Plesset perturbation MP2         2.8938
2
  3.1927
2
  2.8959
2
2.8632
2
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.