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Comparison of levels of theory for P-B


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 1.5037
3
PM3 1.5579
3
PM6 1.8437
3
composite G2 1.7978
3
G3 1.7978
3
G3B3 1.7927
3
G4 1.7864
3
CBS-Q 1.7978
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 cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(T+d)Z aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
hartree fock HF 1.7401
3
1.8808
3
1.7923
3
1.8701
3
1.7970
3
1.7967
3
1.7972
3
1.7902
3
1.7912
3
1.7897
3
1.9885
1
1.7963
3
1.8022
3
1.7879
3
1.7833
3
1.8026
3
1.7878
3
1.7834
3
1.9900
1
1.9898
1
2.0178
1
1.8171
2
ROHF   1.7532
1
1.7223
1
1.7653
1
1.7218
1
1.7218
1
1.7229
1
1.7184
1
1.7184
1
    1.7200
1
1.7288
1
1.7182
1
1.7152
1
1.7313
1
1.7186
1
1.7155
1
1.9900
1
     
density functional LSDA 1.6432
2
1.7054
2
1.7054
2
1.7400
2
1.7086
2
1.7086
2
1.7087
2
1.7003
2
1.7003
2
1.7030
2
  1.7029
2
1.7154
2
1.6988
2
  1.7149
2
1.6985
2
  1.8720
1
1.8733
1
   
BLYP 1.7685
3
1.8496
3
1.8017
3
1.8586
3
1.8084
3
1.8085
3
1.8100
3
1.8006
3
1.8021
3
1.8021
3
1.9438
1
1.8042
3
1.8141
3
1.7963
3
  1.8149
3
1.7965
3
  1.9426
1
1.9442
1
1.9770
1
1.9531
1
B1B95 1.7392
3
1.9259
1
1.7755
3
1.8258
3
1.7797
3
1.7797
3
1.7804
3
1.7734
3
1.7743
3
1.7745
3
1.9137
1
1.7767
3
1.7849
3
1.7718
3
  1.7855
3
1.7717
3
  1.9133
1
1.9139
1
1.9352
1
1.9214
1
B3LYP 1.7533
3
1.8368
3
1.7876
3
1.8448
3
1.7937
3
1.7937
3
1.7948
3
1.7862
3
1.7873
3
1.7871
3
1.9347
1
1.7899
3
1.7991
3
1.7826
3
1.7787
3
1.7998
3
1.7826
3
1.7788
3
1.9341
1
1.9352
1
1.9650
1
1.9436
1
B3LYPultrafine   1.8368
3
    1.7937
3
1.7937
3
1.7948
3
1.7862
3
  1.9503
1
1.9347
1
1.7899
3
1.7992
3
1.7826
3
  1.7998
3
1.7826
3
  1.9341
1
1.9352
1
1.9650
1
1.9436
1
B3PW91 1.7439
3
1.8249
3
1.7805
3
1.8313
3
1.7848
3
1.7848
3
1.7854
3
1.7774
3
1.7783
3
1.7788
3
1.9178
1
1.7816
3
1.7900
3
1.7754
3
  1.7906
3
1.7753
3
  1.9175
1
1.9186
1
1.9436
1
1.9265
1
mPW1PW91 1.7398
3
1.8218
3
1.7774
3
1.8279
3
1.7815
3
1.7814
3
1.7821
3
1.7744
3
1.7753
3
1.7755
3
1.9153
1
1.7785
3
1.7866
3
1.7725
3
  1.7873
3
1.7725
3
  1.9150
1
1.9162
1
1.9403
1
1.9239
1
M06-2X 1.7385
3
1.8225
3
1.7768
3
1.8281
3
1.7839
3
1.7840
3
1.7846
3
1.7762
3
1.7771
3
1.7773
3
1.7690
3
1.7798
3
1.7878
3
1.7740
3
  1.7882
3
1.7735
3
  1.9341
1
1.9343
1
1.9577
1
1.9412
1
PBEPBE 1.7511
3
1.8288
3
1.7889
3
1.8360
3
1.7928
3
1.7929
3
1.7939
3
1.7860
3
1.7870
3
1.7874
3
1.9144
1
1.7897
3
1.7980
3
1.7838
3
  1.7986
3
1.7839
3
  1.9138
1
1.9153
1
1.9395
1
1.9229
1
PBEPBEultrafine   1.8288
3
    1.7928
3
1.7928
3
1.7939
3
1.7860
3
  1.9266
1
1.9144
1
1.7896
3
1.7981
3
1.7838
3
  1.7988
3
1.7839
3
  1.9138
1
1.9153
1
1.9395
1
1.9229
1
PBE1PBE 1.7378
3
1.9247
1
1.7769
3
1.8263
3
1.7806
3
1.7806
3
1.7813
3
1.7739
3
1.7748
3
1.7749
3
1.9121
1
1.7779
3
1.7858
3
1.7722
3
  1.7865
3
1.7722
3
  1.9120
1
1.9130
1
1.9364
1
1.9205
1
HSEh1PBE 1.7388
3
1.8211
3
1.7774
3
1.8276
3
1.7816
3
1.7815
3
1.7823
3
1.7747
3
1.7756
3
1.7758
3
1.9134
1
1.7787
3
1.7868
3
1.7729
3
  1.7875
3
1.7729
3
  1.9133
1
1.9143
1
1.9381
1
1.9220
1
TPSSh 1.7526
3
1.8419
3
1.7915
3
1.8437
3
1.7936
3
1.7936
3
1.7941
3
1.7862
3
1.7872
3
1.7878
3
1.9334
1
1.7907
3
1.7989
3
1.7840
3
1.7805
3
1.7994
3
1.7840
3
1.7805
3
1.9332
1
1.9330
1
1.9584
1
1.9413
1
wB97X-D 1.7423
3
1.8256
3
1.7788
3
1.8320
3
1.7843
3
1.7843
3
1.7847
3
1.7772
3
1.7777
3
1.7780
3
1.9281
1
1.7807
3
1.7909
3
1.7745
3
1.7699
3
1.7912
3
1.7744
3
1.7699
3
1.9275
1
1.9283
1
1.9564
1
1.9373
1
B97D3 1.9837
1
2.0460
1
1.9509
1
2.0432
1
1.9591
1
1.9593
1
1.9617
1
1.9490
1
1.9528
1
1.9513
1
1.8037
2
1.9560
1
1.9625
1
1.9443
1
1.9400
1
1.9646
1
1.9445
1
1.9399
1
1.9347
1
1.9363
1
1.9648
1
1.7929
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 cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(T+d)Z aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Moller Plesset perturbation MP2 1.7564
3
1.8535
3
1.7970
3
1.8576
3
1.7879
3
1.7879
3
1.7883
3
1.7851
3
1.7862
3
1.7839
3
1.9245
1
1.7904
3
1.8043
3
1.7824
3
1.7752
3
1.8067
3
1.7826
3
1.7757
3
1.9283
1
1.9281
1
1.9650
1
1.9351
1
MP2=FULL 1.7555
3
1.8532
3
1.7960
3
1.8570
3
1.7845
3
1.7842
3
1.7851
3
1.7832
3
1.7843
3
1.7751
3
1.9163
1
1.7888
3
1.8015
3
1.7716
3
1.7684
3
1.8034
3
1.7701
3
1.7683
3
1.9092
1
1.9211
1
1.9590
1
1.9192
1
ROMP2 1.6883
1
  1.7531
1
1.7996
1
1.7463
1
1.7463
1
1.7477
1
1.7459
1
1.7459
1
1.7491
1
  1.7482
1
1.7675
1
1.7487
1
  1.7709
1
    1.9274
1
     
MP3         1.7811
3
  1.7823
3
      1.9368
1
1.7855
3
1.8010
3
1.7770
3
        1.9401
1
1.9400
1
1.9793
1
1.9488
1
MP3=FULL   1.8465
3
1.7884
3
1.8521
3
1.7779
3
1.7782
3
1.7789
3
1.7772
3
1.7782
3
1.7697
3
1.9291
1
1.7840
3
1.7982
3
1.7656
3
  1.8006
3
1.7646
3
  1.9205
1
  1.9732
1
1.9329
1
MP4   1.8712
3
    1.8021
3
      1.8021
3
  1.9357
1
1.8068
3
1.8217
3
1.7968
3
  1.8244
3
1.7973
3
  1.9392
1
1.9391
1
1.9805
1
1.9473
1
MP4=FULL   1.8710
3
    1.7987
3
      1.8001
3
  1.9267
1
  1.8187
3
1.7850
3
  1.8209
3
1.7106
2
  1.9185
1
1.9322
1
1.9743
1
1.9305
1
B2PLYP 1.7611
3
1.8492
3
1.7951
3
1.8563
3
1.7967
3
1.7967
3
1.7977
3
1.7906
3
1.7918
3
1.7918
3
1.9324
1
1.7956
3
1.8066
3
1.7885
3
  1.8079
3
1.7890
3
  1.9333
1
1.9340
1
1.9650
1
1.9416
1
B2PLYP=FULL 1.7608
3
1.8491
3
1.7947
3
1.8561
3
1.7955
3
1.7955
3
1.7965
3
1.7901
3
1.7911
3
1.7887
3
1.9298
1
1.7951
3
1.8056
3
1.7853
3
  1.8068
3
1.7848
3
  1.9275
1
1.9316
1
1.9633
1
1.9365
1
B2PLYP=FULLultrafine 1.7608
3
1.8491
3
1.7948
3
1.8561
3
1.7955
3
1.7955
3
1.7965
3
1.7901
3
1.7911
3
1.7887
3
1.9297
1
1.7951
3
1.8056
3
1.7853
3
  1.8070
3
1.7848
3
  1.9275
1
1.9316
1
1.9632
1
1.9361
1
Configuration interaction CID   1.8536
3
1.7914
3
1.8585
3
1.7839
3
    1.7808
3
    1.9406
1
  1.9802
1
1.9517
1
        1.9431
1
1.9428
1
1.9818
1
1.9516
1
CISD   1.8606
3
1.7957
3
1.8657
3
1.7883
3
    1.7851
3
    1.9402
1
  1.9800
1
1.9512
1
        1.9426
1
1.9424
1
1.9816
1
1.9510
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 cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(T+d)Z aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Quadratic configuration interaction QCISD   1.8711
3
1.8061
3
1.8783
3
1.7981
3
1.7990
3
1.7995
3
1.7949
3
1.7965
3
1.7951
3
1.9391
1
1.8025
3
1.8184
3
1.7919
3
  1.8204
3
1.7919
3
  1.9427
1
1.9424
1
1.9834
1
1.9515
1
QCISD(T)         1.8035
3
    1.8013
3
    1.9371
1
1.8087
3
1.8254
3
1.7992
3
  1.8282
3
1.7997
3
  1.9404
1
1.9405
1
1.9821
1
1.9486
1
QCISD(T)=FULL         1.7999
3
  1.8011
3
      1.9281
1
  1.8221
3
1.7869
3
1.7833
3
1.8243
3
1.7847
3
1.7829
3
1.9198
1
1.9342
1
1.9758
1
1.9317
1
QCISD(TQ)         1.8023
3
  1.8038
3
          1.8256
3
1.7996
3
1.7166
2
1.7516
2
1.7253
2
1.7170
2
    1.9830
1
 
QCISD(TQ)=FULL         1.7219
2
  1.7232
2
          1.7471
2
1.7156
2
1.7104
2
1.7489
2
1.7117
2
1.7102
2
       
Coupled Cluster CCD   1.8566
3
1.7966
3
1.8620
3
1.7878
3
1.7885
3
1.7891
3
1.7851
3
1.7867
3
1.7854
3
1.9407
1
1.7923
3
1.8075
3
1.7821
3
  1.8097
3
1.7823
3
  1.9439
1
1.9436
1
1.9838
1
1.9527
1
CCSD         1.7955
3
1.9634
1
1.9627
1
1.9509
1
1.9558
1
1.7936
3
1.9392
1
1.8003
3
1.8164
3
1.7906
3
1.7816
3
1.8186
3
1.7907
3
1.7025
2
1.9430
1
1.9427
1
1.9836
1
1.9518
1
CCSD=FULL         1.7918
3
        1.7829
3
1.9317
1
1.7984
3
1.8130
3
1.7780
3
1.6960
2
1.8149
3
1.7761
3
1.6958
2
1.9229
1
1.9367
1
1.9773
1
1.9350
1
CCSD(T)         1.8007
3
1.8014
3
1.9596
1
1.7986
3
1.9529
1
1.9546
1
1.9371
1
1.8061
3
1.8227
3
1.7970
3
1.7886
3
1.8256
3
1.7975
3
1.7891
3
1.9405
1
1.9406
1
1.9821
1
1.9487
1
CCSD(T)=FULL         1.7971
3
          1.9282
1
1.8041
3
1.8194
3
1.7849
3
1.7812
3
1.8220
3
1.7827
3
1.7809
3
1.9198
1
1.9343
1
1.9758
1
1.9317
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 cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(T+d)Z aug-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 1.9015
3
1.8431
3
1.8856
3
1.8165
3
1.8722
3
1.8718
3
    1.8123
2
density functional BLYP                 1.9422
1
B1B95                 1.9122
1
B3LYP 1.8885
3
1.8439
3
1.8770
3
1.8233
3
1.8529
3
1.8451
3
    1.7971
2
B3LYPultrafine                 1.9335
1
B3PW91                 1.9170
1
mPW1PW91                 1.9146
1
M06-2X                 1.9328
1
PBEPBE                 1.7926
2
PBEPBEultrafine                 1.9133
1
PBE1PBE                 1.9114
1
HSEh1PBE                 1.9127
1
TPSSh                 1.9314
1
wB97X-D 1.8729
3
1.8332
3
1.8596
3
1.8109
3
1.8419
3
1.8319
3
    1.9272
1
B97D3                 1.9339
1
Moller Plesset perturbation MP2 1.8949
3
1.8378
3
1.8764
3
1.8132
3
1.8646
3
1.8615
3
    1.8103
2
MP2=FULL                 1.9206
1
MP3                 1.9374
1
MP3=FULL                 1.9338
1
MP4=FULL                 1.9318
1
B2PLYP                 1.9318
1
B2PLYP=FULL                 1.9302
1
B2PLYP=FULLultrafine                 1.9303
1
Configuration interaction CID                 1.9412
1
CISD                 1.9408
1
Quadratic configuration interaction QCISD                 1.9407
1
QCISD(T)                 1.9382
1
QCISD(T)=FULL                 1.9323
1
QCISD(TQ)                 1.9392
1
Coupled Cluster CCD                 1.9418
1
CCSD                 1.9410
1
CCSD=FULL                 1.9363
1
CCSD(T)                 1.9383
1
CCSD(T)=FULL                 1.9323
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.