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Comparison of levels of theory for P-N


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 1.4878
9
PM3 1.5891
9
PM6 1.6393
8
composite G2 1.5839
9
G3 1.5364
3
G3B3 1.6026
9
G3MP2 1.4550
1
G4 1.5900
9
CBS-Q 1.5364
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-pV(T+d)Z cc-pCVTZ aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
hartree fock HF 1.6123
9
1.6432
9
1.5901
9
1.6528
9
1.5838
9
1.5838
9
1.5824
9
1.5783
9
1.5836
8
1.5697
9
1.5718
7
1.5900
9
1.5984
9
1.5745
9
1.5128
3
1.5985
9
1.5737
9
1.5104
3
1.4480
1
  1.4485
1
1.4489
1
1.5998
7
1.5677
9
density functional LSDA 1.5569
3
1.5459
3
1.5295
3
1.5867
3
1.5209
3
1.5209
3
1.5143
3
1.5126
3
1.5126
3
1.5100
3
    1.5304
3
1.5101
3
1.5114
2
1.5235
3
1.5118
2
1.5044
2
    1.4867
1
1.4866
1
   
BLYP 1.6782
9
1.6972
9
1.6257
9
1.7130
9
1.6266
9
1.6256
9
1.6238
9
1.6186
9
1.6186
9
1.6100
9
1.6260
7
1.6500
7
1.6385
9
1.6140
9
  1.6610
7
1.6358
7
      1.5019
1
1.5020
1
1.6601
7
1.6357
7
B1B95 1.6481
9
1.6099
7
1.5926
9
1.6683
9
1.5915
9
1.5915
9
1.5900
9
1.5857
9
1.5857
9
1.5793
9
1.5946
7
1.6146
7
1.6042
9
1.5828
9
1.5061
2
1.6032
9
1.5945
8
1.5000
2
    1.4772
1
1.4774
1
1.6247
7
1.6027
7
B3LYP 1.6609
9
1.6696
9
1.6033
9
1.6826
9
1.6025
9
1.6025
9
1.6012
9
1.5964
9
1.5964
9
1.5887
9
1.6046
7
1.6051
9
1.6151
9
1.5925
9
1.5022
3
1.6138
9
1.5912
9
1.4982
3
1.4826
1
  1.4833
1
1.4835
1
1.6364
7
1.6135
7
B3LYPultrafine   1.6893
7
    1.6025
9
1.6232
7
1.6238
7
1.6173
7
  1.6088
7
1.6046
7
1.6267
7
1.6366
7
1.6135
7
  1.6372
7
1.5982
8
      1.4833
1
1.4835
1
1.6364
7
1.6135
7
B3PW91 1.6577
9
1.6662
9
1.6002
9
1.6781
9
1.5986
9
1.5986
9
1.5969
9
1.5924
9
1.5924
9
1.5858
9
1.6011
7
1.6224
7
1.6114
9
1.5893
9
  1.6333
7
1.6100
7
      1.4823
1
1.4823
1
1.6325
7
1.6100
7
mPW1PW91 1.6513
9
1.6610
9
1.5959
9
1.6726
9
1.5942
9
1.5942
9
1.5926
9
1.5882
9
1.5882
9
1.5817
9
1.5972
7
1.6179
7
1.6069
9
1.5852
9
  1.6288
7
1.6058
7
      1.4788
1
1.4789
1
1.6280
7
1.6058
7
M06-2X 1.6430
7
1.6679
7
1.5895
9
1.6818
7
1.5895
9
1.6106
7
1.6109
7
1.6058
7
1.6058
7
1.5984
7
1.5734
9
1.6134
7
1.6225
7
1.6033
7
  1.6241
7
1.6034
7
      1.4726
1
1.4728
1
1.6234
7
1.6034
7
PBEPBE 1.6707
9
1.6908
9
1.6202
9
1.7050
9
1.6190
9
1.6190
9
1.6169
9
1.6120
9
1.6120
9
1.6050
9
1.6203
7
1.6429
7
1.6320
9
1.6085
9
1.5267
2
1.6543
7
1.6298
7
1.5192
2
1.4995
1
  1.5004
1
1.5005
1
1.6535
7
1.6298
7
PBEPBEultrafine   1.7122
7
    1.6399
7
1.6399
7
1.6401
7
1.6332
7
  1.6253
7
1.6203
7
1.6429
7
1.6538
7
1.6297
7
  1.6543
7
1.6298
7
      1.5004
1
1.5005
1
1.6535
7
1.6298
7
PBE1PBE 1.6609
7
1.6145
7
1.6145
7
1.6951
7
1.5948
9
1.6151
7
1.6152
7
1.6094
7
1.6094
7
1.6022
7
1.5979
7
1.6187
7
1.6285
7
1.6065
7
  1.6295
7
1.6066
7
      1.4799
1
1.4801
1
1.6288
7
1.6066
7
HSEh1PBE 1.6626
7
1.6629
9
1.6151
7
1.6968
7
1.5956
9
1.6160
7
1.5941
9
1.6103
7
1.6103
7
1.6027
7
1.5986
7
1.6197
7
1.6296
7
1.5867
9
  1.6305
7
1.6073
7
      1.4802
1
1.4803
1
1.6297
7
1.6073
7
TPSSh 1.6780
7
1.6957
7
1.6262
7
1.7100
7
1.6067
9
1.6258
7
1.6053
9
1.6198
7
1.6198
7
1.5939
9
1.6074
7
1.6290
7
1.6397
7
1.5972
9
1.4879
1
1.6404
7
1.6160
7
1.4878
1
    1.4884
1
1.4885
1
1.6396
7
1.6160
7
wB97X-D 1.6534
7
1.6693
7
1.5908
9
1.6836
7
1.5908
9
1.6095
7
1.5900
9
1.6036
7
1.5850
9
1.5971
7
1.5925
7
1.5932
9
1.5997
9
1.5822
9
1.4740
1
1.6235
7
1.5816
9
1.4739
1
    1.4745
1
1.4747
1
1.6228
7
1.6009
7
B97D3 1.6995
7
1.6918
9
1.6373
7
1.7306
7
1.6167
9
1.6374
7
1.6151
9
1.6306
7
1.6099
9
1.6217
7
1.5949
9
1.6191
9
1.6515
7
1.6056
9
1.4949
1
1.6518
7
1.6043
9
1.4948
1
    1.4955
1
1.4955
1
1.6509
7
1.6014
9
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-pV(T+d)Z cc-pCVTZ aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Moller Plesset perturbation MP2 1.6814
9
1.7158
9
1.6053
9
1.7349
9
1.6341
9
1.6157
9
1.6140
9
1.6262
9
1.6066
9
1.5834
9
1.6132
7
1.6005
9
1.6333
9
1.5869
9
1.4703
3
1.6353
9
1.5866
9
1.4666
3
1.5216
1
  1.5217
1
1.5232
1
1.6570
7
1.6256
7
MP2=FULL 1.6811
9
1.7156
9
1.6045
9
1.7344
9
1.6136
9
1.6136
9
1.6118
9
1.6057
9
1.6057
9
1.5779
9
1.6096
7
1.6369
7
1.6314
9
1.5817
9
1.4665
3
1.6547
7
1.6184
7
1.4620
3
1.5162
1
  1.5178
1
1.5191
1
1.6533
7
1.6181
7
MP3         1.5969
9
  1.6142
9
      1.6128
6
1.6357
6
1.6502
6
1.6219
6
            1.4754
1
1.4765
1
1.6541
6
1.6235
6
MP3=FULL   1.7057
6
1.6326
6
1.7247
6
1.6119
9
1.6304
6
1.6103
7
1.6223
6
1.6223
6
1.6133
6
1.6097
6
1.6347
6
1.6482
6
1.6169
6
  1.6521
6
1.6171
6
      1.4729
1
1.4738
1
1.6508
6
1.6169
6
MP4   1.7297
8
    1.6077
9
    1.5309
1
1.6069
8
  1.6358
6
1.6642
6
1.6800
6
1.5973
9
  1.6852
6
1.6493
6
      1.5286
1
1.5295
1
1.6837
6
1.6490
6
MP4=FULL   1.7528
6
    1.6558
6
      1.6478
6
  1.6325
6
  1.6775
6
1.6411
6
  1.6811
6
1.6414
6
      1.5260
1
1.5272
1
1.6794
6
1.6411
6
B2PLYP 1.6790
7
1.7031
7
1.6271
7
1.7233
7
1.6032
9
1.6273
7
1.6280
7
1.6204
7
1.6204
7
1.6131
7
1.6084
7
1.6317
7
1.6429
7
1.5919
9
  1.6453
7
1.6188
7
      1.4991
1
1.4997
1
1.6443
7
1.5047
1
B2PLYP=FULL 1.6789
7
1.7030
7
1.6268
7
1.7232
7
1.6265
7
1.6265
7
1.6274
7
1.6201
7
1.6201
7
1.6114
7
1.6074
7
1.6313
7
1.6423
7
1.6163
7
  1.6443
7
1.6167
7
      1.4982
1
1.4987
1
1.6432
7
1.5029
1
B2PLYP=FULLultrafine 1.6788
7
1.7030
7
1.6268
7
1.7232
7
1.6024
9
1.6266
7
1.6274
7
1.6201
7
1.6201
7
1.6114
7
1.6076
7
1.6314
7
1.6167
9
1.5932
9
  1.6444
7
1.5924
9
    1.4972
1
1.4982
1
1.4987
1
1.6434
7
1.5029
1
Configuration interaction CID   1.6617
9
1.5834
9
1.6736
9
1.5890
9
    1.5819
9
    1.5803
7
  1.6152
7
1.5888
7
            1.4732
1
1.4740
1
1.6168
7
1.5894
7
CISD   1.6601
8
1.5880
9
1.6732
9
1.5905
9
    1.5834
9
    1.5811
7
  1.6163
7
1.5897
7
            1.4757
1
1.4763
1
1.6177
7
1.5902
7
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-pV(T+d)Z cc-pCVTZ aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Quadratic configuration interaction QCISD   1.6829
9
1.6078
9
1.7001
9
1.6016
9
1.6026
9
1.6016
9
1.5936
9
1.5935
9
1.5871
9
1.5993
7
1.6245
7
1.6191
9
1.5902
9
  1.6418
7
1.6099
7
  1.4909
1
  1.4908
1
1.4915
1
1.6406
7
1.6097
7
QCISD(T)         1.6258
8
    1.6221
7
    1.6103
7
1.6359
7
1.6300
9
1.6007
9
  1.6466
8
1.6011
9
      1.5029
1
1.5040
1
1.6540
7
1.6220
7
QCISD(T)=FULL         1.6293
7
  1.6303
7
      1.6071
7
  1.6486
7
1.6151
7
1.6067
7
1.6517
7
1.6150
7
1.4960
1
    1.5000
1
1.5010
1
1.5268
1
1.5028
1
Coupled Cluster CCD   1.6804
9
1.5936
9
1.6945
9
1.6008
9
1.6008
9
1.5992
9
1.5925
9
1.5925
9
1.5730
9
1.5949
7
1.6188
7
1.6164
9
1.5760
9
  1.5393
3
1.5757
9
      1.4849
1
1.4859
1
1.6353
7
1.6053
7
CCSD         1.6136
8
1.6192
7
1.6201
7
1.6102
7
1.6102
7
1.6038
7
1.5979
7
1.6227
7
1.6363
7
1.6072
7
1.4855
1
1.6401
7
1.6084
7
1.4859
1
    1.4885
1
1.4893
1
1.6389
7
1.4944
1
CCSD=FULL         1.6170
7
        1.5985
7
1.5946
7
1.6214
7
1.6343
7
1.6021
7
1.4819
1
1.6369
7
1.6018
7
1.4815
1
    1.4852
1
1.4858
1
1.6356
7
1.4883
1
CCSD(T)   1.5826
1
    1.6308
7
1.6308
7
1.6318
7
1.6212
7
1.6212
7
1.6155
7
1.6095
7
1.6349
7
1.6287
9
1.5994
9
1.6098
7
1.6311
9
1.5997
9
1.4992
1
1.5016
1
  1.5016
1
1.5029
1
1.6530
7
1.6211
7
CCSD(T)=FULL         1.6087
9
          1.6062
7
1.6337
7
1.6475
7
1.6142
7
1.6057
7
1.6507
7
1.6142
7
1.4949
1
    1.4987
1
1.4996
1
1.6493
7
1.6138
7
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-pV(T+d)Z cc-pCVTZ 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 1.6565
9
1.6016
9
1.7181
9
1.6011
9
1.6517
9
1.6371
9
    1.5635
9
density functional BLYP                 1.6266
7
B1B95 1.5561
1
1.5040
1
            1.5951
7
B3LYP 1.6911
9
1.6176
9
1.6982
9
1.6174
9
1.6841
9
1.6644
9
    1.5869
9
B3LYPultrafine                 1.6053
7
B3PW91                 1.6019
7
mPW1PW91                 1.5980
7
M06-2X                 1.5960
7
PBEPBE                 1.6023
9
PBEPBEultrafine                 1.6212
7
PBE1PBE                 1.5988
7
HSEh1PBE                 1.5994
7
TPSSh                 1.6081
7
wB97X-D 1.6936
7
1.6299
7
1.6891
7
1.6286
7
1.6752
7
1.6667
7
    1.5932
7
B97D3                 1.6176
7
Moller Plesset perturbation MP2 1.7504
9
1.6360
9
1.7260
9
1.6337
9
1.7185
9
1.7103
9
    1.5914
9
MP2=FULL                 1.6127
7
MP3                 1.6151
6
MP3=FULL                 1.6124
6
MP4                 1.6387
6
MP4=FULL                 1.6356
6
B2PLYP                 1.6101
7
B2PLYP=FULL                 1.6090
7
B2PLYP=FULLultrafine                 1.6091
7
Configuration interaction CID                 1.5823
7
CISD                 1.5832
7
Quadratic configuration interaction QCISD                 1.6018
7
QCISD(T)                 1.6132
7
QCISD(T)=FULL                 1.6102
7
Coupled Cluster CCD                 1.5973
7
CCSD                 1.6004
7
CCSD=FULL                 1.5973
7
CCSD(T)                 1.6123
7
CCSD(T)=FULL                 1.6093
7
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.