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III.G.1.a.

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 1.4005
2
PM3 1.4354
3
PM6 1.5117
2
composite G2 1.5364
3
G3 1.5364
3
G3B3 1.5184
3
G4 1.5121
3
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
hartree fock HF 1.5676
3
1.5983
3
1.5577
3
1.5983
3
1.5224
5
1.5364
3
1.5309
3
1.5289
3
1.5255
2
1.5181
3
1.4463
1
1.5441
3
1.5527
3
1.5232
3
1.5128
3
1.5492
3
1.5202
3
1.5104
3
1.4480
1
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
 
SVWN   1.5857
3
    1.5209
3
  1.5144
3
                       
BLYP 1.5724
3
1.6037
3
1.5476
3
1.6067
3
1.5387
3
1.5387
3
1.5406
2
1.5315
3
1.5315
3
1.5274
3
    1.5477
3
1.5277
3
  1.5213
1
     
B1B95 1.5801
3
1.5363
3
1.5202
3
1.5778
3
1.5105
3
1.5113
3
1.5059
3
1.5053
3
1.5053
3
1.5024
3
    1.5206
3
1.5029
3
1.5061
2
1.5150
3
1.5369
1
1.5000
2
 
B3LYP 1.5883
3
1.5840
3
1.5271
3
1.5859
3
1.5184
3
1.5184
3
1.5129
3
1.5118
3
1.5231
2
1.5081
3
1.4812
1
1.5184
3
1.5273
3
1.5090
3
1.5022
3
1.5220
3
1.5047
3
1.4982
3
1.4826
1
B3LYPultrafine         1.5184
3
                      1.4866
2
   
B3PW91 1.6211
2
1.5826
3
1.5253
3
1.5832
3
1.5156
3
1.5156
3
1.5100
3
1.5091
3
1.5200
2
1.5062
3
    1.5250
3
1.5071
3
  1.5006
1
     
mPW1PW91 1.6167
2
1.5792
3
1.5334
2
1.5800
3
1.5117
3
1.5117
3
1.5064
3
1.5055
3
1.5055
3
1.5025
3
    1.5211
3
1.5036
3
  1.4968
1
     
M06-2X         1.5041
3
                           
PBEPBE 1.5823
2
1.6007
3
1.5560
2
1.6176
2
1.5344
3
1.5344
3
1.5274
3
1.5274
3
1.5274
3
1.5243
3
1.4980
1
  1.5557
2
1.5246
3
1.5267
2
  1.5047
1
1.5192
2
1.4995
1
PBEPBEultrafine         1.5121
1
                           
PBE1PBE         1.5125
3
                           
HSEh1PBE         1.5130
3
                           
TPSSh         1.5236
3
  1.5192
3
            1.5163
3
         
Moller Plesset perturbation MP2 1.6063
2
1.6548
3
1.5104
3
1.6579
3
1.5377
4
1.5468
3
1.5384
3
1.5391
3
1.5391
3
1.4808
3
  1.4925
3
1.5602
3
1.4875
4
1.4703
3
1.5542
3
1.4764
3
1.4666
3
1.5216
1
MP2=FULL 1.6061
2
1.6551
3
1.4891
2
1.6587
2
1.5368
4
1.5458
3
1.5374
3
1.5384
3
1.5443
2
1.4541
2
    1.5595
3
1.4705
3
1.4665
3
1.5504
1
  1.4354
2
1.5162
1
MP3         1.5256
3
  1.5754
3
                       
MP3=FULL         1.5748
3
                           
MP4   1.6589
2
    1.5059
3
    1.5309
1
1.4809
2
        1.4977
3
         
B2PLYP         1.5160
3
                1.4983
3
         
Configuration interaction CID   1.6277
2
1.5124
2
1.6282
2
1.5281
3
    1.5218
3
                     
CISD   1.5725
1
1.5291
2
1.6214
2
1.5312
3
    1.5467
2
                     
Quadratic configuration interaction QCISD   1.6111
3
1.5521
2
1.6355
2
1.5271
3
1.5387
2
1.5216
3
1.5183
3
1.5183
3
1.5240
2
    1.5399
3
1.5255
2
        1.4909
1
QCISD(T)         1.5490
2
    1.5058
1
        1.5574
2
1.5317
2
  1.5863
1
1.5277
2
   
Coupled Cluster CCD   1.6316
2
1.5064
2
1.6322
2
1.5321
3
1.5491
2
1.5388
2
1.5253
3
1.5429
2
1.4761
2
    1.5438
3
1.4780
2
  1.5534
2
1.4716
2
   
CCSD         1.5380
2
    1.4935
1
                     
CCSD(T)   1.5826
1
    1.5128
1
1.5128
1
1.5121
1
1.5047
1
1.5047
1
  1.4983
1
  1.5552
2
1.5216
3
  1.5504
2
1.5247
2
  1.5016
1
CCSD(T)=FULL         1.5397
2
                           

average calculated bond lengths (Å)
Methods with effective core potentials (select basis sets)
CEP-31G CEP-31G* CEP-121G CEP-121G* LANL2DZ SDD
hartree fock HF 1.6389
2
1.6013
2
1.9264
2
1.6030
2
1.6687
2
1.6199
2
density functional B1B95 1.5561
1
1.5040
1
       
B3LYP 1.6083
2
1.5413
2
1.6606
2
1.5427
2
1.6551
2
1.5902
2
Moller Plesset perturbation MP2 1.6620
2
1.5656
2
1.5958
2
1.5633
2
1.6361
2
1.6381
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.