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III.G.1.a.

Comparison of levels of theory for P-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 AM1 1.3900
23
PM3 1.3446
37
PM6 1.5012
38
composite G2 1.4461
36
G3 1.4461
36
G3B3 1.4700
37
G4 1.4672
36
CBS-Q 1.4471
36

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-pCVDZ cc-pCVTZ
hartree fock HF 1.4356
35
1.4688
37
1.4472
37
1.4759
37
1.4235
76
1.4473
37
1.4478
37
1.4489
37
1.4500
37
1.4489
36
1.4082
15
1.4551
37
1.4612
37
1.4508
37
1.4480
37
1.4613
37
1.4504
37
1.4478
37
1.4662
25
1.5995
8
1.4176
3
1.4056
3
ROHF 1.4001
8
1.4249
11
1.4022
11
1.4269
8
1.4063
12
1.4056
11
1.4051
11
1.4061
11
1.4067
8
1.4057
8
    1.4202
11
1.4101
11
1.4059
8
1.4180
8
1.4077
8
1.4051
8
  1.7872
2
   
density functional LSDA 1.4713
37
1.4987
37
1.4817
37
1.5140
37
1.4810
37
1.4808
37
1.4821
37
1.4823
37
1.4807
37
1.4778
37
  1.6367
8
1.4915
37
1.4782
37
1.4333
14
1.4913
37
1.5032
23
1.4329
14
1.6235
8
1.6249
8
   
SVWN   1.5074
37
    1.4843
33
1.6301
8
1.4821
37
1.6380
8
1.6324
8
1.6245
8
    1.6397
8
1.6275
8
  1.6442
8
1.6292
8
  1.6235
8
1.6249
8
   
BLYP 1.4837
35
1.5071
37
1.4821
37
1.5158
37
1.4834
37
1.4822
37
1.4833
37
1.4831
37
1.4812
37
1.4801
36
  1.6429
8
1.4941
37
1.4783
37
  1.4509
13
    1.6292
8
1.6305
8
   
B1B95 1.4616
37
1.4748
37
1.4650
37
1.4945
37
1.4636
37
1.4643
37
1.4652
37
1.4660
37
1.4648
37
1.4625
37
  1.6211
8
1.4759
37
1.4628
37
1.4177
15
1.4752
37
1.4874
23
1.4172
15
1.6097
8
1.6107
8
   
B3LYP 1.4673
37
1.4927
37
1.4693
37
1.5010
37
1.4696
37
1.4692
37
1.4703
37
1.4702
37
1.4938
23
1.4679
36
1.4222
13
1.4728
37
1.4814
37
1.4670
37
1.4641
37
1.4808
37
1.4667
37
1.4638
37
1.4813
25
1.6177
8
1.4340
3
1.4187
3
B3LYPultrafine         1.4696
37
  1.4355
5
        1.6571
7
1.6340
8
1.5037
20
  1.6381
8
1.4670
36
  1.6166
8
1.6177
8
   
B3PW91 1.4922
24
1.4922
37
1.4690
37
1.4988
37
1.4677
37
1.4679
37
1.4688
37
1.4701
37
1.4934
23
1.4672
36
  1.6268
8
1.4796
37
1.4675
37
  1.4385
13
    1.6150
8
1.6159
8
   
mPW1PW91 1.4831
26
1.4889
37
1.4888
24
1.4953
37
1.4647
37
1.4649
37
1.4659
37
1.4674
37
1.4664
37
1.4646
36
  1.6237
8
1.4768
37
1.4652
37
  1.5104
21
1.6171
8
  1.6123
8
1.6132
8
   
M06-2X 1.6084
8
1.6471
8
1.6248
8
1.6639
8
1.4607
37
1.6148
8
1.6205
8
1.6195
8
1.6158
8
1.6097
8
  1.6201
8
1.6239
8
1.6128
8
  1.6279
8
1.6140
8
  1.6094
8
1.6104
8
   
PBEPBE 1.5088
23
1.5068
37
1.5046
24
1.5364
24
1.4816
37
1.4812
37
1.4822
37
1.4834
37
1.4815
37
1.4800
36
1.4373
12
1.6396
8
1.4925
37
1.4797
37
1.4334
15
1.6263
9
1.5066
23
1.4328
15
1.6064
9
1.6285
8
   
PBEPBEultrafine         1.4862
35
            1.6671
7
1.6434
8
1.6311
8
  1.6479
8
1.6329
8
  1.6272
8
1.6285
8
   
PBE1PBE 1.6186
8
1.6296
8
1.6296
8
1.6689
8
1.4664
37
1.6180
8
1.6239
8
1.6248
8
1.6203
8
1.6139
8
  1.6251
8
1.6286
8
1.6172
8
  1.6327
8
1.6186
8
  1.6137
8
1.6148
8
   
HSEh1PBE 1.6195
8
1.6552
8
1.6301
8
1.6698
8
1.4669
37
1.6186
8
1.6247
8
1.6253
8
1.6208
8
1.6144
8
  1.6257
8
1.6294
8
1.6176
8
  1.6335
8
1.6191
8
  1.6141
8
1.6152
8
   
TPSSh   1.6844
7
1.6581
7
1.6993
7
1.4679
36
1.6453
7
1.4690
36
1.6533
7
      1.6532
7
1.6565
7
1.4681
36
  1.6613
7
1.6463
7
  1.6137
8
1.6148
8
   
Moller Plesset perturbation MP2 1.4795
24
1.4861
37
1.4583
37
1.4960
37
1.4536
42
1.4511
36
1.4377
56
1.4606
37
1.4534
36
1.4545
31
  1.4595
37
1.4684
37
1.4507
42
1.4884
20
1.4720
37
1.4567
36
1.5063
16
1.4706
25
1.6060
8
1.4228
3
1.4090
3
MP2=FULL 1.4794
24
1.4863
37
1.4815
24
1.5198
24
1.4535
42
1.4501
36
1.4511
36
1.4609
37
1.4780
22
1.4763
23
  1.6125
8
1.4669
37
1.4606
30
1.4834
20
1.5297
16
1.4828
20
1.5063
15
1.4666
25
1.6016
8
1.4221
3
1.4065
3
ROMP2 1.4173
8
1.4382
8
1.4123
8
1.4429
7
1.4130
7
1.4043
7
1.4037
7
1.4177
8
1.4241
5
1.4092
7
    1.4274
8
1.4111
7
1.4084
7
1.4248
7
1.4111
7
1.4086
7
       
MP3         1.4634
37
  1.4588
36
        1.6388
7
1.6468
7
1.6334
7
        1.6034
8
1.6059
8
   
MP3=FULL         1.4680
36
  1.4622
32
        1.6385
7
1.6452
7
1.6298
7
        1.5995
8
1.6014
8
   
MP4 1.4199
2
1.5073
29
    1.4680
36
    1.4295
15
1.4813
23
    1.6165
8
1.6238
8
1.4650
34
  1.6345
8
1.6153
8
  1.6073
8
1.6106
8
   
MP4=FULL   1.6631
8
    1.6221
8
      1.6094
8
      1.6221
8
1.6070
8
  1.6320
8
1.6107
8
  1.6032
8
1.6062
8
   
B2PLYP 1.4135
1
1.4509
1
1.4223
1
1.4567
1
1.4210
30
1.4226
1
1.4223
1
1.4257
1
1.4233
1
1.4233
1
  1.4272
1
1.4367
1
1.4226
29
  1.4362
1
1.4233
1
  1.4204
1
1.4203
1
   
B2PLYP=FULL 1.4135
1
1.4510
1
1.4223
1
1.4568
1
1.4256
1
1.4223
1
1.4219
1
1.4258
1
1.4231
1
1.4227
1
  1.4271
1
1.4362
1
1.4223
1
  1.4356
1
1.4219
1
  1.4192
1
1.4188
1
   
B2PLYP=FULLultrafine         1.4229
13
                                 
Configuration interaction CID   1.5154
23
1.4865
23
1.5268
23
1.4620
37
    1.4630
37
          1.4160
6
        1.5996
8
1.6016
8
   
CISD   1.5041
29
1.4874
23
1.5281
23
1.4626
37
    1.4885
23
          1.4167
6
        1.5998
8
1.6018
8
   
Quadratic configuration interaction QCISD 1.4224
2
1.4985
37
1.4843
30
1.5278
24
1.4680
37
1.4646
30
1.4566
36
1.4695
37
1.4644
32
1.4818
23
  1.6157
8
1.4731
37
1.4692
30
  1.6327
8
1.6131
8
  1.5694
10
1.6087
8
   
QCISD(T)         1.4698
37
1.4164
6
1.4161
6
1.4322
15
      1.6174
8
1.4857
29
1.4729
29
  1.5035
23
1.5019
19
  1.6080
8
1.6110
8
   
Coupled Cluster CCD 1.4219
2
1.5051
30
1.4872
24
1.5288
24
1.4668
37
1.4631
30
1.4643
30
1.4685
37
1.4798
23
1.4809
23
  1.6144
8
1.4720
37
1.4686
30
  1.4994
23
1.4988
19
  1.6054
8
1.6077
8
1.4272
3
1.4130
3
CCSD         1.4677
37
1.4152
6
1.4149
6
1.4881
15
      1.6154
8
1.5419
14
1.5281
14
1.6076
8
1.6322
8
1.6127
8
1.5382
6
1.6060
8
1.6084
8
   
CCSD=FULL         1.6210
8
            1.6150
8
1.6217
8
1.6057
8
1.6030
8
1.6298
8
1.6082
8
1.8032
4
1.6019
8
1.6039
8
   
CCSD(T)   1.4730
1
    1.4869
26
1.4176
15
1.4161
6
1.4321
15
1.4264
1
  1.4259
1
1.6172
8
1.4856
29
1.4728
29
1.5294
13
1.5033
23
1.5018
19
1.5394
12
1.4878
21
1.6108
8
1.4301
3
1.4157
3
CCSD(T)=FULL         1.5177
17
            1.6170
8
1.5704
11
1.5549
11
1.5244
13
1.6324
8
1.6108
8
1.5848
9
1.5834
9
1.6064
8
1.4294
3
1.4134
3

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 1.4887
37
1.4643
37
1.4881
37
1.4649
37
1.4750
37
1.4716
37
density functional B1B95 1.4702
15
1.4464
14
       
B3LYP 1.5148
37
1.4864
37
1.5143
37
1.4860
37
1.5011
37
1.4945
37
Moller Plesset perturbation MP2 1.5110
37
1.4807
37
1.5089
37
1.4795
37
1.4933
37
1.4891
37
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.