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III.G.1.a.

Comparison of levels of theory for P-O


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 1.4786
12
PM3 1.4884
17
PM6 1.5309
25
composite G2 1.5051
23
G3 1.4993
25
G3B3 1.5309
26
G4 1.5156
24
CBS-Q 1.5053
22

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
hartree fock HF 1.6143
25
1.5827
26
1.5088
26
1.6180
26
1.4885
46
1.5001
26
1.5016
26
1.4929
26
1.4932
26
1.4865
26
1.4283
6
1.5056
26
1.5178
26
1.4917
26
1.4681
15
1.5213
26
1.4844
22
1.4736
13
1.4983
13
1.5669
3
 
ROHF 1.5420
5
1.5387
6
1.4681
7
1.5638
5
1.4481
7
1.4481
7
1.4486
7
1.4395
7
1.4382
6
1.4333
5
  1.4589
1
1.4639
7
1.4406
7
1.4367
4
1.4665
6
1.4402
6
1.4367
4
  1.6288
1
 
density functional LSDA 1.6299
26
1.5670
26
1.5331
26
1.6332
26
1.5327
26
1.5325
26
1.5349
26
1.5255
26
1.5259
26
1.5153
26
  1.5726
9
1.5517
26
1.5231
26
1.4636
5
1.5542
26
1.5127
10
1.4616
5
1.5884
3
1.5914
3
 
SVWN   1.6040
24
    1.5334
24
1.5659
9
1.5354
24
1.5594
9
1.5606
9
1.5487
9
    1.5850
9
1.5571
9
  1.5896
9
1.5562
5
  1.5884
3
1.5914
3
 
BLYP 1.6663
24
1.6313
25
1.5585
25
1.6651
25
1.5577
25
1.5575
25
1.5608
25
1.5511
25
1.5516
25
1.5395
25
  1.6110
8
1.5773
25
1.5480
25
  1.5255
6
    1.6177
3
1.6220
3
 
B1B95 1.6066
22
1.5378
22
1.5170
22
1.6176
22
1.5131
22
1.5138
22
1.5148
22
1.5064
22
1.5069
22
1.4993
22
  1.5665
9
1.5311
22
1.5044
22
1.4547
5
1.5332
22
1.5055
12
1.4531
5
1.5867
3
1.5891
3
 
B3LYP 1.6371
26
1.6070
26
1.5361
26
1.6387
26
1.5345
26
1.5342
26
1.5370
26
1.5278
26
1.5410
21
1.5178
26
1.4651
6
1.5414
26
1.5532
26
1.5253
26
1.5058
13
1.5625
24
1.5248
20
1.5054
13
1.5315
13
1.6000
3
 
B3LYPultrafine         1.5345
26
  1.4961
3
        1.6259
3
1.5845
5
1.5155
10
  1.5927
5
1.5261
23
  1.5967
3
1.6000
3
 
B3PW91 1.6495
20
1.6056
25
1.5346
25
1.6366
25
1.5327
25
1.5324
25
1.5344
25
1.5257
25
1.5398
20
1.5171
25
  1.5833
8
1.5514
25
1.5237
25
  1.5013
6
    1.5925
3
1.5952
3
 
mPW1PW91 1.6323
22
1.5997
26
1.5364
23
1.6302
26
1.5270
26
1.5267
26
1.5286
26
1.5199
26
1.5203
26
1.5117
26
  1.5694
9
1.5453
26
1.5237
24
  1.5505
15
1.5518
5
  1.5887
3
1.5911
3
 
M06-2X 1.6441
9
1.6243
9
1.5558
9
1.6575
9
1.5228
24
1.5591
9
1.5616
9
1.5539
9
1.5548
9
1.5451
9
  1.5651
9
1.5765
9
1.5520
9
  1.5809
9
1.5498
5
  1.5897
3
1.5919
3
 
PBEPBE 1.6656
21
1.6247
26
1.5660
20
1.6703
20
1.5507
26
1.5505
26
1.5528
26
1.5437
26
1.5442
26
1.5343
26
1.4809
6
1.5937
9
1.5699
26
1.5413
26
1.4788
5
1.6108
9
1.5433
9
1.4768
5
1.5820
4
1.6145
3
 
PBEPBEultrafine         1.5252
16
            1.6395
3
1.5997
5
1.5732
5
  1.6081
5
1.5760
5
  1.6109
3
1.6145
3
 
PBE1PBE 1.6356
5
1.5605
5
1.5605
5
1.6692
5
1.5196
22
1.5595
5
1.5630
5
1.5525
5
1.5537
5
1.5439
5
  1.5658
5
1.5770
5
1.5504
5
  1.5842
5
1.5524
5
  1.5891
3
1.5917
3
 
HSEh1PBE 1.6590
9
1.6347
9
1.5623
9
1.6690
9
1.5290
24
1.5643
9
1.5670
9
1.5581
9
1.5592
9
1.5489
9
  1.5709
9
1.5832
9
1.5559
9
  1.5875
9
1.5532
5
  1.5898
3
1.5924
3
 
TPSSh   1.6999
3
1.6142
3
1.7346
3
1.5818
25
1.6160
3
1.5827
25
1.6107
3
      1.6257
3
1.6365
3
1.5759
25
  1.6470
3
1.6114
3
  1.5981
3
1.6009
3
 
Moller Plesset perturbation MP2 1.6392
21
1.6117
26
1.5381
26
1.6444
26
1.5367
26
1.5394
25
1.5328
33
1.5240
26
1.5282
25
1.5226
25
  1.5367
26
1.5540
26
1.5295
25
1.5395
7
1.5723
24
1.5249
11
1.5404
7
1.5336
13
1.6011
3
1.4909
1
MP2=FULL 1.6413
20
1.6178
24
1.5482
22
1.6509
22
1.5353
26
1.5379
25
1.5438
25
1.5257
25
1.5409
20
1.5311
20
  1.5744
9
1.5567
24
1.5286
23
1.5360
7
1.5754
15
1.5260
8
1.5435
6
1.5296
13
1.5958
3
1.4890
1
ROMP2 1.5664
4
1.5647
4
1.5033
4
1.5818
3
1.4839
3
1.4839
3
1.4860
3
1.4735
4
1.4750
4
1.4682
3
  1.5183
1
1.5064
4
1.4730
3
1.4522
2
1.5047
3
1.4613
2
1.4527
2
     
MP3         1.5240
26
  1.5744
25
        1.6143
3
1.6284
3
1.5944
3
        1.5857
3
1.5892
3
 
MP3=FULL         1.5732
25
  1.5417
11
        1.6134
3
1.6267
3
1.5907
3
        1.5821
3
1.5848
3
 
MP4   1.6594
20
    1.5561
22
    1.4915
2
1.5447
16
    1.5791
5
1.6031
5
1.5430
22
  1.6177
5
1.5898
4
  1.6006
3
1.6064
3
 
MP4=FULL   1.6614
5
    1.5725
5
      1.5627
5
      1.6015
5
1.5673
5
  1.6148
5
1.5681
5
  1.5965
3
1.6014
3
 
B2PLYP         1.5163
15
                1.5852
16
             
B2PLYP=FULLultrafine         1.4781
3
                               
Configuration interaction CID   1.6032
21
1.5319
21
1.6455
19
1.5201
25
    1.5137
23
                    1.5800
3
1.5832
3
 
CISD   1.6069
21
1.5343
21
1.6493
19
1.5212
25
    1.5189
21
                    1.5814
3
1.5844
3
 
Quadratic configuration interaction QCISD   1.6176
26
1.5461
22
1.6687
22
1.5410
24
1.5438
22
1.5459
23
1.5277
24
1.5275
22
1.5333
18
  1.5736
9
1.5479
20
1.5190
16
  1.5975
9
1.5567
5
  1.5635
4
1.5956
3
 
QCISD(T)         1.5482
23
    1.5002
2
      1.5885
8
1.5670
13
1.5212
9
  1.5629
9
1.5303
8
  1.5973
3
1.6021
3
 
Coupled Cluster CCD   1.6099
22
1.5375
22
1.6491
22
1.5274
26
1.5371
22
1.5413
22
1.5188
24
1.5340
18
1.5253
18
  1.5667
9
1.5403
19
1.5156
14
  1.5587
14
1.5098
9
  1.5878
3
1.5916
3
 
CCSD         1.5333
25
    1.4753
2
      1.5870
4
1.5958
8
1.5624
8
1.5908
3
1.6144
4
1.5713
4
1.5649
2
1.5901
3
1.5940
3
 
CCSD=FULL         1.5663
5
            1.5682
5
1.5817
5
1.5465
5
1.5580
4
1.5925
5
1.5485
5
1.5873
3
1.5860
3
1.5891
3
 
CCSD(T)   1.6028
1
    1.5430
16
1.5071
2
1.4913
1
1.4881
2
1.4757
1
  1.4847
1
1.5874
8
1.5633
15
1.5234
18
1.5979
3
1.5611
11
1.5266
10
1.6002
3
1.5691
4
1.6013
3
1.4872
1
CCSD(T)=FULL         1.5578
12
            1.5750
9
1.5912
9
1.5448
6
1.5664
4
1.6012
9
1.5582
5
1.5664
4
1.5924
3
1.5963
3
1.4850
1

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 1.6230
26
1.5170
26
1.6206
26
1.5161
26
1.6079
26
1.6005
26
density functional B1B95 1.5917
6
1.4948
6
       
B3LYP 1.6478
26
1.5528
25
1.6464
25
1.5531
25
1.6322
26
1.6260
25
Moller Plesset perturbation MP2 1.6525
26
1.5552
26
1.6525
25
1.5570
26
1.6412
26
1.6247
26
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.