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III.G.1.a.

Comparison of levels of theory for P-P


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 1.6730
4
PM3 2.0070
12
PM6 2.0740
12
composite G2 2.0597
12
G3 2.0597
12
G3B3 2.1039
12
G4 2.1141
10
CBS-Q 2.0597
12

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(D+d)Z cc-pV(T+d)Z aug-cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ
hartree fock HF 2.0289
12
2.2274
12
2.0499
12
2.1985
12
2.0911
22
2.0598
12
2.0604
12
2.0593
12
2.0594
12
2.0606
12
2.1062
9
2.0703
12
2.0791
12
2.0634
12
2.0775
11
2.0820
12
2.0636
12
1.9592
5
1.8571
1
2.1384
8
1.8517
1
1.8654
2
1.8519
2
ROHF         1.9562
1
                                   
density functional LSDA 2.0850
12
2.2151
12
2.0767
12
2.2251
12
2.0940
12
2.0940
12
2.0938
12
2.0892
12
2.0893
12
2.0841
12
  1.9020
2
2.1081
12
2.0861
12
1.9786
2
2.1090
12
1.9378
4
1.9761
2
1.8980
1
1.8878
1
1.8873
1
   
SVWN   2.2475
12
    2.1134
10
1.9042
2
2.0939
12
1.8940
2
1.8940
2
1.8928
2
    1.9109
2
1.8944
2
  1.9125
2
1.8943
2
      1.8873
1
   
BLYP 2.1144
12
2.2913
12
2.1172
12
2.2709
12
2.1351
12
2.1351
12
2.1352
12
2.1332
12
2.1333
12
2.1243
12
  1.9279
2
2.1473
12
2.1264
12
  2.1979
9
    1.9205
1
1.9113
1
1.9109
1
   
B1B95 2.0713
12
2.2132
12
2.0664
12
2.2136
12
2.0779
12
2.0802
12
2.0803
12
2.0791
12
2.0791
12
2.0761
12
  1.8873
2
2.0962
12
2.0762
12
1.9666
2
2.0957
12
1.9257
4
1.9645
2
1.8842
1
1.8766
1
1.8763
1
   
B3LYP 2.0883
12
2.2625
12
2.0888
12
2.2402
12
2.1055
12
2.1052
12
2.1053
12
2.1029
12
1.9435
4
2.0970
12
2.1374
9
2.1095
12
2.1190
12
2.0991
12
1.9961
5
2.1202
12
2.0990
12
1.9953
5
1.8971
1
2.1685
8
1.8884
1
   
B3LYPultrafine         2.1056
12
            1.9036
1
1.9101
2
2.0121
3
  1.9122
2
2.0951
11
      1.8884
1
   
B3PW91 1.9188
4
2.2512
12
2.0781
12
2.2253
12
2.0919
12
2.0919
12
2.0920
12
2.0896
12
1.9349
4
2.0859
12
  1.8965
2
2.1071
12
2.0881
12
  2.1565
9
    1.8924
1
1.8842
1
1.8840
1
   
mPW1PW91 1.9125
4
2.2451
12
1.9262
4
2.2187
12
2.0857
12
2.0857
12
2.0858
12
2.0837
12
2.0838
12
2.0804
12
  1.8914
2
2.1012
12
2.0828
12
  2.1259
10
1.8856
2
  1.8877
1
1.8799
1
1.8797
1
   
M06-2X 1.8525
2
1.9566
2
1.8700
2
1.9669
2
2.0767
12
1.8820
2
1.8823
2
1.8746
2
1.8746
2
1.8766
2
  1.8827
2
1.8902
2
1.8782
2
  1.8929
2
1.8781
2
  1.8793
1
1.8724
1
1.8721
1
   
PBEPBE 1.9399
4
2.2723
12
1.9530
4
2.0567
4
2.1133
12
2.1133
12
2.1133
12
2.1118
12
2.1118
12
2.1054
12
2.1438
9
1.9181
2
2.0128
6
2.1079
12
1.9970
2
1.9270
2
2.1293
10
1.9943
2
1.9129
1
1.9044
1
1.9044
1
   
PBEPBEultrafine         2.1440
11
            1.9189
1
1.9251
2
1.9112
2
  1.9269
2
1.9114
2
      1.9044
1
   
PBE1PBE 1.8671
2
1.8813
2
1.8813
2
1.9773
2
2.0770
12
1.8914
2
1.8916
2
1.8837
2
1.8837
2
1.8839
2
  1.8921
2
1.8992
2
1.8863
2
  1.9016
2
1.8865
2
      1.8807
1
   
HSEh1PBE 1.8683
2
1.9722
2
1.8822
2
1.9792
2
2.0957
11
1.8927
2
1.8929
2
1.8848
2
1.8848
2
1.8849
2
  1.8931
2
1.9003
2
1.8871
2
  1.9029
2
1.8873
2
  1.8894
1
1.8818
1
1.8816
1
   
TPSSh   1.9750
1
1.8952
1
1.9793
1
2.1092
11
1.9020
1
2.1094
11
1.8957
1
      1.9030
1
1.9091
1
2.1071
11
  1.9103
1
1.8946
1
      1.8885
1
   
Moller Plesset perturbation MP2 1.9989
4
2.3469
12
2.0831
12
2.3160
12
2.1011
12
2.1010
12
2.1174
14
2.1004
12
2.1006
12
2.1021
12
  2.1146
12
2.1299
12
2.1046
12
2.1007
10
2.1384
12
1.9996
6
1.9536
4
1.9342
1
2.1666
8
1.9203
1
2.1613
8
1.9194
2
MP2=FULL 1.9984
4
2.3483
12
1.9521
4
2.1334
4
2.0984
12
2.0984
12
2.0991
12
2.0997
12
1.9608
4
1.9526
4
  1.9337
2
2.1277
12
2.0853
11
2.0956
10
2.1482
9
1.9161
3
1.9614
3
1.9310
1
2.1527
8
1.9097
1
2.1587
8
1.9136
2
MP3         2.0906
12
  2.1072
11
        1.9018
1
1.9130
1
1.8943
1
        1.9017
1
1.8887
1
1.8896
1
   
MP3=FULL         2.1059
11
  2.1291
10
        1.9031
1
1.9115
1
1.8912
1
            1.8821
1
   
MP4   2.1728
4
    2.1097
12
    2.0284
3
1.9686
4
    1.9428
2
1.9536
2
2.0072
5
  1.9588
2
1.9314
2
  1.9354
1
1.9222
1
1.9226
1
   
MP4=FULL   2.1768
2
    1.9350
2
      1.9297
2
      1.9514
2
1.9249
2
  1.9563
2
1.9214
2
      1.9135
1
   
B2PLYP 1.8895
1
2.0094
1
1.9048
1
2.0161
1
2.1206
11
1.9172
1
1.9171
1
1.9099
1
1.9099
1
1.9090
1
  1.9176
1
1.9247
1
2.1370
10
  1.9270
1
1.9088
1
  1.9118
1
1.9020
1
1.9021
1
   
B2PLYP=FULL 1.8894
1
2.0097
1
1.9044
1
2.0162
1
1.9165
1
1.9165
1
1.9164
1
1.9098
1
1.9098
1
1.9065
1
  1.9179
1
1.9241
1
1.9075
1
  1.9264
1
1.9066
1
      1.8993
1
   
B2PLYP=FULLultrafine         2.2301
1
                                   
Configuration interaction CID   2.0482
4
1.9183
4
2.0485
4
2.0774
12
    1.9655
6
                        1.8766
1
   
CISD   2.0524
4
1.9210
4
2.0519
4
2.0791
12
    1.9245
4
                        1.8788
1
   
Quadratic configuration interaction QCISD   2.3116
12
1.9364
4
2.0770
4
2.0957
12
1.9507
4
1.9897
6
2.0948
12
2.0819
11
1.9424
4
  1.9100
2
2.0051
6
1.9421
4
  1.9254
2
1.8992
2
  1.9114
1
1.8955
1
1.8956
1
   
QCISD(T)         2.0009
6
    2.0227
3
      1.9247
2
1.9811
4
1.9585
4
  1.9855
4
1.9585
4
  1.9261
1
1.9110
1
1.9112
1
   
Coupled Cluster CCD   2.0699
4
1.9303
4
2.0690
4
2.0911
12
1.9441
4
1.9435
4
1.9783
6
1.9353
4
1.9369
4
  1.9035
2
2.0024
6
1.9363
4
  1.9635
4
1.9363
4
  1.9061
1
1.8897
1
1.8902
1
   
CCSD         2.1037
11
    2.0116
3
      1.9071
2
1.9179
2
1.8965
2
1.8894
1
1.9233
2
1.8972
2
1.8895
1
1.9095
1
1.8936
1
1.8938
1
   
CCSD=FULL         1.9009
2
            1.9073
2
1.9159
2
1.8915
2
1.8866
1
1.9211
2
1.8885
2
1.8859
1
    1.8848
1
   
CCSD(T)   2.0210
1
    2.1132
11
2.0239
3
1.9210
1
2.0219
3
1.9126
1
  1.9071
2
1.9230
2
2.1236
11
2.0954
11
1.9054
1
2.1303
11
2.0958
11
1.9053
1
1.9249
1
1.9095
1
1.9101
1
2.1684
8
2.1342
8
CCSD(T)=FULL         2.0905
11
            1.9235
2
2.1433
9
2.1072
9
1.9023
1
2.1510
9
1.9064
3
1.9020
1
1.9231
1
1.9058
1
1.9011
1
2.1658
8
1.9052
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 2.2011
12
2.0917
12
2.2029
12
2.0866
12
2.2207
12
2.2183
12
density functional B1B95 2.2974
9
2.2033
8
       
B3LYP 2.2582
12
2.1360
12
2.2562
12
2.1330
12
2.2777
12
2.2611
12
Moller Plesset perturbation MP2 2.3246
12
2.1456
12
2.3197
12
2.1413
12
2.3443
12
2.3372
12
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.