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Comparison of levels of theory for P-Si


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 1.7416
4
PM3 1.6289
4
PM6 1.9451
4
composite G2 2.1160
4
G3 2.1417
4
G3B3 2.1386
4
G4 2.1224
4
CBS-Q 2.1417
4

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 Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(T+d)Z cc-pCVTZ
hartree fock HF 2.0798
4
2.1789
3
2.1197
4
2.2323
4
2.1351
4
2.1351
4
2.1369
4
2.1332
4
2.1332
4
2.1236
4
  2.1378
4
2.0509
4
2.1425
4
2.1272
4
2.1220
4
2.1473
4
2.1286
4
2.1227
4
2.1037
1
2.1055
1
ROHF 2.0065
3
2.1975
3
2.0711
3
2.1877
3
2.0831
3
2.0831
3
2.0850
3
2.0821
3
2.0821
3
2.0465
3
  2.0551
1
  2.0896
3
2.0784
3
2.0747
3
2.0958
3
2.0806
3
2.0757
3
2.0447
1
2.0454
1
density functional LSDA 2.0566
4
2.1816
4
2.1126
4
2.2145
4
2.1292
4
2.1548
4
2.1294
4
2.1223
4
2.1223
4
2.1429
4
  2.0890
1
  2.1619
4
2.1442
4
2.0688
3
2.1635
4
2.1447
4
2.0688
3
2.0747
1
2.0770
1
BLYP 2.1108
4
2.2922
4
2.1703
4
2.2846
4
2.0973
4
2.1900
4
2.1906
4
2.1872
4
2.1872
4
2.1758
4
  2.1196
1
  2.1943
4
2.1777
4
    2.1109
1
  2.1042
1
2.1066
1
B1B95 2.0700
4
  2.1235
4
2.2312
4
2.1376
4
2.1376
4
2.1074
3
2.1351
4
2.1351
4
2.1294
4
  2.0756
1
  2.1453
4
2.1319
4
2.1034
4
2.1482
4
2.1328
4
2.1036
4
2.0643
1
2.0660
1
B3LYP 2.0847
4
2.2597
4
2.1407
4
2.2531
4
2.1580
4
2.1580
4
2.1587
4
2.1546
4
2.1546
4
2.1463
4
  2.1561
4
2.0691
4
2.1636
4
2.1485
4
2.1436
4
2.1662
4
2.1495
4
2.1439
4
2.0788
1
2.0808
1
B3LYPultrafine   2.1716
1
    2.1580
4
2.0952
1
2.0952
1
2.0912
1
      2.0929
1
  2.0993
1
2.0853
1
  2.1010
1
2.1876
3
  2.0788
1
2.0808
1
B3PW91 2.0794
4
2.2513
4
2.1343
4
2.2423
4
2.1484
4
2.1484
4
2.1490
4
2.1449
4
2.1449
4
2.1385
4
  2.0859
1
  2.1555
4
2.1411
4
        2.0732
1
2.0751
1
mPW1PW91 2.0735
4
2.2449
4
2.1284
4
2.2363
4
2.1420
4
2.1420
4
2.1426
4
2.1388
4
2.1388
4
2.1327
4
  2.0807
1
  2.1493
4
2.1355
4
  2.0898
1
2.0746
1
  2.0683
1
2.0701
1
M06-2X 1.9945
1
2.1419
1
2.0915
4
2.1499
1
2.1293
4
2.0708
1
2.0706
1
2.0675
1
2.0675
1
2.0638
1
  2.0709
1
  2.0775
1
2.0662
1
  2.0799
1
2.0661
1
  2.0611
1
2.0622
1
PBEPBE 2.0998
4
2.2774
4
2.1592
4
2.2679
4
2.1749
4
2.1749
4
2.1753
4
2.1726
4
2.1726
4
2.1630
4
  2.1089
1
2.0282
4
2.1807
4
2.1654
4
2.1352
4
2.2051
2
2.1885
2
2.1354
4
2.0949
1
2.0971
1
PBEPBEultrafine   2.1900
1
    2.1109
1
2.1109
1
2.1107
1
2.1075
1
      2.1089
1
  2.1157
1
2.1013
1
  2.1167
1
2.1013
1
  2.0949
1
2.0971
1
PBE1PBE 2.0096
1
  2.0711
1
2.1652
1
2.1425
4
2.0824
1
2.0823
1
2.0785
1
2.0785
1
2.0732
1
  2.0816
1
  2.0883
1
2.0753
1
  2.0904
1
2.0756
1
  2.0693
1
2.0710
1
HSEh1PBE 2.0110
1
2.2172
4
2.0724
1
2.1676
1
2.1449
4
2.0843
1
2.1456
4
2.0802
1
2.0802
1
2.0746
1
  2.0832
1
  2.0900
1
2.1136
4
  2.0920
1
2.0768
1
  2.0705
1
2.0723
1
TPSSh   2.1756
1
2.0811
1
2.1752
1
2.1235
4
2.0913
1
2.1235
4
2.0872
1
  2.0705
4
  2.0906
1
  2.0984
1
2.1182
4
  2.1001
1
2.0837
1
  2.0775
1
2.0794
1
wB97X-D     1.9905
4
  1.9958
4
  1.9956
4
  1.9935
4
    1.9958
4
  1.9956
4
1.9933
4
    1.9934
4
     
B97D3   2.0492
4
    2.0354
4
  2.0858
4
  2.0825
4
  2.0759
4
      2.0801
4
    2.1390
4
     
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 Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(T+d)Z cc-pCVTZ
Moller Plesset perturbation MP2 2.0893
4
2.2723
4
2.1044
4
2.2654
4
2.0440
4
2.1178
4
2.1181
4
2.0419
4
2.1130
4
2.1505
4
  2.1236
4
2.0630
4
2.1386
4
2.1192
4
1.9882
1
2.1784
4
2.1541
4
1.9883
1
1.9901
1
1.9898
1
MP2=FULL 2.0882
4
2.2881
4
2.1017
4
2.2760
4
2.1500
4
2.1500
4
2.1156
4
2.1122
4
2.1122
4
2.1080
4
  2.1367
1
  2.1691
4
2.1449
4
1.9856
1
2.2025
2
2.1139
4
1.9852
1
1.9863
1
1.9872
1
ROMP2 2.0573
3
2.0737
1
2.0986
3
2.2415
3
2.1131
3
2.1131
3
2.1137
3
2.1083
3
2.1083
3
2.1121
3
  2.0922
1
  2.1329
3
2.1131
3
2.0732
3
2.1398
3
2.0844
3
2.0748
3
2.0812
1
2.0813
1
MP3         2.1430
4
  2.1214
4
        2.0061
1
  2.1344
1
2.1170
1
        1.9955
1
1.9953
1
MP3=FULL         2.0881
4
  2.0879
4
        2.0068
1
  2.1335
1
1.9957
1
        1.9922
1
1.9936
1
MP4   2.3110
4
    2.1627
4
      2.1680
3
    2.0136
1
  2.1459
1
2.0923
3
  2.1503
1
2.1269
1
  2.0022
1
2.1215
1
MP4=FULL   2.2441
1
    2.1347
1
      2.0025
1
        2.1439
1
2.0022
1
  2.1486
1
2.0011
1
  1.9979
1
2.1199
1
B2PLYP 1.9874
1
2.1526
1
2.0751
1
2.1549
1
2.1520
4
2.0885
1
2.0890
1
2.0860
1
2.0860
1
2.0833
1
  2.0905
1
  2.0981
1
2.1182
4
  2.1030
1
2.0861
1
  2.0793
1
2.0805
1
B2PLYP=FULL 1.9873
1
2.1527
1
2.0743
1
2.1548
1
2.0877
1
2.0877
1
2.0882
1
2.0858
1
2.0858
1
2.0802
1
  2.0907
1
  2.0974
1
2.0832
1
  2.1022
1
2.0831
1
  2.0766
1
2.0789
1
Configuration interaction CID   2.2697
4
2.0991
4
2.2593
4
2.1143
4
    2.1082
4
                      2.0052
1
2.0052
1
CISD   2.2888
4
2.1098
4
2.2742
4
2.1255
4
    2.1199
4
                      2.0247
1
2.0249
1
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 Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(T+d)Z cc-pCVTZ
Quadratic configuration interaction QCISD   2.3376
4
2.1281
4
2.3117
4
2.1449
4
2.1449
4
2.1456
4
2.1403
4
2.1403
4
2.1442
4
  2.1137
1
  2.1696
4
2.1444
4
  2.1226
1
2.1023
1
  2.0983
1
2.0981
1
QCISD(T)         2.1544
4
            2.1010
1
  2.1781
4
2.1513
4
  2.1866
4
2.1532
4
  2.0842
1
2.0843
1
QCISD(T)=FULL         2.0939
1
  2.0940
1
            2.1107
1
2.0834
1
2.0759
1
2.1264
1
2.0806
1
2.0749
1
2.0762
1
2.0791
1
QCISD(TQ)         2.1056
1
  2.1057
1
            2.1229
1
2.1006
1
2.0906
1
2.1423
1
2.1024
1
     
QCISD(TQ)=FULL             2.1023
1
            2.1202
1
2.0935
1
  2.1390
1
       
Coupled Cluster CCD   2.2793
4
2.1006
4
2.2687
4
2.1158
4
2.1158
4
2.1162
4
2.1098
4
2.1098
4
2.1121
4
  2.0174
1
  2.1621
4
2.1126
4
  2.1687
4
2.0811
3
  2.0005
1
2.0004
1
CCSD         2.1408
4
        2.0982
1
  2.0911
1
  2.1144
1
2.0771
1
2.0655
1
2.1199
1
  2.0659
1
2.0710
1
2.0711
1
CCSD=FULL         2.0846
1
        2.0670
1
  2.0911
1
  2.1134
1
2.0697
1
2.0600
1
2.1187
1
2.0665
1
2.0593
1
2.0611
1
2.0638
1
CCSD(T)         2.0951
1
            2.0990
1
  2.1753
4
2.1487
4
2.1104
3
2.1812
4
2.1508
4
2.1118
3
2.0808
1
2.0809
1
CCSD(T)=FULL         2.0624
2
            2.0996
1
  2.1095
1
2.0800
1
2.1058
3
2.1131
1
2.0768
1
2.1058
3
2.0716
1
2.0752
1
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 Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(T+d)Z cc-pCVTZ

average calculated bond lengths (Å)
Methods with effective core potentials (select basis sets)
daug-cc-pVDZ daug-cc-pVTZ daug-cc-pVQZ Sadlej_pVTZ CEP-31G CEP-31G* CEP-121G CEP-121G* LANL2DZ SDD
hartree fock HF         2.2468
4
2.1532
4
2.2484
4
2.1492
4
2.2209
4
2.1769
3
density functional B3LYP         2.2776
4
2.1769
4
2.2771
4
2.1746
4
2.2508
4
2.2629
4
Moller Plesset perturbation MP2         2.2944
4
2.1773
4
2.2916
4
2.1738
4
2.2640
4
2.2835
4
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.