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Comparison of levels of theory for P-Al


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 1.7243
2
PM3 2.0083
2
PM6 2.2428
2
composite G2 2.1080
1
G3 2.1811
2
G3B3 2.1672
2
G4 2.1615
2
CBS-Q 2.1811
2

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
hartree fock HF 2.0072
2
2.2950
2
2.1702
2
2.3077
2
2.1881
2
2.1881
2
2.1903
2
2.1824
2
2.1824
2
2.1818
2
  2.1930
2
2.1772
2
2.2044
2
2.1898
2
2.1839
2
2.2128
2
2.1926
2
2.1847
2
ROHF   2.3905
1
2.2473
1
2.4009
1
2.2695
1
2.2695
1
2.2713
1
2.2624
1
2.2624
1
    2.2732
1
  2.2800
1
2.2647
1
2.2585
1
2.2891
1
2.2677
1
2.2594
1
density functional LSDA 1.9926
2
  2.1262
2
2.1984
2
2.1384
2
2.1384
2
2.1388
2
2.1301
2
2.1301
2
2.1284
2
  2.1370
2
  2.1500
2
2.1323
2
  2.1517
2
2.1322
2
 
BLYP 2.1327
2
2.2331
2
2.1647
2
2.2463
2
2.2582
2
2.1821
2
2.1829
2
2.1751
2
2.1751
2
2.1713
2
  2.1812
2
  2.1920
2
2.1754
2
       
B1B95 1.9923
2
  2.1332
2
2.2135
2
2.1444
2
2.1444
2
2.1448
2
2.1380
2
2.1380
2
2.1396
2
  2.1465
2
  2.1584
2
2.1448
2
  2.1615
2
2.1455
2
 
B3LYP 2.0080
2
2.2231
2
2.1488
2
2.2351
2
2.1644
2
2.1644
2
2.1653
2
2.1579
2
2.1579
2
2.1554
2
  2.1649
2
2.1601
2
2.1761
2
2.1602
2
2.1541
2
2.1798
2
2.1612
2
2.1545
2
B3LYPultrafine   2.2232
2
    2.1645
2
2.1645
2
2.1653
2
2.1580
2
      2.1650
2
  2.1761
2
2.1603
2
  2.1798
2
2.1612
2
 
B3PW91 2.0001
2
2.2126
2
2.1406
2
2.2203
2
2.1516
2
2.1516
2
2.1520
2
2.1446
2
2.1446
2
2.1444
2
  2.1527
2
  2.1646
2
2.1494
2
       
mPW1PW91 1.9964
2
2.2106
2
2.1372
2
2.2180
2
2.1477
2
2.1477
2
2.1481
2
2.1409
2
2.1409
2
2.1410
2
  2.1491
2
  2.1609
2
2.1461
2
  2.1642
2
2.1468
2
 
M06-2X 1.9929
2
2.2123
2
2.1228
3
2.2259
2
2.1507
2
2.1507
2
2.1515
2
2.1449
2
2.1449
2
2.1464
2
  2.1563
2
  2.1646
2
2.1541
2
  2.1688
2
2.1548
2
 
PBEPBE 2.1199
2
2.2176
2
2.1521
2
2.2259
2
2.1636
2
2.1636
2
2.1642
2
2.1569
2
2.1569
2
2.1553
2
  2.1638
2
2.2477
2
2.1750
2
2.1597
2
  2.1778
2
2.1602
2
 
PBEPBEultrafine   2.2178
2
    2.1635
2
2.1635
2
2.1642
2
2.1569
2
      2.1638
2
  2.1750
2
2.1596
2
  2.1777
2
2.1601
2
 
PBE1PBE 1.9949
2
  2.1376
2
2.2181
2
2.1479
2
2.1479
2
2.1483
2
2.1414
2
2.1414
2
2.1413
2
  2.1494
2
  2.1610
2
2.1465
2
  2.1642
2
2.1473
2
 
HSEh1PBE 1.9965
2
2.2126
2
2.1386
2
2.2203
2
2.1496
2
2.1496
2
2.1501
2
2.1429
2
2.1429
2
2.1425
2
  2.1508
2
  2.1626
2
2.1476
2
  2.1662
2
2.1483
2
 
TPSSh   2.2167
2
2.1442
2
2.2195
2
2.1509
2
2.1509
2
2.1512
2
2.1438
2
  2.1535
2
  2.1526
2
  2.1646
2
2.1492
2
  2.1677
2
2.1497
2
 
wB97X-D     2.1432
2
  2.1539
2
  2.1547
2
  2.1496
2
    2.1551
2
  2.1547
2
2.1544
2
    2.1551
2
 
B97D3   2.2788
2
    2.2556
2
  2.2008
2
  2.2540
2
  2.2513
2
      2.2537
2
    2.2408
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
Moller Plesset perturbation MP2 1.9806
2
2.2119
2
2.1154
2
2.2204
2
2.1361
2
2.1267
2
2.1277
2
2.1318
2
2.1203
2
2.1261
2
  2.1338
2
2.1357
2
2.1515
2
2.1317
2
2.1204
2
2.1591
2
2.1338
2
2.1212
2
MP2=FULL 1.9801
2
2.2119
2
2.1122
2
2.2201
2
2.1231
2
2.1231
2
2.1242
2
2.1195
2
2.1195
2
2.1145
2
  2.1338
2
  2.1487
2
2.1227
2
2.0895
2
2.1556
2
2.1190
2
2.0869
2
ROMP2 2.0583
1
  2.1736
1
2.2838
1
2.1810
1
2.1810
1
2.1857
1
2.1852
1
2.1852
1
2.1842
1
  2.1846
1
  2.1993
1
2.1864
1
  2.2124
1
   
MP3         2.1410
2
  2.1424
2
        2.1506
2
  2.1728
2
2.1489
2
       
MP3=FULL         2.1381
2
  2.1397
2
        2.1518
2
  2.1704
2
2.1405
2
       
MP4   2.2324
2
    2.1487
2
      2.1414
2
    2.1573
2
  2.1789
2
2.1537
2
  2.1874
2
2.1563
2
 
MP4=FULL   2.2326
2
    2.1452
2
      2.1409
2
        2.1762
2
2.1449
2
  2.1835
2
2.1412
2
 
B2PLYP 2.0009
2
2.2217
2
2.1403
2
2.2320
2
2.1541
2
2.1541
2
2.1550
2
2.1477
2
2.1477
2
2.1490
2
  2.1570
2
  2.1706
2
2.1540
2
  2.1759
2
2.1557
2
 
B2PLYP=FULL 2.0007
2
2.2218
2
2.1392
2
2.2319
2
2.1527
2
2.1527
2
2.1537
2
2.1473
2
2.1473
2
2.1448
2
  2.1568
2
  2.1696
2
2.1509
2
  2.1747
2
2.1507
2
 
Configuration interaction CID   2.2424
2
2.1353
2
2.2544
2
2.1496
2
    2.1429
2
                     
CISD   2.2518
2
2.1427
2
2.2629
2
2.1571
2
    2.1498
2
                     
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
Quadratic configuration interaction QCISD   2.2705
2
2.1600
2
2.2824
2
2.1753
2
2.1753
2
2.1763
2
2.1672
2
2.1672
2
2.1728
2
  2.1831
2
  2.2063
2
2.1768
2
  2.2140
2
2.1793
2
 
QCISD(T)         2.1746
2
            2.1823
2
  2.2070
2
2.1769
2
  2.2138
2
2.1798
2
 
QCISD(T)=FULL         2.1703
2
  2.1713
2
            2.2036
2
2.1665
2
2.1263
2
2.2095
2
2.1622
2
2.1239
2
QCISD(TQ)         2.1714
2
  2.1726
2
            2.2049
2
2.1768
2
2.1633
2
2.2129
2
2.1800
2
2.1646
2
QCISD(TQ)=FULL         2.1677
2
                2.1385
1
  2.1885
1
2.2087
2
2.1627
2
 
Coupled Cluster CCD   2.2395
2
2.1365
2
2.2515
2
2.1508
2
2.1508
2
2.1523
2
2.1442
2
2.1442
2
2.1529
2
  2.1609
2
  2.1845
2
2.1584
2
  2.1941
2
2.1613
2
 
CCSD         2.1660
2
            2.1749
2
  2.1981
2
2.1707
2
2.1574
2
2.2067
2
2.1734
2
2.1584
2
CCSD=FULL         2.1622
2
            2.1747
2
  2.1949
2
2.1604
2
2.1215
2
2.2027
2
2.1563
2
2.1189
2
CCSD(T)         2.1687
2
            2.1763
2
  2.2002
2
2.1719
2
2.1583
2
2.2079
2
2.1745
2
2.1597
2
CCSD(T)=FULL         2.1642
2
            2.1756
2
  2.1970
2
2.1615
2
2.1223
2
2.2037
2
2.1577
2
2.1200
2
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

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         2.3214
2
2.2040
2
2.3192
2
2.2021
2
2.3105
2
2.3023
2
density functional B3LYP         2.2546
2
2.1835
2
2.2547
2
2.1831
2
2.2432
2
2.2247
2
Moller Plesset perturbation MP2         2.2391
2
2.1598
2
2.2326
2
2.1506
2
2.2207
2
2.2107
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.