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Comparison of levels of theory for Al-Na


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 PM3 2.7556
1
PM6 2.5906
1
composite G2 3.2019
1
G3 3.2019
1
G3B3 3.1697
1
G4 3.1642
1
CBS-Q 3.2019
1

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-pCVTZ aug-cc-pCVTZ
hartree fock HF 2.4629
1
3.2627
1
3.2137
1
3.2284
1
3.2030
1
3.2030
1
3.1980
1
3.2155
1
3.2155
1
3.2065
1
  3.2424
1
3.2078
1
3.2170
1
3.2111
1
3.2080
1
3.2177
1
3.2098
1
3.2079
1
3.2089
1
3.2077
1
density functional LSDA 2.4956
1
3.1030
1
3.1030
1
3.1007
1
3.0889
1
3.0889
1
3.0890
1
3.0873
1
3.0873
1
3.0723
1
  3.1059
1
  3.0954
1
3.0817
1
  3.0889
1
3.0801
1
  3.0825
1
3.0821
1
BLYP 2.5281
1
3.1925
1
3.1590
1
3.1846
1
3.1717
1
3.1717
1
3.1712
1
3.1720
1
3.1720
1
3.1584
1
  3.1889
1
  3.1728
1
3.1648
1
  3.1680
1
3.1637
1
  3.1677
1
3.1676
1
B1B95 2.4926
1
  3.1557
1
3.1544
1
3.1409
1
3.1409
1
3.1394
1
3.1475
1
3.1475
1
3.1351
1
  3.1716
1
  3.1487
1
3.1427
1
  3.1468
1
3.1415
1
  3.1427
1
3.1421
1
B3LYP 2.5056
1
3.1757
1
3.1395
1
3.1599
1
3.1457
1
3.1457
1
3.1444
1
3.1473
1
3.1473
1
3.1353
1
  3.1641
1
3.1680
1
3.1481
1
3.1410
1
3.1373
1
3.1444
1
3.1400
1
3.1347
1
3.1419
1
3.1415
1
B3LYPultrafine   3.1755
1
    3.1458
1
3.1458
1
3.1444
1
3.1474
1
      3.1644
1
  3.1482
1
3.1412
1
  3.1445
1
3.1402
1
  3.1420
1
3.1417
1
B3PW91 2.5002
1
3.2087
1
3.1741
1
3.1697
1
3.1553
1
3.1553
1
3.1545
1
3.1619
1
3.1619
1
3.1483
1
  3.1842
1
  3.1631
1
3.1542
1
  3.1612
1
3.1533
1
  3.1544
1
3.1539
1
mPW1PW91 2.4944
1
3.2035
1
3.1685
1
3.1657
1
3.1508
1
3.1508
1
3.1495
1
3.1581
1
3.1581
1
3.1449
1
  3.1810
1
  3.1588
1
3.1505
1
  3.1571
1
3.1493
1
  3.1505
1
3.1497
1
M06-2X 2.4804
1
3.1550
1
3.1200
1
3.1035
1
3.0933
1
3.0933
1
3.0916
1
3.0960
1
3.0960
1
3.0855
1
  3.1139
1
  3.1004
1
3.0934
1
  3.0989
1
3.0926
1
  3.0915
1
3.0914
1
PBEPBE 2.5163
1
3.1978
1
3.1661
1
3.1750
1
3.1617
1
3.1617
1
3.1608
1
3.1664
1
3.1664
1
3.1514
1
  3.1871
1
3.1795
1
3.1672
1
3.1579
1
  3.1629
1
3.1559
1
  3.1596
1
3.1586
1
PBEPBEultrafine   3.1976
1
    3.1616
1
3.1616
1
3.1607
1
3.1665
1
      3.1873
1
  3.1672
1
3.1578
1
  3.1628
1
3.1558
1
  3.1596
1
3.1585
1
PBE1PBE 2.4930
1
  3.1572
1
3.1608
1
3.1456
1
3.1456
1
3.1444
1
3.1528
1
3.1528
1
3.1395
1
  3.1741
1
  3.1530
1
3.1451
1
  3.1510
1
3.1438
1
  3.1451
1
3.1443
1
HSEh1PBE 2.4943
1
3.1953
1
3.1596
1
3.1670
1
3.1516
1
3.1516
1
3.1504
1
3.1580
1
3.1580
1
3.1445
1
  3.1784
1
  3.1582
1
3.1504
1
  3.1561
1
3.1492
1
  3.1502
1
3.1495
1
TPSSh 2.5092
1
3.2208
1
3.1866
1
3.1944
1
3.1778
1
3.1778
1
3.1771
1
3.1856
1
3.1856
1
3.1722
1
  3.2100
1
  3.1870
1
3.1774
1
3.1747
1
3.1855
1
3.1763
1
3.1727
1
3.1773
1
3.1767
1
wB97X-D 2.4842
1
3.2451
1
3.2000
1
3.1549
1
3.1420
1
3.1420
1
3.1390
1
3.1438
1
3.1438
1
3.1374
1
  3.1647
1
  3.1513
1
3.1438
1
3.1385
1
3.1493
1
3.1434
1
3.1364
1
3.1412
1
3.1410
1
B97D3 2.5309
1
3.4340
1
3.4112
1
3.4282
1
3.4146
1
3.4146
1
3.4126
1
3.4200
1
3.4200
1
3.4088
1
3.2474
1
3.4368
1
  3.4177
1
3.4136
1
3.4068
1
3.4145
1
3.4138
1
3.4000
1
3.4136
1
3.4132
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-pCVTZ aug-cc-pCVTZ
Moller Plesset perturbation MP2 2.4771
1
3.2796
1
3.1681
1
3.2392
1
3.1519
1
3.1519
1
3.1496
1
3.1591
1
3.1591
1
3.1723
1
  3.2200
1
3.1882
1
3.2062
1
3.1770
1
3.1728
1
3.2118
1
3.1785
1
3.1735
1
3.1749
1
3.1760
1
MP2=FULL 2.4725
1
3.2794
1
3.1588
1
3.2371
1
3.1343
1
3.1343
1
3.1354
1
3.1382
1
3.1382
1
3.1114
1
  3.2101
1
  3.2000
1
3.1287
1
3.0731
1
3.2008
1
3.1300
1
2.9867
1
3.1281
1
3.1275
1
ROMP2 2.4769
1
  3.1682
1
3.2389
1
3.1520
1
3.1520
1
3.1497
1
3.1591
1
3.1591
1
3.1723
1
  3.2201
1
  3.2062
1
3.1771
1
  3.2119
1
    3.1752
1
3.1764
1
MP3         3.1388
1
  3.1371
1
        3.2219
1
  3.2073
1
3.1721
1
        3.1704
1
3.1717
1
MP3=FULL   3.2977
1
3.1472
1
3.2545
1
3.1218
1
3.1218
1
3.1236
1
3.1285
1
3.1285
1
3.1087
1
  3.2159
1
  3.2008
1
3.1242
1
  3.2050
1
3.1260
1
  3.1307
1
3.1303
1
MP4   3.3090
1
    3.1398
1
      3.1482
1
    3.2325
1
  3.2141
1
3.1761
1
  3.2217
1
3.1788
1
  3.1749
1
3.1765
1
MP4=FULL   3.3086
1
    3.1223
1
      3.1284
1
        3.2075
1
3.1265
1
  3.2114
1
3.1280
1
  3.1344
1
3.1339
1
B2PLYP 2.4911
1
3.2032
1
3.1421
1
3.1812
1
3.1427
1
3.1427
1
3.1408
1
3.1460
1
3.1460
1
3.1450
1
  3.1784
1
  3.1625
1
3.1496
1
  3.1619
1
3.1496
1
  3.1485
1
3.1485
1
B2PLYP=FULL 2.4899
1
3.2032
1
3.1388
1
3.1805
1
3.1365
1
3.1365
1
3.1357
1
3.1387
1
3.1387
1
3.1241
1
  3.1753
1
  3.1602
1
3.1336
1
  3.1580
1
3.1334
1
  3.1334
1
3.1330
1
B2PLYP=FULLultrafine 2.4897
1
3.2030
1
3.1390
1
3.1807
1
3.1365
1
3.1365
1
3.1357
1
3.1387
1
3.1387
1
3.1240
1
  3.1755
1
  3.1603
1
3.1336
1
  3.1581
1
3.1335
1
  3.1335
1
3.1331
1
Configuration interaction CID   3.3028
1
3.1531
1
3.2628
1
3.1365
1
    3.1461
1
                      3.1662
1
3.1669
1
CISD   3.3047
1
3.1609
1
3.2630
1
3.1437
1
    3.1533
1
                      3.1713
1
3.1718
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-pCVTZ aug-cc-pCVTZ
Quadratic configuration interaction QCISD   3.3242
1
3.1640
1
3.2819
1
3.1461
1
3.1461
1
3.1446
1
3.1565
1
3.1565
1
3.1716
1
  3.2472
1
  3.2161
1
3.1753
1
  3.2210
1
3.1762
1
  3.1730
1
3.1733
1
QCISD(T)         3.1498
1
    3.1599
1
      3.2562
1
  3.2220
1
3.1786
1
  3.2281
1
3.1795
1
  3.1760
1
3.1759
1
QCISD(T)=FULL         3.1321
1
  3.1346
1
            3.2152
1
3.1281
1
3.0699
1
3.2176
1
3.1289
1
2.9794
1
3.1402
1
3.1381
1
QCISD(TQ)         3.1499
1
  3.1484
1
            3.2230
1
3.1786
1
3.1762
1
3.2296
1
3.1795
1
3.1758
1
   
QCISD(TQ)=FULL         3.1325
1
  3.1351
1
            3.2165
1
3.1289
1
3.0707
1
3.2195
1
3.1299
1
2.9803
1
   
Coupled Cluster CCD   3.3186
1
3.1519
1
3.2789
1
3.1349
1
3.1349
1
3.1339
1
3.1454
1
3.1454
1
3.1647
1
  3.2291
1
  3.2066
1
3.1682
1
  3.2128
1
3.1693
1
  3.1662
1
3.1667
1
CCSD         3.1465
1
        3.1706
1
  3.2462
1
  3.2152
1
3.1742
1
3.1721
1
3.2202
1
3.1751
1
3.1721
1
3.1719
1
3.1722
1
CCSD=FULL         3.1297
1
        3.1119
1
  3.2399
1
  3.2091
1
3.1262
1
3.0718
1
3.2105
1
3.1272
1
2.9845
1
3.1379
1
3.1366
1
CCSD(T)         3.1500
1
3.1500
1
3.1486
1
3.1600
1
3.1600
1
3.1735
1
  3.2557
1
  3.2215
1
3.1780
1
3.1759
1
3.2277
1
3.1791
1
3.1756
1
3.1755
1
3.1754
1
CCSD(T)=FULL         3.1325
1
            3.2503
1
  3.2149
1
3.1282
1
3.0701
1
3.2173
1
3.1290
1
2.9797
1
3.1403
1
3.1382
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-pCVTZ aug-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         3.2139
1
3.2088
1
3.2431
1
3.2198
1
3.2475
1
3.2591
1
density functional B3LYP         3.2142
1
3.1993
1
3.2184
1
3.2000
1
3.2419
1
3.1729
1
wB97X-D         3.1845
1
3.1729
1
3.1958
1
3.1761
1
3.2075
1
3.1783
1
Moller Plesset perturbation MP2         3.2657
1
3.1859
1
3.2618
1
3.1771
1
3.2840
1
3.2709
1
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.