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Comparison of levels of theory for Si-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 1.7268
3
PM3 1.6537
2
PM6 1.9092
5
composite G2 2.1594
4
G3 2.1594
4
G3B3 2.2053
4
G4 2.2507
5
CBS-Q 2.1594
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 cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(T+d)Z
hartree fock HF 2.1181
3
2.2392
4
2.1688
4
2.2429
4
2.2102
5
2.1598
4
2.1628
4
2.1613
4
2.1689
3
2.1623
4
2.2512
2
2.1689
5
2.1740
4
2.1849
4
2.1697
3
2.1990
4
2.1763
3
2.1710
3
2.3652
1
density functional LSDA 2.1632
4
2.1524
3
2.1408
3
2.2384
4
2.1902
4
2.1587
3
2.1599
3
2.1865
4
2.1543
3
2.1520
3
    2.1669
3
2.1522
3
2.0909
1
2.1684
3
2.0714
2
2.0915
1
 
SVWN   2.2296
5
    2.2372
3
  2.1898
5
        2.1870
5
             
BLYP 2.1485
3
2.2285
4
2.2078
4
2.2440
4
2.2305
5
2.2286
4
2.2296
4
2.2267
4
2.1947
3
2.1917
3
2.2998
1
  2.2348
4
2.1909
4
  2.3739
1
     
B1B95 2.1503
3
2.1561
3
2.1459
3
2.2008
3
2.1589
3
2.1595
3
2.1609
3
2.1585
3
2.1590
3
2.1594
3
    2.1702
3
2.1595
3
2.0681
2
2.1718
3
2.0748
2
2.0687
2
 
B3LYP 2.1648
3
2.2113
4
2.1875
4
2.2581
4
2.2052
4
2.1765
4
2.1782
4
2.1737
4
2.0875
2
2.1715
4
2.3498
1
2.1792
5
2.1850
4
2.1998
4
2.1715
3
2.2143
4
2.1771
3
2.1721
3
2.3505
1
B3LYPultrafine         2.1780
3
          2.2670
1
    2.3539
1
    2.2529
5
   
B3PW91 2.1144
2
2.2048
4
2.1821
4
2.2474
4
2.1673
4
2.1674
4
2.1969
4
2.1950
4
2.0787
2
2.1643
4
2.2597
1
  2.2045
4
2.1652
4
  2.3530
1
     
mPW1PW91 2.1079
2
2.2013
4
2.0658
2
2.2069
3
2.1626
4
2.1909
4
2.1918
4
2.1614
4
2.1650
3
2.1643
3
2.2529
1
  2.1998
4
2.1613
4
  2.3499
1
     
M06-2X     2.1575
5
  2.1602
5
                           
PBEPBE 2.0782
2
2.2100
3
2.0837
2
2.1487
2
2.1826
3
2.1827
3
2.1840
3
2.1811
3
2.1812
3
2.1791
3
2.3497
1
  2.1915
3
2.1799
3
2.0898
2
2.0836
1
2.2113
2
2.0908
2
 
PBEPBEultrafine         2.3494
1
                           
PBE1PBE         2.1576
5
                           
HSEh1PBE   2.2063
5
    2.2152
4
  2.2701
5
            2.2660
5
         
TPSSh         2.1838
5
  2.1847
5
    2.1805
5
      2.1815
5
         
wB97X-D     2.1419
5
  2.1526
5
  2.1537
5
  2.1515
5
    2.1562
5
2.1537
5
2.1537
5
    2.1552
5
   
B97D3   2.2472
5
    2.2218
5
      2.2204
5
              2.1907
5
   
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
Moller Plesset perturbation MP2 2.1561
2
2.2828
4
2.1849
4
2.2873
4
2.2271
5
2.1777
4
2.1792
4
2.2252
5
2.1767
3
2.1809
4
2.1632
1
2.1836
5
2.1991
4
2.2029
4
2.1452
3
2.2263
4
2.1868
3
2.1861
2
2.3000
2
MP2=FULL 2.1554
2
2.2833
4
2.1341
3
2.2549
3
2.1968
4
2.1731
4
2.1748
4
2.1709
4
2.0916
2
2.0833
2
2.1571
1
  2.1948
4
2.0911
2
2.1369
3
2.1877
2
2.1564
2
2.1118
1
2.2833
2
MP3         2.1695
3
  2.1650
5
          2.2865
1
           
MP3=FULL         2.1624
5
  2.2212
5
                       
MP4   2.2522
3
2.2583
1
2.4060
1
2.2104
4
  2.1828
1
2.2580
2
2.1071
2
  2.1765
1
    2.2047
2
  2.2968
1
     
B2PLYP         2.1785
5
                2.2277
5
         
B2PLYP=FULLultrafine         2.3411
1
                           
Configuration interaction CID   2.1759
3
2.1224
3
2.2349
3
2.1651
4
  2.2500
1
2.1608
4
    2.2378
1
  2.2704
1
2.1545
1
         
CISD   2.1780
3
2.1259
3
2.2365
3
2.1680
4
2.1615
1
2.2527
1
2.0797
2
    2.2400
1
  2.2730
1
2.1578
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 cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(T+d)Z
Quadratic configuration interaction QCISD   2.2471
4
2.1400
3
2.2550
3
2.2032
4
2.1053
2
2.1823
4
2.1760
4
2.1798
3
2.1034
2
2.1638
1
  2.2052
4
2.1524
3
  2.2824
1
     
QCISD(T)         2.1885
4
  2.2715
1
2.3059
2
    2.2614
1
  2.1955
3
2.1387
3
  2.1722
3
2.1212
2
   
Coupled Cluster CCD   2.1599
2
2.1327
3
2.2502
3
2.1976
4
2.0954
2
2.1201
3
2.1694
4
2.0890
2
2.0952
2
2.1566
1
  2.2001
4
2.1460
3
  2.1785
3
2.0981
2
   
CCSD         2.1783
4
  2.2597
1
2.2993
2
    2.2475
1
  2.2817
1
2.1675
1
  2.1988
1
     
CCSD(T)         2.2049
3
2.2598
2
  2.3054
2
        2.1943
3
2.1908
4
2.0861
1
2.1708
3
2.1199
2
   
CCSD(T)=FULL         2.2751
2
                  2.0750
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 cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(T+d)Z

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 2.2792
4
2.2053
4
2.3261
4
2.2102
4
2.2838
4
2.2434
4
density functional B1B95 2.3824
1
2.3311
2
       
B3LYP 2.3754
4
2.2488
4
2.3714
4
2.2429
4
2.3293
4
2.2570
4
Moller Plesset perturbation MP2 2.4093
4
2.2306
4
2.4014
4
2.2373
4
2.3543
4
2.2860
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.