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You are here: Calculated > Geometry > Calculated geometry > One type of bond

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 2.0500
9
PM3 2.0413
7
PM6 1.9498
12
composite G2 2.1799
9
G3 2.1799
9
G3B3 2.2168
10
G3MP2 2.3523
1
G4 2.2160
12
CBS-Q 2.1799
9

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 aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
hartree fock HF 2.0989
9
2.2446
10
2.1612
11
2.2506
10
2.1857
12
2.1641
11
2.1656
11
2.1660
11
2.1660
10
2.1627
11
2.1811
9
2.1705
12
2.1763
11
2.1733
11
2.1645
10
2.1866
11
2.1698
10
2.1649
10
2.3660
1
2.3652
1
2.3654
1
2.3731
1
2.3659
1
2.3658
1
2.2036
8
2.1662
12
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
2.3178
1
2.3130
1
2.3130
1
2.3247
1
2.3154
1
2.3148
1
   
BLYP 2.1438
10
2.2570
11
2.2090
11
2.2712
11
2.2295
12
2.2279
11
2.2284
11
2.2264
11
2.2147
10
2.2094
10
2.2402
9
2.2444
8
2.2352
11
2.2091
11
  2.2519
8
2.2377
8
  2.3652
1
2.3621
1
2.3620
1
2.3723
1
2.3647
1
2.3639
1
2.2518
8
2.2376
8
B1B95 2.1146
10
2.1902
8
2.1612
10
2.2273
10
2.1741
10
2.1743
10
2.1742
10
2.1740
10
2.1721
10
2.1694
10
2.1916
8
2.2015
8
2.1838
10
2.1715
10
2.0681
2
2.1842
10
2.1720
10
2.0687
2
2.3332
1
2.3316
1
2.3316
1
2.3398
1
2.3334
1
2.3326
1
2.1894
7
2.1962
8
B3LYP 2.1320
10
2.2428
10
2.1861
11
2.2606
11
2.2034
11
2.1921
11
2.1929
11
2.1906
11
2.1910
10
2.1842
11
2.2089
8
2.1920
12
2.2006
11
2.1963
11
2.1835
10
2.2109
11
2.1892
10
2.1836
10
2.3527
1
2.3505
1
2.3499
1
2.3599
1
2.3521
1
2.3514
1
2.2278
8
2.2141
8
B3LYPultrafine   2.2787
7
    2.1950
10
2.2197
8
2.2202
8
2.2194
8
  2.2119
8
2.2153
9
2.2208
8
2.2285
8
2.2143
8
  2.2280
8
2.2187
12
  2.3527
1
2.3500
1
2.3499
1
2.3599
1
2.3521
1
2.3514
1
2.2278
8
2.2141
8
B3PW91 2.1244
10
2.2285
11
2.1800
11
2.2495
11
2.1831
11
2.1825
11
2.1933
11
2.1925
11
2.1823
10
2.1762
11
2.2075
9
2.2121
8
2.2017
11
2.1787
11
  2.2190
8
2.2063
8
  2.3445
1
2.3425
1
2.3429
1
2.3517
1
2.3445
1
2.3441
1
2.2190
8
2.2062
8
mPW1PW91 2.1185
10
2.2242
11
2.1672
10
2.2337
10
2.1777
11
2.1872
11
2.1876
11
2.1768
11
2.1774
10
2.1736
10
2.2024
9
2.2072
8
2.1963
11
2.1737
11
  2.2137
8
2.2012
8
  2.3416
1
2.3399
1
2.3403
1
2.3491
1
2.3418
1
2.3414
1
2.2137
8
2.2011
8
M06-2X 2.1111
8
2.2381
8
2.1527
12
2.2511
8
2.1736
12
2.2012
8
2.2016
8
2.2004
8
2.1982
8
2.1954
8
2.1644
12
2.2034
8
2.2107
8
2.1977
8
  2.2106
8
2.1973
8
  2.3389
1
2.3361
1
2.3357
1
2.3458
1
2.3377
1
2.3368
1
2.2104
8
2.1972
8
PBEPBE 2.1301
10
2.2446
10
2.1885
10
2.2547
10
2.2036
10
2.2030
10
2.2034
10
2.2025
10
2.2006
10
2.1960
10
2.2272
9
2.2304
8
2.2116
10
2.1983
10
2.0898
2
2.2201
9
2.2072
9
2.0908
2
2.3498
1
2.3477
1
2.3480
1
2.3572
1
2.3501
1
2.3495
1
2.2371
8
2.2243
8
PBEPBEultrafine   2.2730
8
    2.2297
8
2.2290
8
2.2292
8
2.2293
8
  2.2218
8
2.2195
8
2.2304
8
2.2375
8
2.2244
8
  2.2371
8
2.2244
8
  2.3498
1
2.3477
1
2.3480
1
2.3572
1
2.3501
1
2.3495
1
2.2371
8
2.2243
8
PBE1PBE 2.1196
8
2.1927
8
2.1927
8
2.2589
8
2.1744
12
2.2055
8
2.2050
8
2.2057
8
2.2033
8
2.1988
8
2.1966
8
2.2075
8
2.2139
8
2.2019
8
  2.2139
8
2.2019
8
  2.3414
1
2.3398
1
2.3402
1
2.3488
1
2.3417
1
2.3412
1
2.2139
8
2.2018
8
HSEh1PBE 2.1214
8
2.2257
12
2.1942
8
2.2613
8
2.1983
11
2.2067
8
2.2221
12
2.2074
8
2.2050
8
2.2003
8
2.1979
8
2.2093
8
2.2159
8
2.2178
12
  2.2158
8
2.2035
8
  2.3420
1
2.3403
1
2.3406
1
2.3494
1
2.3421
1
2.3416
1
2.2158
8
2.2034
8
TPSSh 2.1303
8
2.2644
8
2.2021
8
2.2679
8
2.1897
12
2.2121
8
2.1898
12
2.2134
8
2.2112
8
2.1837
12
2.2041
8
2.2155
8
2.2224
8
2.1860
12
2.2044
8
2.2223
8
2.2093
8
2.2042
8
2.3483
1
2.3458
1
2.3461
1
2.3552
1
2.3481
1
2.3473
1
2.2223
8
2.2093
8
wB97X-D 2.1132
8
2.2537
7
2.1541
12
2.2596
7
2.1655
12
2.1937
8
2.1651
12
2.1938
8
2.1620
12
2.1871
8
2.1846
8
2.1668
12
2.1704
12
2.1624
12
2.1848
8
2.2032
8
2.1630
12
2.1848
8
2.3405
1
2.3386
1
2.3390
1
2.3480
1
2.3404
1
2.3400
1
2.2030
8
2.1902
8
B97D3 2.1529
8
2.2602
12
2.2228
8
2.2894
8
2.2199
12
2.2345
8
2.2200
12
2.2341
8
2.2168
12
2.2278
8
2.2165
12
2.2146
12
2.2436
8
2.2149
11
2.2245
8
2.2432
8
2.2296
12
2.2243
8
2.3548
1
2.3516
1
2.3514
1
2.3620
1
2.3536
1
2.3526
1
2.2431
8
2.2295
12
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 aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Moller Plesset perturbation MP2 2.1392
10
2.2778
11
2.1793
11
2.2860
11
2.2068
12
2.1867
11
2.1874
11
2.2043
12
2.1845
10
2.1860
11
2.2020
9
2.1927
12
2.2076
11
2.1960
11
2.1875
11
2.2205
11
2.1912
10
2.2004
10
2.3541
1
2.3001
2
2.3464
1
2.3601
1
2.3469
1
2.3469
1
2.2353
8
2.2126
8
MP2=FULL 2.1386
10
2.2783
11
2.1756
11
2.2858
11
2.1917
11
2.1825
11
2.1833
11
2.1819
11
2.1827
10
2.1721
10
2.1953
9
2.2182
8
2.2033
11
2.1783
10
2.1756
11
2.2221
10
2.1886
10
2.1782
9
2.3438
1
2.2834
2
2.3271
1
2.3542
1
2.3357
1
2.3353
1
2.2309
8
2.1954
8
MP3         2.1707
4
  2.1669
6
      2.2501
2
2.2655
2
2.2779
3
2.2569
2
        2.3567
1
2.3490
1
2.3484
1
2.3631
1
2.3486
1
2.3488
1
2.2760
2
2.2558
2
MP3=FULL   2.2998
2
2.2353
2
2.3051
2
2.1638
6
2.2525
2
2.2131
6
2.2519
2
2.2540
2
2.2459
2
2.2444
2
2.2659
2
2.2690
2
2.2455
2
  2.2728
2
2.2432
2
  2.3480
1
2.3308
1
2.3311
1
2.3582
1
2.3398
1
2.3396
1
2.2728
2
2.2418
2
MP4   2.2741
5
2.2583
1
2.4060
1
2.2057
5
  2.1828
1
2.2580
2
2.1844
4
  2.2303
3
2.2728
2
2.2815
2
2.2344
4
  2.2889
3
2.2631
2
  2.3562
1
2.3487
1
2.3477
1
2.3624
1
2.3486
1
2.3476
1
2.2842
2
2.2629
2
MP4=FULL   2.3073
2
    2.2590
2
      2.2608
2
  2.2514
2
  2.2763
2
2.2524
2
  2.2809
2
2.2511
2
  2.3486
1
2.3305
1
2.3295
1
2.3579
1
2.3397
1
2.3392
1
2.2807
2
2.2499
2
B2PLYP 2.1347
8
2.2740
8
2.1995
8
2.2837
8
2.1901
12
2.2156
8
2.2160
8
2.2150
8
2.2129
8
2.2106
8
2.2075
8
2.2196
8
2.2288
8
2.2079
12
  2.2301
8
2.2136
8
  2.3501
1
2.3461
1
2.3457
1
2.3572
1
2.3471
1
2.3462
1
2.2300
8
2.2133
8
B2PLYP=FULL 2.1345
8
2.2741
8
2.1984
8
2.2837
8
2.2152
8
2.2142
8
2.2146
8
2.2146
8
2.2123
8
2.2056
8
2.2056
8
2.2194
8
2.2274
8
2.2096
8
  2.2286
8
2.2085
8
  2.3469
1
2.3403
1
2.3402
1
2.3554
1
2.3440
1
2.3432
1
2.2285
8
2.2087
8
B2PLYP=FULLultrafine 2.1345
8
2.2741
8
2.1984
8
2.2837
8
2.2294
12
2.2142
8
2.2146
8
2.2146
8
2.2123
8
2.2056
8
2.2056
8
2.2194
8
2.2421
12
2.2235
12
  2.2286
8
2.2225
12
  2.3469
1
2.3403
1
2.3403
1
2.3554
1
2.3441
1
2.3435
1
2.2285
8
2.2085
8
Configuration interaction CID   2.2580
10
2.1691
11
2.2812
10
2.1761
11
  2.2500
1
2.1729
11
    2.1977
9
  2.2262
9
2.1929
9
        2.3567
1
2.3487
1
2.3481
1
2.3632
1
2.3487
1
2.3485
1
2.2235
8
2.1977
8
CISD   2.2618
10
2.1721
11
2.2846
10
2.1794
11
2.1615
1
2.2527
1
2.1781
10
    2.1996
9
  2.2283
9
2.1950
9
        2.3562
1
2.3482
1
2.3476
1
2.3627
1
2.3483
1
2.3480
1
2.2249
8
2.2081
7
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 aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Quadratic configuration interaction QCISD   2.2796
10
2.1842
11
2.3026
10
2.2014
11
2.1942
10
2.1928
11
2.1895
11
2.1904
10
2.1912
10
2.2039
9
2.2254
8
2.2149
11
2.1973
11
  2.2464
9
2.2144
8
  2.3572
1
2.3488
1
2.3482
1
2.3638
1
2.3488
1
2.3486
1
2.2417
8
2.2141
8
QCISD(T)         2.2016
11
  2.2715
1
2.2284
9
    2.2237
9
2.2345
8
2.2341
11
2.2009
11
  2.2310
11
2.2114
9
  2.3566
1
2.3487
1
2.3495
1
2.3630
1
2.3485
1
2.3476
1
2.2528
8
2.2246
8
QCISD(T)=FULL         2.2215
8
  2.2203
8
      2.2128
8
  2.2440
8
2.2122
8
2.2009
8
2.2479
8
2.1522
7
2.2111
7
2.3491
1
2.3307
1
2.3301
1
2.3585
1
2.3400
1
2.3394
1
2.2479
8
2.2085
8
QCISD(TQ)         2.3398
1
          2.3452
1
        2.3691
1
                   
QCISD(TQ)=FULL         2.3354
1
              2.3605
1
                         
Coupled Cluster CCD   2.2734
9
2.1776
11
2.2944
10
2.1944
11
2.1872
10
2.1857
11
2.1822
11
2.1837
10
2.1848
10
2.1984
9
2.2194
8
2.2087
11
2.1916
11
  2.2207
11
2.1869
10
  2.3584
1
2.3501
1
2.3498
1
2.3650
1
2.3501
1
2.3500
1
2.2363
8
2.2089
8
CCSD         2.1911
11
2.2148
8
2.2200
9
2.2183
9
2.2117
8
2.2115
8
2.2119
9
2.2238
8
2.2419
9
2.2077
9
2.2021
8
2.2358
9
2.2130
8
2.0957
4
2.3574
1
2.3491
1
2.3485
1
2.3640
1
2.3491
1
2.3489
1
2.2402
8
2.2128
8
CCSD=FULL         2.2121
8
        2.1963
8
2.2010
8
2.2233
8
2.2326
8
2.2005
8
2.1686
7
2.2357
8
2.1969
8
2.1239
4
2.3484
1
2.3312
1
2.3315
1
2.3589
1
2.3404
1
2.3400
1
2.2357
8
2.1964
8
CCSD(T)         2.2071
10
2.2185
9
2.2236
8
2.2274
9
2.2202
8
2.2220
8
2.2181
8
2.2335
8
2.2331
11
2.1998
11
2.1986
9
2.2299
11
2.2029
10
2.1944
7
2.3567
1
2.3488
1
2.3495
1
2.3631
1
2.3487
1
2.3478
1
2.2519
8
2.2238
8
CCSD(T)=FULL         2.2315
10
          2.2120
8
2.2334
8
2.2432
8
2.2115
8
2.1863
9
2.2471
8
2.2079
8
2.1894
6
2.3492
1
2.3309
1
2.3302
1
2.3586
1
2.3401
1
2.3396
1
2.2471
8
2.2077
8
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 aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ

average calculated bond lengths (Å)
Methods with effective core potentials (select basis sets)
CEP-31G CEP-31G* CEP-121G CEP-121G* LANL2DZ SDD cc-pVTZ-PP aug-cc-pVTZ-PP Def2TZVPP
hartree fock HF 2.2727
10
2.1969
11
2.2850
10
2.1913
11
2.2386
10
2.2482
10
    2.1600
12
density functional BLYP                 2.2319
8
B1B95 2.3824
1
2.3311
2
            2.1913
8
B3LYP 2.3167
11
2.2346
11
2.3129
11
2.2292
11
2.2744
10
2.2566
11
    2.2032
12
B3LYPultrafine                 2.2083
8
B3PW91                 2.2008
8
mPW1PW91                 2.1960
8
M06-2X                 2.1925
8
PBEPBE                 2.1947
12
PBEPBEultrafine                 2.2192
8
PBE1PBE                 2.1965
8
HSEh1PBE                 2.1979
8
TPSSh                 2.2038
8
wB97X-D 2.2881
7
2.2261
8
2.2818
7
2.2185
8
2.2310
7
2.2562
7
    2.1848
8
B97D3                 2.2242
8
Moller Plesset perturbation MP2 2.3421
11
2.2251
11
2.3316
11
2.2210
11
2.2819
11
2.2801
11
    2.1779
12
MP2=FULL                 2.1990
8
MP3                 2.2506
2
MP3=FULL                 2.2454
2
MP4                 2.3462
1
MP4=FULL                 2.2521
2
B2PLYP                 2.2070
8
B2PLYP=FULL                 2.2051
8
B2PLYP=FULLultrafine                 2.2051
8
Configuration interaction CID                 2.1912
8
CISD                 2.1931
8
Quadratic configuration interaction QCISD                 2.2073
8
QCISD(T)                 2.2175
8
QCISD(T)=FULL                 2.2116
8
Coupled Cluster CCD                 2.2021
8
CCSD                 2.2059
8
CCSD=FULL                 2.1997
8
CCSD(T)                 2.2166
8
CCSD(T)=FULL                 2.2107
8
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.