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III.G.1.a.

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 1.9185
4
PM3 2.0963
5
PM6 1.9216
6
composite G2 2.2101
5
G3 2.2101
5
G3B3 2.2649
5
G4 2.2507
5
CBS-Q 2.2101
5

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 2.1511
5
2.3119
5
2.2155
5
2.3026
5
2.2305
9
2.2104
5
2.2136
5
2.2138
5
2.2143
5
2.2129
5
2.2512
2
2.1689
5
2.2265
5
2.2324
5
2.2295
5
2.2473
5
2.2195
5
2.2144
5
2.2919
2
ROHF 2.1053
1
2.2081
1
2.2198
1
2.3142
1
2.1405
1
2.1409
1
2.2283
1
2.2307
1
2.1393
1
2.1399
1
2.2205
1
  2.2352
1
2.1428
1
  2.1569
1
2.1441
1
   
density functional LSDA 2.2061
5
2.2179
5
2.1910
5
2.3132
5
2.2098
5
2.2101
5
2.2105
5
2.2050
5
2.2053
5
2.1996
5
    2.2162
5
2.2008
5
2.1804
2
2.2170
5
2.1395
3
2.1808
2
 
SVWN   2.2296
5
    2.2372
3
  2.1898
5
                       
BLYP 2.2112
5
2.3269
5
2.2278
5
2.2828
5
2.2257
5
2.2509
5
2.2517
5
2.2942
5
2.2681
5
2.2404
5
2.2998
1
  2.2561
5
2.2180
5
  2.2887
2
     
B1B95 2.1941
5
2.2576
5
2.2309
5
2.3091
5
2.2435
5
2.2447
5
2.2458
5
2.2466
5
2.2469
5
2.2196
5
    2.2551
5
2.2207
5
2.2031
3
2.2550
5
2.2091
3
2.2036
3
 
B3LYP 2.2084
5
2.3032
5
2.2469
5
2.3308
5
2.2648
5
2.2419
5
2.2435
5
2.2412
5
2.2433
4
2.2357
5
2.2543
2
2.1792
5
2.2513
5
2.2592
5
2.2549
5
2.2744
5
2.2602
5
2.2335
5
2.3090
2
B3LYPultrafine         2.2647
5
          2.2670
1
    2.3539
1
    2.2529
5
   
B3PW91 2.1905
4
2.2948
5
2.2399
5
2.3182
5
2.2310
5
2.2312
5
2.2553
5
2.2553
5
2.2029
4
2.2271
5
2.2597
1
  2.2638
5
2.2289
5
  2.2620
2
     
mPW1PW91 2.1678
4
2.2898
5
2.2123
4
2.3125
5
2.2252
5
2.2478
5
2.2492
5
2.2265
5
2.2269
5
2.2433
5
2.2529
1
  2.2580
5
2.2239
5
  2.2581
2
     
M06-2X         2.1602
5
                           
PBEPBE 2.1847
4
2.3109
5
2.1852
4
2.2959
4
2.2073
5
2.2323
5
2.2082
5
2.2308
5
2.2051
5
2.2239
5
2.3182
2
  2.2383
5
2.2024
5
2.1577
3
2.1939
2
2.2378
3
2.1584
3
2.2860
1
PBEPBEultrafine         2.3349
3
                           
PBE1PBE         2.1576
5
                           
HSEh1PBE         2.2152
4
                           
TPSSh         2.1838
5
  2.1847
5
            2.1815
5
         
Moller Plesset perturbation MP2 2.2133
4
2.3748
5
2.2355
5
2.3628
5
2.2513
5
2.2326
5
2.2646
7
2.2305
5
2.2311
5
2.2365
5
2.1632
1
2.1836
5
2.2573
5
2.2544
5
2.2214
4
2.2791
5
2.2384
5
2.2744
3
2.3000
2
MP2=FULL 2.2243
3
2.3757
5
2.2096
4
2.3577
4
2.2473
5
2.2283
5
2.2302
5
2.2289
5
2.2016
4
2.2030
3
2.1571
1
  2.2532
5
2.2200
4
2.2143
4
2.1877
2
2.0620
1
2.2777
2
2.2833
2
MP3         2.2275
5
  2.1650
5
          2.2865
1
           
MP3=FULL         2.1624
5
  2.2212
5
                       
MP4   2.3863
4
2.2583
1
2.4060
1
2.2627
5
  2.1828
1
2.2580
2
2.2322
3
  2.1765
1
    2.2047
2
  2.2968
1
     
B2PLYP         2.1785
5
                2.2277
5
         
B2PLYP=FULLultrafine         2.3411
1
                           
Configuration interaction CID   2.3121
4
2.1990
4
2.3389
4
2.2209
5
  2.2500
1
2.2189
5
    2.2378
1
  2.2704
1
2.1545
1
         
CISD   2.3158
4
2.2025
4
2.3416
4
2.2240
5
2.1615
1
2.2527
1
2.2051
3
    2.2400
1
  2.2730
1
2.1578
1
         
Quadratic configuration interaction QCISD   2.3483
5
2.2142
4
2.3607
4
2.2530
5
2.2210
3
2.2370
5
2.2331
5
2.2523
5
2.2201
3
2.1638
1
  2.2629
5
2.2278
4
  2.2824
1
    2.2489
1
QCISD(T)         2.2439
5
  2.2715
1
2.3059
2
    2.2614
1
  2.2743
4
2.2215
4
  2.2570
4
2.2378
3
   
Coupled Cluster CCD   2.3533
3
2.2073
4
2.3548
4
2.2477
5
2.2130
3
2.2026
4
2.2265
5
2.2109
3
2.2134
3
2.1566
1
  2.2577
5
2.2220
4
  2.2559
4
2.2157
3
   
CCSD         2.1783
4
  2.2597
1
2.2993
2
    2.2475
1
  2.2817
1
2.1675
1
  2.1988
1
     
CCSD(T)   2.4145
1
    2.2697
4
2.2598
2
2.2706
1
2.3054
2
2.2705
1
  2.2607
1
  2.2731
4
2.2465
5
2.0861
1
2.2557
4
2.2367
3
  2.2624
1
CCSD(T)=FULL         2.2268
3
                  2.0750
1
       

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 2.3313
5
2.2492
5
2.3707
5
2.2543
5
2.3292
5
2.3159
5
density functional B1B95 2.3853
2
2.3311
2
       
B3LYP 2.4262
5
2.3016
5
2.4249
5
2.2982
5
2.3836
5
2.3417
5
Moller Plesset perturbation MP2 2.4571
5
2.2783
5
2.4532
5
2.2852
5
2.4087
5
2.3771
5
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.