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Comparison of levels of theory for S-S


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 2.0926
36
PM3 2.0132
38
PM6 2.0579
48
composite G2 2.0955
47
G3 2.0948
47
G3B3 2.1264
50
G3MP2 1.9145
6
G4 2.1097
51
CBS-Q 2.1022
39

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 Sadlej_pVTZ daug-cc-pVDZ daug-cc-pVTZ
hartree fock HF 2.1172
50
2.2878
50
2.0848
51
2.2532
51
2.0935
51
2.0936
51
2.1094
46
2.0998
51
2.1029
50
2.0840
51
2.1359
33
2.1046
51
2.1069
51
2.0880
51
2.1115
30
2.1065
51
2.0911
50
2.1075
31
2.0312
11
2.0955
42
1.9943
16
2.0874
6
2.1685
23
2.2636
3
1.8992
1
2.2340
19
2.0859
48
ROHF   2.1691
6
1.9381
8
2.1228
5
1.9486
8
1.9486
8
1.9495
8
1.9533
8
1.9522
7
  1.8601
1
1.9572
7
1.9484
8
1.9489
8
1.8960
5
1.9466
7
1.9496
7
1.8959
5
1.9481
3
2.1192
12
1.8746
3
  2.1983
8
    1.8870
1
1.8691
1
density functional LSDA 2.0668
34
2.1166
26
1.9978
34
2.1690
34
2.0139
34
2.0140
34
2.0150
34
2.0171
34
2.0172
34
1.9942
34
  2.0553
12
2.0224
34
1.9996
34
  2.0218
34
2.0090
15
2.0007
1
2.0548
8
2.1363
28
2.0315
12
2.3253
2
2.1952
20
2.2231
3
     
BLYP 2.1899
50
2.3397
51
2.1496
51
2.3243
51
2.1208
51
2.1658
50
2.1675
51
2.1718
51
2.1765
50
2.1600
41
2.2574
21
2.2256
33
2.1702
51
2.1499
51
  2.2343
34
2.2304
28
  2.0748
9
2.1953
29
2.0643
13
2.3770
2
2.2743
20
2.2781
3
  2.3014
19
2.2820
19
B1B95 2.1374
51
2.2047
24
2.0888
51
2.2514
51
2.1004
51
2.1012
51
2.1038
50
2.1044
51
2.1045
51
2.0824
51
2.2226
13
2.1545
33
2.1077
51
2.0860
51
1.8988
4
2.1061
51
2.1025
40
1.8976
4
2.0316
9
2.1166
31
1.9944
16
2.0882
6
2.1637
23
2.2370
3
  2.2185
17
2.2102
19
B3LYP 2.1621
50
2.3045
51
2.1162
51
2.2797
51
2.1337
51
2.1338
51
2.1351
51
2.1388
51
2.1553
40
2.1145
51
2.1758
31
2.1390
51
2.1719
51
2.1189
51
2.1392
31
2.1395
51
2.1048
50
2.1387
31
2.0488
11
2.1173
44
2.0170
16
2.1122
6
2.2005
23
2.2600
3
1.9415
1
2.2698
19
2.2500
19
B3LYPultrafine   2.3726
28
    2.1377
50
2.2104
28
2.1926
31
2.2152
28
  2.2328
21
2.2259
21
2.2157
28
2.2081
29
2.1523
40
  2.2090
29
2.1160
51
  2.3550
2
2.2238
22
2.1075
6
2.3632
2
2.2428
20
2.2600
3
  2.2698
19
2.2500
19
B3PW91 2.1546
48
2.2914
50
2.1005
51
2.2680
49
2.1144
51
2.1146
51
2.1154
51
2.1178
51
2.1339
40
2.1056
42
2.2041
21
2.1710
33
2.1211
51
2.0999
51
  2.1723
35
2.2035
24
  2.0411
9
2.1456
29
2.0272
13
2.3534
2
2.2202
20
2.2485
3
  2.2475
19
2.2275
19
mPW1PW91 2.1478
48
2.2791
51
2.0999
50
2.2600
50
2.1079
51
2.1070
51
2.1078
51
2.1104
51
2.1145
50
2.0996
42
2.1967
21
2.1628
33
2.1136
51
2.0931
51
  2.1557
35
2.1439
33
  2.0367
9
2.1388
29
2.0221
13
2.3501
2
2.2126
20
2.2446
3
  2.2396
19
2.2196
19
M06-2X 2.1712
33
2.3124
33
2.0899
51
2.2980
33
2.1026
51
2.1517
33
2.1532
33
2.1547
33
2.1551
33
2.1352
33
2.0730
51
2.1652
31
2.1604
32
2.1390
33
  2.1582
33
2.1390
33
  2.0524
5
2.1373
29
2.0215
13
2.3469
2
2.2096
20
2.2430
3
  2.2336
19
2.2149
19
PBEPBE 2.1724
48
2.3213
42
2.1370
40
2.3082
40
2.1458
41
2.1459
41
2.1482
41
2.1506
41
2.1411
50
2.1159
50
2.1489
34
2.1890
33
2.1486
42
2.1320
41
1.9303
3
2.1837
34
2.1511
38
1.9283
3
2.0527
9
2.1460
31
2.0269
15
2.1489
5
2.2081
22
2.2562
3
1.9220
1
2.2640
19
2.2433
19
PBEPBEultrafine   2.3813
28
    2.1602
42
2.2058
28
2.2098
28
2.2109
28
  2.2268
21
2.2198
21
2.2113
28
2.2052
29
2.1853
29
  2.2068
29
2.1858
29
  2.3515
2
2.2172
22
2.1104
6
2.3593
2
2.2354
20
2.2563
3
  2.2640
19
2.2433
19
PBE1PBE 2.1996
29
2.1862
24
2.1589
29
2.3204
29
2.1101
47
2.1716
29
2.1737
29
2.1747
29
2.1751
29
2.1521
29
2.1940
21
2.1758
29
2.1767
29
2.1569
29
  2.1770
29
2.1572
29
  2.3422
2
2.1693
26
2.0719
10
2.3495
2
2.2098
20
2.2437
3
  2.2369
19
2.2169
19
HSEh1PBE 2.1854
33
2.2849
50
2.1455
33
2.3087
33
2.1149
49
2.1588
33
2.1157
49
2.1623
33
2.1628
33
2.1392
33
2.1971
21
2.1633
33
2.1641
33
2.1010
49
  2.1641
33
2.1443
33
  2.0536
6
2.1391
29
2.0222
13
2.3503
2
2.2131
20
2.2446
3
  2.2402
19
2.2205
19
TPSSh 2.2483
24
2.3690
28
2.1836
28
2.3515
28
2.0903
52
2.1961
28
2.0952
51
2.1981
28
2.2274
24
2.0896
47
2.2103
21
2.2004
28
2.1910
29
2.0832
51
2.1982
23
2.2013
28
2.1804
28
2.1981
23
2.3495
2
2.2080
22
2.1010
6
2.3569
2
2.2399
19
2.2521
3
  2.2544
19
2.2337
19
wB97X-D 2.2316
24
2.3578
24
2.0766
51
2.3462
24
2.0847
51
2.2064
24
2.0857
51
2.2102
24
2.0868
51
2.1881
24
2.1945
21
2.0884
51
2.0878
51
2.0753
51
2.1880
22
2.2136
24
2.0753
51
2.1880
22
2.3416
2
2.2210
20
2.1792
4
2.3490
2
2.2599
17
2.2455
3
  2.2365
19
2.2161
19
B97D3 2.2735
24
2.2546
51
2.2346
24
2.4170
24
2.1153
51
2.2472
24
2.1176
51
2.2530
24
2.1195
51
2.2285
24
2.0874
50
2.1430
51
2.2516
24
2.1032
51
2.2259
22
2.2536
24
2.1222
51
2.2258
22
2.3554
2
2.2813
18
2.3519
2
2.3628
2
2.3340
15
2.2590
3
  2.2750
19
2.1116
51
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 Sadlej_pVTZ daug-cc-pVDZ daug-cc-pVTZ
Moller Plesset perturbation MP2 2.1360
40
2.3223
41
2.1130
51
2.2893
43
2.1060
51
2.1289
51
2.1270
51
2.0808
47
2.1081
47
2.1074
40
2.2149
21
2.1280
51
2.1387
51
2.1040
49
2.1464
28
2.1413
51
2.1178
39
2.1463
28
2.0409
11
2.0972
45
2.0205
14
2.1097
6
2.1858
23
2.2496
3
1.9278
1
2.2902
19
2.2386
19
MP2=FULL 2.1348
40
2.3197
42
2.1160
50
2.2939
42
2.1273
51
2.1268
51
2.1038
47
2.1139
39
2.1253
36
2.1072
40
2.2091
21
2.1849
33
2.1370
51
2.1007
49
2.1414
28
2.1626
38
2.1368
33
2.1453
27
2.0372
11
2.0875
45
2.0093
14
2.1064
6
2.1793
23
2.2402
3
1.9282
1
2.2867
19
2.2258
19
ROMP2 2.0442
7
1.9124
1
1.9733
5
2.1831
5
1.9865
7
1.9865
7
1.9867
7
1.9921
5
1.9922
5
1.9613
7
1.9077
1
1.9981
5
1.9931
7
1.9643
7
  1.9983
7
      2.1767
10
1.9437
3
  2.2162
8
    1.9530
1
1.9211
1
MP3         2.1183
50
  2.0903
51
      2.2280
20
2.2095
27
2.2179
27
2.1858
26
        2.1183
5
2.1838
24
2.0455
8
2.3647
2
2.2273
20
2.0668
1
  2.2872
18
2.2524
18
MP3=FULL   2.4462
23
2.2197
23
2.4356
23
2.0886
51
2.2237
21
2.0892
51
2.2383
23
2.2385
23
2.2104
23
2.2245
20
2.2089
27
2.2163
27
2.1789
26
  2.2519
22
2.2094
22
  2.3486
2
2.2018
22
2.0874
6
2.3595
2
2.2367
19
2.2480
3
  2.2851
18
2.2301
16
MP4 2.1214
8
2.3346
40
    2.1343
50
    2.0139
2
2.1685
36
  2.2461
20
2.2255
27
2.2352
27
2.1477
35
  2.2369
27
2.1784
23
  2.0618
9
2.1831
25
2.0308
9
2.3649
2
2.2417
20
2.2560
3
  2.3189
18
2.2720
18
MP4=FULL   2.3990
19
    2.2239
27
      2.2271
27
  2.2414
20
  2.2332
27
2.1855
27
  2.2345
27
2.1707
25
  2.3485
2
2.2136
22
1.9815
4
2.3587
2
2.2373
20
2.2487
3
  2.3159
18
2.2585
18
B2PLYP 2.2368
28
2.4070
28
2.1952
28
2.3975
28
2.1357
46
2.2071
28
2.1979
29
2.2112
28
2.2000
29
2.1766
27
2.2153
21
2.2114
28
2.2153
28
2.0948
46
  2.2162
28
2.1656
30
  2.1628
4
2.1873
25
2.0705
9
2.3594
2
2.2442
19
2.2538
3
  2.2711
19
2.2398
19
B2PLYP=FULL 2.2367
28
2.3851
29
2.1948
28
2.3976
28
2.1950
29
2.2065
28
2.1970
29
2.2110
28
2.2113
28
2.1771
28
2.2137
21
2.2110
28
2.2147
28
2.1835
28
  2.2155
28
2.1828
28
  2.3480
2
2.2096
22
2.1031
6
2.3573
2
2.2423
19
2.2511
3
  2.2704
19
2.2361
19
B2PLYP=FULLultrafine 2.2636
24
2.4365
24
2.2250
24
2.4302
24
2.1224
52
2.2364
24
2.2387
24
2.2408
24
2.2411
24
2.2053
24
2.2137
21
2.2403
24
2.1326
52
2.1042
52
  2.2446
24
2.1031
52
  2.3480
2
2.2367
20
2.1855
4
2.3573
2
2.2778
17
2.2511
3
  2.2704
19
2.2360
19
Configuration interaction CID 2.1038
8
2.3176
49
2.1028
41
2.3039
41
2.0997
51
2.0535
1
  2.1172
41
    2.1735
19
  2.2229
22
2.1992
21
        2.1784
3
2.1733
23
2.0474
7
2.3645
2
2.2072
20
2.0557
1
  2.2426
19
2.1944
17
CISD 2.1039
8
2.3213
49
2.1058
40
2.3098
40
2.1311
51
2.0640
2
  2.1202
40
    2.1907
21
  2.2240
22
2.2000
21
        2.1789
3
2.1742
23
1.9283
5
2.3642
2
2.2200
19
2.2513
3
  2.2434
19
2.1952
17
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 Sadlej_pVTZ daug-cc-pVDZ daug-cc-pVTZ
Quadratic configuration interaction QCISD 2.1214
10
2.3680
50
2.1081
50
2.3396
49
2.1464
50
2.1214
50
2.1190
51
2.1230
51
2.1402
41
2.1253
37
2.1931
19
2.1780
33
2.1441
42
2.1235
38
  2.1847
32
2.1496
32
  2.0490
11
2.1285
33
1.9786
11
2.3655
2
2.2574
18
2.0669
1
  2.2638
19
2.2142
17
QCISD(T)         2.1286
49
1.9591
2
1.9593
2
2.2417
23
2.0909
2
  2.2215
21
2.1896
32
2.1773
35
2.1438
35
  2.1803
35
2.1435
35
  2.1489
5
2.1833
27
2.0715
11
2.3657
2
2.2368
20
2.0731
1
  2.2818
19
2.2436
19
QCISD(T)=FULL         2.2059
27
  2.2060
27
      2.2169
21
  2.2028
23
2.1780
27
2.1647
22
2.2212
27
2.1622
25
2.1416
18
2.3491
2
2.2363
20
2.1792
4
2.3594
2
2.2799
17
2.0691
1
  2.2791
19
2.2294
16
QCISD(TQ)         1.9859
7
  1.9867
7
      1.9208
3
  2.0033
7
1.9744
7
1.9526
2
2.0097
7
1.9171
1
1.9037
1
  1.9454
2
1.9465
2
  1.9457
2
    1.9472
1
1.9171
1
QCISD(TQ)=FULL         1.9842
7
  1.9967
5
      1.9023
1
  2.0018
7
2.0001
3
1.9009
1
2.0086
7
1.9107
1
                1.9463
1
1.9107
1
Coupled Cluster CCD 2.1198
10
2.3326
46
2.1008
50
2.3153
50
2.1128
51
2.1162
50
2.1137
49
2.1204
50
2.1440
38
2.1210
37
2.2037
21
2.1716
33
2.1433
41
2.1230
37
  2.1591
35
2.1256
35
  2.0456
11
2.1244
33
1.9583
14
2.1546
4
2.1914
22
2.2556
3
  2.2596
19
2.2100
17
CCSD   2.1739
2
    2.1250
42
2.2355
21
2.2354
21
2.2299
22
2.2233
23
2.1694
27
2.2066
21
2.1919
29
2.1746
34
2.1409
33
2.1615
25
2.1991
28
2.1641
28
2.1196
19
2.1432
5
2.1722
27
2.0447
12
2.3658
2
2.2231
20
2.2554
3
  2.2628
19
2.2277
19
CCSD=FULL         2.1720
30
        2.1609
27
2.1872
19
2.1907
29
2.1868
30
2.1476
29
2.1527
26
2.1733
27
2.1299
27
2.0966
15
2.3489
2
2.1813
23
2.0550
7
2.3601
2
2.2172
20
2.2479
3
  2.2603
19
2.2026
17
CCSD(T)   2.2196
2
    2.1346
47
2.2246
24
2.2368
23
2.2396
23
2.2278
25
2.1958
19
2.2207
21
2.1875
32
2.1611
37
2.1259
38
2.1644
26
2.1644
37
2.1496
32
2.1364
19
2.1071
7
2.1649
29
2.0487
13
2.1182
6
2.1946
23
2.2569
3
  2.2725
15
2.2420
19
CCSD(T)=FULL         2.1589
35
          2.2157
21
2.1864
32
2.1771
28
2.1540
32
2.1596
26
2.1952
32
2.1387
30
2.0383
15
2.0670
9
2.1380
31
2.0322
14
2.1146
6
2.1893
23
2.0690
1
  2.2703
15
2.2279
16
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 Sadlej_pVTZ 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 2.2510
51
2.1061
51
2.2516
51
2.1050
51
2.3257
50
2.2858
48
    2.0614
50
ROHF                 1.8613
1
density functional BLYP                 2.2561
21
B1B95 2.1895
18
2.0465
18
2.2355
2
2.0865
2
2.2615
2
2.2448
2
    2.1867
21
B3LYP 2.2981
51
2.1481
51
2.2999
51
2.1456
51
2.3228
50
2.3090
51
    2.0819
50
B3LYPultrafine                 2.2250
21
B3PW91                 2.2031
21
mPW1PW91                 2.1957
21
M06-2X                 2.1921
21
PBEPBE                 2.0797
50
PBEPBEultrafine                 2.2186
21
PBE1PBE                 2.1930
21
HSEh1PBE                 2.1961
21
TPSSh                 2.2092
21
wB97X-D 2.3638
24
2.2213
24
2.3615
24
2.2193
24
2.3743
20
2.3629
24
    2.1931
21
B97D3                 2.2299
21
Moller Plesset perturbation MP2 2.2944
43
2.1358
51
2.3273
43
2.1323
51
2.3193
42
2.5606
42
    2.0703
50
MP2=FULL                 2.2043
21
ROMP2                 1.9080
1
MP3                 2.2268
20
MP3=FULL                 2.2235
20
MP4                 2.3247
15
MP4=FULL                 2.2370
20
B2PLYP                 2.2134
21
B2PLYP=FULL                 2.2117
21
B2PLYP=FULLultrafine                 2.2117
21
Configuration interaction CID                 2.1891
21
CISD                 2.1898
21
Quadratic configuration interaction QCISD                 2.2061
21
QCISD(T)                 2.2061
17
QCISD(T)=FULL                 2.2141
21
QCISD(TQ)                 1.9216
3
QCISD(TQ)=FULL                 1.9027
1
Coupled Cluster CCD                 2.2025
21
CCSD                 2.2051
21
CCSD=FULL                 2.2001
21
CCSD(T)                 2.2051
17
CCSD(T)=FULL                 2.1997
19
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.