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Comparison of levels of theory for H-H


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 1.1234
20
PM3 1.2874
20
PM6 1.1484
33
composite G2 1.1739
22
G3 1.1728
22
G3B3 1.1538
27
G3MP2 1.2761
5
G4 1.1410
28
CBS-Q 1.1737
22

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) 6-311+G(3df,2pd) TZVP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ Sadlej_pVTZ daug-cc-pVDZ daug-cc-pVTZ
hartree fock HF 1.1583
32
1.1452
33
1.1319
32
1.1057
29
1.1175
32
1.1386
32
1.1378
28
1.1416
32
1.1366
32
1.1400
32
1.1292
10
1.3551
5
1.1453
35
1.1471
32
1.1383
32
1.1652
12
1.1280
32
1.1324
33
1.1508
12
0.7555
1
0.9142
4
1.1352
35
ROHF   1.2792
2
1.2792
2
1.2601
2
1.2601
2
1.2526
2
1.2601
2
1.1923
2
1.1016
2
      1.1029
2
1.2134
2
1.1038
2
0.9934
2
0.9093
2
0.9011
2
0.8992
2
  0.7487
1
0.7353
1
density functional LSDA 1.0690
19
1.1390
24
1.0455
19
1.0424
19
1.1305
25
1.1283
25
1.1315
25
1.1221
25
1.1135
25
1.1298
25
0.7640
3
0.7641
1
1.0843
14
1.1311
25
1.1146
25
0.7634
1
1.1095
25
1.1295
22
0.7634
1
  0.7808
2
0.7656
2
BLYP 1.1824
32
1.1756
32
1.1595
27
1.1746
32
1.1331
35
1.1643
32
1.1683
32
1.1326
27
1.1455
32
1.1645
32
0.9740
3
0.7462
1
1.1956
22
1.1657
32
1.1467
32
0.7454
1
1.0795
21
1.0528
16
0.7454
1
  0.9314
4
0.9174
4
B1B95 1.1995
30
1.1999
29
1.1847
30
1.1847
30
1.1606
27
1.1609
27
1.1899
30
1.1810
30
1.1466
27
1.1874
30
0.9672
3
0.7413
1
1.1847
22
1.1894
30
1.1756
30
0.7405
1
1.1678
25
1.1565
22
0.7405
1
  0.9228
4
0.9109
4
B3LYP 1.1713
32
1.1328
30
1.1173
29
1.1473
32
1.1609
33
1.1195
29
1.1642
33
1.1428
32
1.0768
24
1.1562
35
1.0611
10
1.3254
5
1.1467
35
1.1543
32
1.1377
32
1.1596
12
1.1267
26
1.1341
35
1.1456
12
0.7689
1
0.9252
4
0.9124
4
B3LYPultrafine 0.7284
1
1.1818
20
0.7462
1
0.7427
1
1.1609
33
1.1037
16
1.1738
20
1.0922
16
0.7440
1
0.9701
3
0.9685
3
1.3253
5
1.1851
22
1.2013
22
1.1845
22
0.7419
1
1.1735
22
1.1343
33
0.7419
1
  0.9252
4
0.9124
4
B3PW91 1.1545
27
1.1418
32
1.1418
32
1.1435
32
1.1459
32
1.1456
32
1.1299
27
1.1079
29
1.1119
27
1.1466
32
0.9699
3
0.7441
1
1.1797
22
1.1502
32
1.1349
32
0.7434
1
1.0704
21
1.0414
14
0.7434
1
  0.9250
4
0.9139
4
mPW1PW91 1.1506
27
1.1090
29
1.0798
24
1.1401
32
1.1425
32
1.1421
32
1.1450
32
1.1349
32
1.1302
32
1.1433
32
0.9687
3
0.7431
1
1.1763
22
1.1471
32
1.1119
27
0.7425
1
1.1550
29
1.1639
22
0.7425
1
  0.9237
4
0.9127
4
M06-2X 1.1692
19
1.1870
22
1.1468
35
1.1897
22
1.1457
35
1.1924
22
1.1952
22
1.1846
22
1.1783
22
1.1942
22
1.0907
27
0.7385
1
1.1800
22
1.1943
22
1.1787
22
0.7369
1
1.1660
22
1.1167
19
0.7368
1
  0.9765
3
0.9669
3
PBEPBE 1.1590
27
1.1400
30
1.0963
24
1.1454
26
1.1656
33
1.1535
32
1.1689
33
1.1442
32
1.1383
32
1.1542
32
1.0694
10
1.3157
5
1.1839
22
1.1568
32
1.1401
32
0.7502
1
1.1435
24
1.1523
25
0.7502
1
0.7764
1
0.9331
4
0.9211
4
PBEPBEultrafine 0.7345
1
1.1885
20
0.7535
1
0.7505
1
1.1949
30
1.1109
16
1.1773
20
1.0922
16
0.7519
1
0.9781
3
0.9772
3
1.3177
5
1.1839
22
1.2016
22
1.1842
22
0.7502
1
1.1777
22
1.1871
23
0.7502
1
  0.9331
4
0.9211
4
PBE1PBE 1.2090
22
1.2073
21
1.1864
22
1.1893
22
1.1506
35
1.1941
22
1.1960
22
1.1811
22
1.1741
22
1.1945
22
0.9704
3
0.7451
1
1.1883
22
1.1923
22
1.1775
22
0.7446
1
1.1696
22
1.1636
22
0.7446
1
  0.9255
4
0.9146
4
HSEh1PBE 1.2087
22
1.1429
35
1.1865
22
1.1892
22
1.1471
35
1.1920
22
1.1491
35
1.1814
22
1.1739
22
1.1940
22
0.9701
3
0.7449
1
1.1762
22
1.1919
22
1.1381
35
0.7442
1
1.1894
22
1.1624
22
0.7442
1
  0.9254
4
0.9142
4
TPSSh 1.1395
8
1.1895
22
1.1895
22
1.1911
22
1.1413
35
1.1947
22
1.1453
35
1.1867
22
1.0610
8
1.0828
25
1.0833
2
  1.1990
22
1.1965
22
1.1334
35
0.9378
3
1.1712
22
1.1661
22
0.8652
3
  0.9785
3
0.9696
3
wB97X-D 1.1539
13
1.1357
13
1.1243
35
1.1300
13
1.1234
35
1.1283
13
1.1251
35
1.1244
13
1.1213
35
1.1280
13
1.0813
2
  1.1443
35
1.1516
35
1.1215
35
0.9525
3
1.0715
13
1.1307
34
0.8608
3
  0.9226
4
0.9116
4
B97D3 1.2247
7
1.1661
26
1.2914
7
1.2837
7
1.1429
29
1.2074
7
1.1803
29
1.1621
7
1.1288
26
1.2069
7
1.1378
35
  1.1636
29
1.1862
7
1.1319
26
1.0519
2
1.0535
7
1.1477
29
0.9357
2
  0.9275
4
1.0835
27
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) 6-311+G(3df,2pd) TZVP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ Sadlej_pVTZ daug-cc-pVDZ daug-cc-pVTZ
Moller Plesset perturbation MP2 1.1540
27
1.1532
33
1.1399
32
1.1459
32
1.1249
35
1.1364
32
1.1508
33
1.1229
35
1.1295
32
1.0779
24
0.9669
3
1.3165
5
1.1376
35
1.1466
32
1.1036
27
1.0515
9
1.1084
27
1.1193
24
1.1315
12
0.7660
1
0.9241
4
0.9101
4
MP2=FULL 1.1883
25
1.1179
27
1.1481
25
1.1550
25
1.1401
32
1.1152
27
1.1171
27
1.1658
30
1.1070
27
1.1459
25
0.9658
3
0.7371
1
1.1727
22
1.1556
25
1.1305
25
1.1453
12
1.1343
24
1.1555
22
1.2087
10
0.7660
1
0.9236
4
0.9086
4
ROMP2 1.3203
2
1.3168
2
1.3168
2
1.2979
2
1.2979
2
1.2377
2
1.2377
2
1.2144
2
1.0676
2
1.2377
2
    1.0648
2
1.1926
2
1.0900
2
  0.9159
2
      0.7559
1
0.7385
1
MP3 0.7301
1
0.7453
1
0.7453
1
0.7418
1
1.1138
29
0.7354
1
1.1362
35
0.7415
1
0.7404
1
0.7354
1
0.9662
3
0.7395
1
1.1749
22
1.1542
19
1.1343
19
0.7387
1
0.7584
1
0.7400
1
0.7389
1
  0.9249
4
0.7407
2
MP3=FULL   1.1280
13
1.1280
13
1.1267
13
1.1434
35
1.1063
13
1.1365
35
1.1122
13
1.0861
13
1.1071
13
1.0782
2
  1.1735
22
1.1921
22
1.1306
19
  1.0704
13
0.9408
5
    0.9244
4
0.7407
2
MP4 0.7331
1
1.0148
16
0.7478
1
0.7442
1
1.0776
19
0.7369
1
0.7369
1
0.7443
3
1.0186
14
0.7369
1
0.7408
1
0.7413
1
1.1354
14
1.0863
11
1.0675
19
0.7405
1
1.0377
11
1.1301
14
0.7406
1
  0.7606
2
0.7422
2
MP4=FULL 0.7331
1
1.1783
14
0.7478
1
0.7442
1
1.1723
14
0.7369
1
0.7369
1
0.7443
1
1.1521
14
0.7369
1
0.7408
1
0.7413
1
  1.0856
11
1.0573
11
0.7405
1
1.1241
14
1.1135
12
0.7406
1
  0.7606
2
0.7422
2
B2PLYP 1.2118
22
1.1887
22
1.1887
22
1.1939
22
1.1517
35
1.1923
22
1.1958
22
1.1886
22
1.1769
22
1.1940
22
0.9671
3
0.7400
1
1.1789
22
1.1954
22
1.1305
35
0.7390
1
1.1701
22
1.1616
22
0.7391
1
  0.9236
4
0.9105
4
B2PLYP=FULL 1.2118
22
1.1876
22
1.1887
22
1.1939
22
1.1956
22
1.1544
19
1.1953
22
1.1884
22
1.1768
22
1.1933
22
1.0802
2
  1.1787
22
1.1952
22
1.1780
22
  1.1698
22
1.1688
20
    0.9234
4
0.9101
4
B2PLYP=FULLultrafine 1.1185
14
1.1044
14
1.1044
14
1.1001
14
1.0882
29
1.0938
14
1.0941
14
1.0896
14
1.0702
14
1.0938
14
1.0802
2
  1.0685
14
1.0604
24
1.0377
24
  1.0482
14
1.0197
24
    0.9234
4
0.9101
4
Configuration interaction CID 0.7349
1
1.1494
25
1.1114
22
1.1172
22
1.1242
27
0.7378
1
0.7378
1
1.1321
27
0.7428
1
0.7378
1
0.9628
3
0.7421
1
  0.9783
3
0.8742
5
0.7413
1
0.7608
1
0.7424
1
0.7414
1
  0.9227
4
0.7431
2
CISD 0.7349
1
1.0816
24
1.1496
25
1.1557
25
1.1246
27
  0.7385
1
1.1560
25
0.7434
1
0.7385
1
0.7421
1
0.7426
1
  0.9786
3
0.8746
5
0.7418
1
0.7613
1
0.7428
1
0.7419
1
  0.9230
4
0.7435
2
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) 6-311+G(3df,2pd) TZVP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ Sadlej_pVTZ daug-cc-pVDZ daug-cc-pVTZ
Quadratic configuration interaction QCISD 0.7349
1
1.1191
27
1.1191
27
1.1302
27
1.0893
24
1.1187
27
1.1203
27
1.1368
27
1.1414
25
1.1523
25
0.9686
3
0.7426
1
1.1786
22
1.1611
24
1.1529
24
0.7418
1
1.1738
22
1.2002
12
0.7419
1
  0.9274
4
0.7435
2
QCISD(T) 0.7349
1
0.7498
1
0.7498
1
0.7462
1
1.1409
24
0.7385
3
0.7385
3
1.0392
11
0.7435
1
0.7385
1
0.7422
1
0.7427
1
1.2031
17
1.1394
22
1.0695
19
0.7419
1
1.1510
20
1.1376
13
0.7420
1
  0.7621
2
0.7436
2
QCISD(T)=FULL         1.1013
11
  1.0824
9
            1.0875
11
1.0593
11
0.8792
4
1.0378
11
0.8256
4
0.8238
4
  0.9281
4
0.7436
2
QCISD(TQ)         1.5026
3
  0.7385
1
            1.5108
3
  0.7419
1
    0.7422
1
     
QCISD(TQ)=FULL         0.7462
1
  0.7385
1
            0.7608
1
0.7426
1
0.7419
1
0.7617
1
0.7430
1
0.7421
1
     
Coupled Cluster CCD 0.7349
1
1.1200
27
1.1151
22
1.1211
22
1.1273
27
1.1208
27
1.1202
27
1.1300
27
1.1441
25
1.1116
22
0.9681
3
0.7421
1
1.1781
22
1.1619
24
1.1450
24
0.7413
1
1.1770
22
1.2003
12
0.7414
1
  0.9270
4
0.7431
2
CCSD   0.7495
1
0.7495
1
0.7459
1
1.1281
27
0.9100
4
1.1630
7
0.9171
4
0.9718
3
1.0839
16
0.9684
3
0.7426
1
1.1785
22
1.1770
23
1.1807
18
1.1533
7
1.1712
22
1.1831
14
0.8237
4
  0.9274
4
0.7435
2
CCSD=FULL   0.7495
1
0.7495
1
0.7459
1
1.2018
22
0.7385
1
1.3090
4
0.7465
1
0.7434
1
1.0823
16
0.9673
3
0.7426
1
1.1766
22
1.1952
22
1.1753
22
1.1523
7
1.1744
22
1.1934
12
0.8237
4
  0.9268
4
0.7435
2
CCSD(T)   1.3332
5
0.7498
1
0.7462
1
1.1623
23
1.0201
11
0.9359
5
1.0390
11
1.0766
2
1.0675
3
0.7422
3
0.7427
1
1.2220
15
1.0378
13
1.1073
16
1.0708
10
1.1456
22
1.0468
10
0.8452
7
  0.7621
2
0.7436
2
CCSD(T)=FULL   0.7498
1
0.7498
1
0.7462
1
1.1949
20
0.7385
1
0.7385
1
0.7465
1
0.7435
1
0.7385
1
0.7422
1
0.7427
1
1.1364
14
1.2238
17
1.1386
14
0.8792
4
1.1441
14
1.2104
10
0.8238
4
  0.7621
2
0.7436
2
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) 6-311+G(3df,2pd) TZVP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ 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 1.1448
32
1.1599
31
1.1458
32
1.1717
32
1.1545
33
1.1406
32
    1.1226
35
density functional LSDA 0.7639
2
0.7639
2
0.7640
2
0.7640
2
0.7639
2
0.7639
2
     
BLYP 0.7482
1
0.7482
1
0.7462
1
0.7462
1
0.7482
1
0.7482
1
    1.0881
2
B1B95 1.2249
12
1.1893
11
0.7410
3
0.7410
3
0.7424
3
0.7424
3
    1.0799
2
B3LYP 1.1599
32
1.1749
31
1.1480
32
1.1744
32
1.1689
33
1.1548
32
    1.1293
35
B3LYPultrafine 0.7434
1
0.7434
1
0.7418
1
0.7418
1
0.7434
1
0.7434
1
    1.0815
2
B3PW91 0.7440
1
0.7440
1
0.7434
1
0.7434
1
0.7440
1
0.7440
1
    1.0829
2
mPW1PW91 0.7424
1
0.7424
1
0.7423
1
0.7423
1
0.7424
1
0.7424
1
    1.0816
2
M06-2X 0.7375
1
0.7375
1
0.7377
1
0.7377
1
0.7375
1
0.7375
1
    1.0811
2
PBEPBE 0.7514
1
0.7514
1
0.7504
1
0.7504
1
0.7514
1
0.7514
1
    1.1346
35
PBEPBEultrafine 0.7514
1
0.7514
1
0.7504
1
0.7504
1
0.7514
1
0.7514
1
    1.0905
2
PBE1PBE 0.7445
1
0.7445
1
0.7441
1
0.7441
1
0.7445
1
0.7445
1
    1.0830
2
HSEh1PBE 0.7444
1
0.7444
1
0.7439
1
0.7439
1
0.7444
1
0.7444
1
    1.0827
2
TPSSh                 1.0834
2
wB97X-D 1.1384
13
1.1721
12
1.1273
13
1.1594
12
1.1338
13
1.1338
13
    1.0812
2
B97D3                 1.0863
2
Moller Plesset perturbation MP2 1.1576
32
1.1659
31
1.1501
32
1.1699
32
1.1670
33
1.1525
32
    1.1266
35
MP2=FULL 0.7384
1
0.7384
1
0.7373
1
0.7373
1
0.7384
1
0.7384
1
    1.0786
2
MP3 0.7427
1
0.7427
1
0.7415
1
0.7415
1
0.7427
1
0.7427
1
    1.0785
2
MP3=FULL                 1.0761
2
MP4 0.7452
1
0.7452
1
0.7443
1
0.7443
1
0.7452
1
0.7452
1
     
MP4=FULL 0.7452
1
0.7452
1
0.7443
1
0.7443
1
0.7452
1
0.7452
1
     
B2PLYP 0.7400
1
0.7400
1
0.7391
1
0.7391
1
0.7400
1
0.7400
1
    1.0803
2
B2PLYP=FULL                 1.0796
2
B2PLYP=FULLultrafine                 1.0796
2
Configuration interaction CID 0.7465
1
0.7465
1
0.7461
1
0.7461
1
0.7465
1
0.7465
1
    1.0724
2
CISD 0.7469
1
0.7469
1
0.7465
1
0.7465
1
0.7469
1
0.7469
1
    1.0726
2
Quadratic configuration interaction QCISD 0.7469
1
0.7469
1
0.7465
1
0.7465
1
0.7469
1
0.7469
1
    1.0805
2
QCISD(T) 0.7473
1
0.7473
1
0.7465
1
0.7465
1
0.7473
1
0.7473
1
     
Coupled Cluster CCD 0.7465
1
0.7465
1
0.7461
1
0.7461
1
0.7465
1
0.7465
1
    1.0801
2
CCSD 0.7469
1
0.7469
1
0.7465
1
0.7465
1
0.7469
1
0.7469
1
    1.0804
2
CCSD=FULL 0.7469
1
0.7469
1
0.7465
1
0.7465
1
0.7469
1
0.7469
1
    1.0779
2
CCSD(T) 0.7473
1
0.7473
1
0.7465
1
0.7465
1
0.7473
1
0.7473
1
     
CCSD(T)=FULL 0.7473
1
0.7473
1
0.7465
1
0.7465
1
0.7473
1
0.7473
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.