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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 1.1721
21
PM3 1.2911
20
PM6 1.1424
26
composite G2 1.1380
25
G3 1.1058
25
G3B3 1.1277
28
G3MP2 1.2761
5
G4 1.1410
28
CBS-Q 1.1221
24

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 Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ daug-cc-pVDZ daug-cc-pVTZ Sadlej_pVTZ
hartree fock HF 1.1471
25
1.1335
26
1.1160
25
1.1206
25
1.1333
28
1.1243
25
1.1426
26
1.1284
25
1.1219
25
1.1265
25
0.9940
3
1.3551
5
1.1346
28
1.1070
28
1.1339
25
1.1246
25
1.1652
12
1.1095
25
1.1177
26
1.1508
12
0.7484
2
0.7349
2
0.7555
1
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 1.1690
25
1.1652
25
1.1652
25
1.1633
25
1.1133
28
1.1512
25
1.1560
25
1.1359
25
1.1278
25
1.1523
25
0.7463
1
0.7462
1
1.2062
20
  1.1518
25
1.1301
25
0.7454
1
1.0122
14
1.0479
14
0.7454
1
0.7666
2
0.7472
2
 
B1B95 1.1948
23
1.1999
22
1.1801
23
1.1794
23
1.1845
23
1.1846
23
1.1869
23
1.1761
23
1.1683
23
1.1845
23
0.7414
1
0.7413
1
1.1951
20
  1.1853
23
1.1700
23
0.7405
1
1.1549
18
1.1642
20
0.7405
1
0.7584
2
0.7419
2
 
B3LYP 1.1579
25
1.1473
26
1.1300
25
1.1310
25
1.1497
26
1.1339
25
1.1537
26
1.1267
25
1.1188
25
1.1453
28
0.7428
3
1.3254
5
1.1336
28
1.1123
28
1.1396
25
1.1209
25
1.1596
12
1.1298
24
1.1183
28
1.1456
12
0.7610
2
0.7434
2
0.7689
1
B3LYPultrafine 0.7284
1
1.1930
18
0.7462
1
0.7427
1
1.1497
26
1.1063
14
1.1836
18
1.0933
14
0.7440
1
0.7427
1
0.7427
1
1.3253
5
1.1953
20
  1.2121
20
1.1948
20
0.7419
1
1.1818
20
1.1172
26
0.7419
1
0.7610
2
0.7434
2
 
B3PW91 1.1592
25
1.1247
25
1.1247
25
1.1264
25
1.1302
25
1.1299
25
1.1334
25
1.1206
25
1.1141
25
1.1318
25
0.7441
1
0.7441
1
1.1893
20
  1.1346
25
1.1174
25
0.7434
1
1.0033
14
1.0345
12
0.7434
1
0.7601
2
0.7449
2
 
mPW1PW91 1.1551
25
1.1206
25
1.1206
25
1.1226
25
1.1264
25
1.1260
25
1.1294
25
1.1172
25
1.1113
25
1.1281
25
0.7431
1
0.7431
1
1.1857
20
  1.1312
25
1.1144
25
0.7425
1
1.1398
22
1.1721
20
0.7425
1
0.7590
2
0.7440
2
 
M06-2X 1.2156
20
1.1978
20
1.1333
28
1.2006
20
1.1363
28
1.2032
20
1.2062
20
1.1947
20
1.1878
20
1.2054
20
0.7384
1
0.7385
1
1.1899
20
  1.2046
20
1.1884
20
0.7369
1
1.1737
20
1.1678
20
0.7368
1
0.7540
1
0.7387
1
 
PBEPBE 1.1634
25
1.1533
26
1.1361
25
1.1499
24
1.1534
26
1.1376
25
1.1575
26
1.1262
25
1.1188
25
1.1392
25
0.7507
3
1.3157
5
1.1931
20
1.1168
28
1.1407
25
1.1216
25
0.7502
1
1.1477
22
1.1577
23
0.7502
1
0.7688
2
0.7518
2
0.7764
1
PBEPBEultrafine 0.7345
1
1.1995
18
0.7535
1
0.7505
1
1.1901
23
1.1133
14
1.1865
18
1.0920
14
0.7519
1
0.7497
1
0.7507
1
1.3177
5
1.1932
20
  1.2117
20
1.1936
20
0.7502
1
1.1856
20
1.1963
21
0.7502
1
0.7688
2
0.7518
2
 
PBE1PBE 1.2204
20
1.2206
19
1.1970
20
1.2000
20
1.1380
28
1.2048
20
1.2070
20
1.1906
20
1.1831
20
1.2055
20
0.7451
1
0.7451
1
1.1988
20
  1.2022
20
1.1870
20
0.7446
1
1.1775
20
1.1716
20
0.7446
1
0.7613
2
0.7461
2
 
HSEh1PBE 1.2200
20
1.1329
28
1.1971
20
1.1998
20
1.1378
28
1.2027
20
1.1402
28
1.1910
20
1.1828
20
1.2049
20
0.7448
1
0.7449
1
1.1854
20
  1.2018
20
1.1268
28
0.7442
1
1.1993
20
1.1704
20
0.7442
1
0.7612
2
0.7458
2
 
TPSSh 1.1530
6
1.2002
20
1.2002
20
1.2019
20
1.1256
28
1.2056
20
1.1306
28
1.1968
20
1.0531
6
1.0370
18
    1.2105
20
  1.2069
20
1.1169
28
0.9378
3
1.1792
20
1.1743
20
0.8652
3
0.7554
1
0.7420
1
 
wB97X-D 1.1646
11
1.1460
11
1.1054
28
1.1388
11
1.1042
28
1.1363
11
1.1062
28
1.1317
11
1.1022
28
1.1362
11
    1.1313
28
  1.1389
28
1.1031
28
0.9525
3
1.0682
11
1.1140
27
0.8608
3
0.7566
2
0.7424
2
 
B97D3 1.2730
5
1.1507
19
1.3740
5
1.3622
5
1.1222
22
1.2544
5
1.1714
22
1.1911
5
1.1008
19
1.2545
5
1.1216
28
  1.1511
5
  1.2219
5
1.1059
19
1.0519
2
1.0371
5
1.1302
22
0.9357
2
0.7615
2
0.7453
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 Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ daug-cc-pVDZ daug-cc-pVTZ Sadlej_pVTZ
Moller Plesset perturbation MP2 1.1583
25
1.1385
26
1.1209
25
1.1271
25
1.1054
28
1.1186
25
1.1370
26
1.1031
28
1.1092
25
1.1201
25
0.7366
1
1.3165
5
1.1222
28
1.1089
28
1.1290
25
1.1054
25
1.1464
12
1.1096
25
1.1227
22
1.1315
12
0.7555
2
0.7383
2
0.7660
1
MP2=FULL 1.1960
23
1.1208
25
1.1538
23
1.1608
23
1.1228
25
1.1179
25
1.1199
25
1.1549
23
1.1087
25
1.1516
23
0.7366
1
0.7371
1
1.1819
20
  1.1609
23
1.1352
23
1.1453
12
1.1381
22
1.1633
20
1.2087
10
0.7555
2
0.7383
2
0.7660
1
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
1.1340
25
0.7354
1
1.1207
28
0.7415
1
0.7404
1
0.7354
1
0.7391
1
0.7395
1
1.1844
20
  1.2170
20
1.1941
20
0.7387
1
0.7584
1
0.7400
1
0.7389
1
0.7588
2
0.7407
2
 
MP3=FULL   1.1363
11
1.1363
11
1.1339
11
1.1291
28
1.1113
11
1.1212
28
1.1172
11
1.0865
11
1.1123
11
    1.1829
20
  1.2021
20
1.1811
20
  1.0666
11
0.8508
3
  0.7588
2
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 1.2233
20
1.1997
20
1.1997
20
1.2050
20
1.1435
28
1.2033
20
1.2071
20
1.1990
20
1.1863
20
1.2052
20
0.7400
1
0.7400
1
1.1886
20
  1.2057
20
1.1140
28
0.7390
1
1.1781
20
1.1697
20
0.7391
1
0.7579
2
0.7406
2
 
B2PLYP=FULL 1.2233
20
1.1984
20
1.1996
20
1.2050
20
1.2066
20
1.2030
20
1.2065
20
1.1989
20
1.1861
20
1.2045
20
    1.1885
20
  1.2055
20
1.1879
20
  1.1778
20
1.1788
18
  0.7579
2
0.7406
2
 
B2PLYP=FULLultrafine 1.1221
12
1.1086
12
1.1086
12
1.1030
12
1.1020
12
1.0956
12
1.0959
12
1.0905
12
1.0680
12
1.0958
12
    1.0664
12
  1.0973
12
1.0669
12
  1.0412
12
1.0296
12
  0.7579
2
0.7406
2
 
Configuration interaction CID 0.7349
1
1.1558
23
1.1521
23
1.1702
23
1.1278
25
0.7378
1
0.7378
1
1.1363
25
0.7428
1
0.7378
1
0.7416
1
0.7421
1
    0.7603
1
0.7421
3
0.7413
1
0.7608
1
0.7424
1
0.7414
1
0.7612
2
0.7431
2
 
CISD 0.7349
1
1.1202
25
1.1559
23
1.1622
23
1.1282
25
  0.7385
1
1.1627
23
0.7434
1
0.7385
1
0.7421
1
0.7426
1
    0.7609
1
0.7426
3
0.7418
1
0.7613
1
0.7428
1
0.7419
1
0.7618
2
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 Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ daug-cc-pVDZ daug-cc-pVTZ Sadlej_pVTZ
Quadratic configuration interaction QCISD 0.7349
1
1.1218
25
1.1218
25
1.1334
25
1.1314
25
1.1217
25
1.1234
25
1.1407
25
1.1462
23
1.1584
23
0.7421
1
0.7426
1
1.1883
20
  1.1670
22
1.1595
22
0.7418
1
1.1818
20
1.2002
12
0.7419
1
0.7618
2
0.7435
2
 
QCISD(T) 0.7349
1
0.7498
1
0.7498
1
0.7462
1
1.1455
22
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
0.7621
2
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
1.1229
25
1.1554
23
1.1685
23
1.1305
25
1.1240
25
1.1233
25
1.1334
25
1.1492
23
1.1581
23
0.7416
1
0.7421
1
1.1877
20
  1.1679
22
1.1509
22
0.7413
1
1.1853
20
1.2003
12
0.7414
1
0.7612
2
0.7431
2
 
CCSD   0.7495
1
0.7495
1
0.7459
1
1.1314
25
0.7385
2
1.1954
5
0.7465
2
0.7434
1
1.0841
14
0.7421
1
0.7426
1
1.1882
20
  1.1847
21
1.1807
18
1.2375
10
1.1790
20
1.2001
12
0.8237
4
0.7618
2
0.7435
2
 
CCSD=FULL   0.7495
1
0.7495
1
0.7459
1
1.2132
20
0.7385
1
1.3090
4
0.7465
1
0.7434
1
1.0825
14
0.7421
1
0.7426
1
1.1861
20
  1.2052
20
1.1853
20
1.2376
10
1.1825
20
1.1934
12
0.8237
4
0.7618
2
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
1.1505
20
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 Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ daug-cc-pVDZ daug-cc-pVTZ Sadlej_pVTZ

average calculated bond lengths (Å)
Methods with effective core potentials (select basis sets)
daug-cc-pVDZ daug-cc-pVTZ daug-cc-pVQZ Sadlej_pVTZ CEP-31G CEP-31G* CEP-121G CEP-121G* LANL2DZ SDD
hartree fock HF 0.7484
2
0.7349
2
  0.7555
1
1.1284
25
1.1482
24
1.1310
25
1.1654
25
1.1437
26
1.1256
25
ROHF 0.7487
1
0.7353
1
               
density functional LSDA 0.7808
2
0.7656
2
    0.7639
2
0.7639
2
0.7640
2
0.7640
2
0.7639
2
0.7639
2
BLYP 0.7666
2
0.7472
2
    0.7482
1
0.7482
1
0.7462
1
0.7462
1
0.7482
1
0.7482
1
B1B95 0.7584
2
0.7419
2
    1.1939
7
1.1291
6
0.7410
3
0.7410
3
0.7424
3
0.7424
3
B3LYP 0.7610
2
0.7434
2
  0.7689
1
1.1431
25
1.1631
24
1.1296
25
1.1650
25
1.1578
26
1.1394
25
B3LYPultrafine 0.7610
2
0.7434
2
    0.7434
1
0.7434
1
0.7418
1
0.7418
1
0.7434
1
0.7434
1
B3PW91 0.7601
2
0.7449
2
    0.7440
1
0.7440
1
0.7434
1
0.7434
1
0.7440
1
0.7440
1
mPW1PW91 0.7590
2
0.7440
2
    0.7424
1
0.7424
1
0.7423
1
0.7423
1
0.7424
1
0.7424
1
M06-2X 0.7540
1
0.7387
1
    0.7375
1
0.7375
1
0.7377
1
0.7377
1
0.7375
1
0.7375
1
PBEPBE 0.7688
2
0.7518
2
  0.7764
1
0.7514
1
0.7514
1
0.7504
1
0.7504
1
0.7514
1
0.7514
1
PBEPBEultrafine 0.7688
2
0.7518
2
    0.7514
1
0.7514
1
0.7504
1
0.7504
1
0.7514
1
0.7514
1
PBE1PBE 0.7613
2
0.7461
2
    0.7445
1
0.7445
1
0.7441
1
0.7441
1
0.7445
1
0.7445
1
HSEh1PBE 0.7612
2
0.7458
2
    0.7444
1
0.7444
1
0.7439
1
0.7439
1
0.7444
1
0.7444
1
TPSSh 0.7554
1
0.7420
1
               
wB97X-D 0.7566
2
0.7424
2
    1.1475
11
1.1881
10
1.1349
11
1.1736
10
1.1432
11
1.1432
11
B97D3 0.7615
2
0.7453
2
               
Moller Plesset perturbation MP2 0.7555
2
0.7383
2
  0.7660
1
1.1371
25
1.1509
24
1.1299
25
1.1592
25
1.1525
26
1.1335
25
MP2=FULL 0.7555
2
0.7383
2
  0.7660
1
0.7384
1
0.7384
1
0.7373
1
0.7373
1
0.7384
1
0.7384
1
ROMP2 0.7559
1
0.7385
1
               
MP3 0.7588
2
0.7407
2
    0.7427
1
0.7427
1
0.7415
1
0.7415
1
0.7427
1
0.7427
1
MP3=FULL 0.7588
2
0.7407
2
               
MP4 0.7606
2
0.7422
2
    0.7452
1
0.7452
1
0.7443
1
0.7443
1
0.7452
1
0.7452
1
MP4=FULL 0.7606
2
0.7422
2
    0.7452
1
0.7452
1
0.7443
1
0.7443
1
0.7452
1
0.7452
1
B2PLYP 0.7579
2
0.7406
2
    0.7400
1
0.7400
1
0.7391
1
0.7391
1
0.7400
1
0.7400
1
B2PLYP=FULL 0.7579
2
0.7406
2
               
B2PLYP=FULLultrafine 0.7579
2
0.7406
2
               
Configuration interaction CID 0.7612
2
0.7431
2
    0.7465
1
0.7465
1
0.7461
1
0.7461
1
0.7465
1
0.7465
1
CISD 0.7618
2
0.7435
2
    0.7469
1
0.7469
1
0.7465
1
0.7465
1
0.7469
1
0.7469
1
Quadratic configuration interaction QCISD 0.7618
2
0.7435
2
    0.7469
1
0.7469
1
0.7465
1
0.7465
1
0.7469
1
0.7469
1
QCISD(T) 0.7621
2
0.7436
2
    0.7473
1
0.7473
1
0.7465
1
0.7465
1
0.7473
1
0.7473
1
QCISD(T)=FULL 0.7621
2
0.7436
2
               
Coupled Cluster CCD 0.7612
2
0.7431
2
    0.7465
1
0.7465
1
0.7461
1
0.7461
1
0.7465
1
0.7465
1
CCSD 0.7618
2
0.7435
2
    0.7469
1
0.7469
1
0.7465
1
0.7465
1
0.7469
1
0.7469
1
CCSD=FULL 0.7618
2
0.7435
2
    0.7469
1
0.7469
1
0.7465
1
0.7465
1
0.7469
1
0.7469
1
CCSD(T) 0.7621
2
0.7436
2
    0.7473
1
0.7473
1
0.7465
1
0.7465
1
0.7473
1
0.7473
1
CCSD(T)=FULL 0.7621
2
0.7436
2
    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.