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Release 18October 2016
NIST Standard Reference Database 101
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III.G.1.a.

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 1.2044
23
PM3 1.2787
17
PM6 1.1757
28
composite G2 1.1702
27
G3 1.1404
27
G3B3 1.1589
30
G3MP2 1.2761
5
G4 1.1708
30
CBS-Q 1.1683
26

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 daug-cc-pVTZ Sadlej_pVTZ
hartree fock HF 1.1549
22
1.1666
28
1.1516
27
1.1546
27
1.1626
30
1.1574
27
1.1732
28
1.1612
27
1.1551
27
1.1593
27
1.1689
8
1.3551
5
1.1636
30
1.1660
27
1.1575
27
1.1652
12
1.1435
27
1.1228
23
1.1508
12
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
0.7353
1
 
density functional LSDA 1.1825
27
1.1750
28
1.1750
28
1.1778
28
1.1765
28
1.1743
28
1.1784
28
1.1695
28
1.1606
28
1.1751
28
0.7640
3
0.7641
1
1.1989
17
1.1761
28
1.1618
28
0.7634
1
1.1580
28
1.1346
19
0.7634
1
0.7656
2
 
SVWN 0.7360
1
1.1689
30
0.7666
1
0.7633
1
1.1710
30
1.2201
17
1.1727
30
1.2059
17
1.1966
17
1.2222
17
0.7640
1
0.7641
1
1.1840
22
1.2157
17
1.1991
17
0.7634
1
1.1848
17
1.1782
17
0.7634
1
0.7656
2
 
BLYP 1.1768
22
1.2015
27
1.2015
27
1.1981
27
1.1464
30
1.1858
27
1.1902
27
1.1716
27
1.1641
27
1.1864
27
0.7463
1
0.7462
1
1.2261
17
1.1859
27
1.1659
27
0.7454
1
1.0872
16
1.0358
11
0.7454
1
0.7472
2
 
B1B95 1.2088
20
1.2148
25
1.2148
25
1.2126
25
1.2164
25
1.2163
25
1.2185
25
1.2085
25
1.2013
25
1.2161
25
0.7414
1
0.7413
1
1.2145
17
1.2167
25
1.2027
25
0.7405
1
1.1972
20
1.1782
17
0.7405
1
0.7419
2
 
B3LYP 1.1652
22
1.1816
28
1.1668
27
1.1662
27
1.1816
28
1.1680
27
1.1852
28
1.1614
27
1.1540
27
1.1750
30
0.7428
3
1.3254
5
1.1641
30
1.1730
27
1.1557
27
1.1596
12
1.1652
26
1.1499
30
1.1456
12
0.7434
2
0.7689
1
B3LYPultrafine 0.7284
1
1.2135
15
0.7462
1
0.7427
1
1.1816
28
1.1107
11
1.2022
15
1.0946
11
0.7440
1
0.7427
1
0.7427
1
1.3253
5
1.2143
17
1.2324
17
1.2140
17
0.7419
1
1.1973
17
1.1509
28
0.7419
1
0.7434
2
 
B3PW91 1.1668
22
1.1611
27
1.1611
27
1.1614
27
1.1640
27
1.1637
27
1.1669
27
1.1550
27
1.1489
27
1.1652
27
0.7441
1
0.7441
1
1.2070
17
1.1677
27
1.1518
27
0.7434
1
1.0756
16
1.0168
9
0.7434
1
0.7449
2
 
mPW1PW91 1.1624
22
1.1569
27
1.1569
27
1.1575
27
1.1602
27
1.1598
27
1.1629
27
1.1515
27
1.1460
27
1.1614
27
0.7431
1
0.7431
1
1.2030
17
1.1642
27
1.1487
27
0.7425
1
1.1763
24
1.1873
17
0.7425
1
0.7440
2
 
M06-2X 1.2360
17
1.2166
17
1.1338
30
1.2201
17
1.1660
30
1.2232
17
1.2267
17
1.2135
17
1.2054
17
1.2257
17
0.7384
1
0.7385
1
1.2079
17
1.2238
17
1.2064
17
0.7369
1
1.1879
17
1.1821
17
0.7368
1
0.7387
1
 
PBEPBE 1.1707
22
1.1878
28
1.1731
27
1.1857
26
1.1854
28
1.1719
27
1.1890
28
1.1613
27
1.1543
27
1.3802
27
0.7507
3
1.3157
5
1.2103
17
1.1744
27
1.1568
27
0.7502
1
1.1850
24
1.1671
20
0.7502
1
0.7518
2
0.7764
1
PBEPBEultrafine 0.7345
1
1.2194
15
0.7535
1
0.7505
1
1.2230
25
1.1174
11
1.2041
15
1.0908
11
0.7519
1
0.7497
1
0.7507
1
1.3177
5
1.2103
17
1.2305
17
1.2110
17
0.7502
1
1.2004
17
1.2132
18
0.7502
1
0.7518
2
 
PBE1PBE 1.2414
17
1.2155
17
1.2155
17
1.2193
17
1.1675
30
1.2249
17
1.2275
17
1.2086
17
1.1996
17
1.2257
17
0.7451
1
0.7451
1
1.2182
17
1.2208
17
1.2045
17
0.7446
1
1.1921
17
1.1864
17
0.7446
1
0.7461
2
 
HSEh1PBE 1.2409
17
1.1637
30
1.2157
17
1.2192
17
1.1671
30
1.2225
17
1.1695
30
1.2090
17
1.1993
17
1.2251
17
0.7448
1
0.7449
1
1.2026
17
1.2204
17
1.1566
30
0.7442
1
1.2179
17
1.1850
17
0.7442
1
0.7458
2
 
TPSSh 1.2004
3
1.2193
17
1.2194
17
1.2217
17
1.1600
30
1.2260
17
1.1615
30
1.2160
17
1.0171
3
1.0926
20
    1.2321
17
1.2263
17
1.1484
30
0.9378
3
1.1942
17
1.1896
17
0.8652
3
0.7420
1
 
wB97X-D 1.1877
8
1.1668
8
1.1387
30
1.1571
8
1.1363
30
1.1537
8
1.1382
30
1.1478
8
1.1342
30
1.1534
8
    1.1613
30
1.1680
30
1.1350
30
0.9525
3
1.0585
8
1.1462
29
0.8608
3
0.7424
2
 
B97D3 1.5180
2
1.2307
24
1.7928
2
1.7649
2
1.1524
24
1.4961
2
1.4961
2
1.3403
2
1.1811
24
1.4961
2
    1.2413
2
1.4050
2
1.2554
2
1.0519
2
0.9473
2
1.1576
24
0.9357
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 cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ daug-cc-pVTZ Sadlej_pVTZ
Moller Plesset perturbation MP2 1.1653
22
1.1745
28
1.1595
27
1.1642
27
1.1380
30
1.1540
27
1.1699
28
1.1355
30
1.1449
27
1.1546
27
0.7366
1
1.3165
5
1.1531
30
1.1632
27
1.1411
27
1.1464
12
1.1455
27
1.1284
19
1.1315
12
0.7383
2
0.7660
1
MP2=FULL 1.2094
20
1.1594
27
1.1928
25
1.1982
25
1.1576
27
1.1531
27
1.1551
27
1.1896
25
1.1442
27
1.1859
25
0.7366
1
0.7371
1
1.1988
17
1.1952
25
1.1708
25
1.1453
12
1.1446
19
1.1773
17
1.2087
10
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
    0.7385
1
 
MP3 0.7301
1
0.7453
1
0.7453
1
0.7418
1
1.1677
27
0.7354
1
1.1518
30
0.7415
1
0.7404
1
0.7354
1
0.7391
1
0.7395
1
1.2017
17
1.2378
17
1.2134
17
0.7387
1
0.7584
1
0.7400
1
0.7389
1
0.7407
2
 
MP3=FULL   1.1529
8
1.1529
8
1.1485
8
1.1595
30
1.1217
8
1.1524
30
1.1277
8
1.0854
8
1.1224
8
    1.2001
17
1.2204
17
1.1987
17
  1.0552
8
0.8508
3
  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
0.7422
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
0.7422
2
 
B2PLYP 1.2444
17
1.2192
17
1.2192
17
1.2253
17
1.1695
30
1.2237
17
1.2281
17
1.2188
17
1.2036
17
1.2259
17
0.7400
1
0.7400
1
1.2067
17
1.2250
17
1.1457
30
0.7390
1
1.1929
17
1.1846
17
0.7391
1
0.7406
2
 
B2PLYP=FULL 1.2444
17
1.2177
17
1.2192
17
1.2253
17
1.2274
17
1.2235
17
1.2275
17
1.2186
17
1.2035
17
1.2251
17
    1.2066
17
1.2248
17
1.2062
17
  1.1926
17
1.1976
15
  0.7406
2
 
B2PLYP=FULLultrafine 1.1283
9
1.1152
9
1.1152
9
1.1074
9
1.1717
14
1.0985
9
1.0987
9
1.0917
9
1.0614
9
1.0985
9
    1.0599
9
1.0977
9
1.0612
9
  1.0237
9
1.0113
9
  0.7406
2
 
Configuration interaction CID 0.7349
1
1.1925
25
1.1891
25
1.2046
25
1.1609
27
0.7378
1
0.7378
1
1.1434
22
1.1894
6
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
0.7431
2
 
CISD 0.7349
1
1.1569
27
1.1927
25
1.1973
25
1.1613
27
  0.7385
1
1.1954
25
1.1898
6
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
0.7435
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 daug-cc-pVTZ Sadlej_pVTZ
Quadratic configuration interaction QCISD 0.7349
1
1.1602
27
1.1255
22
1.1383
22
1.1657
27
1.1265
22
1.1284
22
1.1474
22
1.1544
20
1.1688
20
0.7421
1
0.7426
1
1.2060
17
1.2023
24
1.1711
19
0.7418
1
1.1964
17
1.2002
12
0.7419
1
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
0.7436
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
0.7436
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
1.1608
27
1.1646
20
1.1792
20
1.1662
27
1.1262
22
1.1283
22
1.1416
22
1.1683
20
1.1685
20
0.7416
1
0.7421
1
1.2055
17
1.2006
24
1.1624
19
0.7413
1
1.1987
17
1.2003
12
0.7414
1
0.7431
2
 
CCSD   0.7495
1
0.7495
1
0.7459
1
1.1367
22
0.7385
2
1.1954
5
0.7465
2
0.7434
1
1.0828
11
0.7421
1
0.7426
1
1.2059
17
1.1988
18
1.1807
18
1.2375
10
1.1930
17
1.2001
12
0.8237
4
0.7435
2
 
CCSD=FULL   0.7495
1
0.7495
1
0.7459
1
1.2346
17
0.7385
1
1.3090
4
0.7465
1
0.7434
1
1.0814
11
0.7421
1
0.7426
1
1.2036
17
1.2239
17
1.2034
17
1.2376
10
1.1974
17
1.1934
12
0.8237
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
1.1505
20
1.0468
10
0.8452
7
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
0.7436
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 daug-cc-pVTZ Sadlej_pVTZ

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 1.1636
27
1.1820
26
1.1659
27
1.1966
27
1.1759
28
1.1603
27
density functional LSDA 0.7639
2
0.7639
2
0.7640
2
0.7640
2
0.7639
2
0.7639
2
SVWN 0.7639
1
0.7639
1
0.7640
1
0.7640
1
0.7639
1
0.7639
1
BLYP 0.7482
1
0.7482
1
0.7462
1
0.7462
1
0.7482
1
0.7482
1
B1B95 1.2401
12
1.2057
11
0.7410
3
0.7410
3
0.7424
3
0.7424
3
B3LYP 1.1795
27
1.1978
26
1.1668
27
1.1982
27
1.1907
28
1.1749
27
B3LYPultrafine 0.7434
1
0.7434
1
0.7418
1
0.7418
1
0.7434
1
0.7434
1
B3PW91 0.7440
1
0.7440
1
0.7434
1
0.7434
1
0.7440
1
0.7440
1
mPW1PW91 0.7424
1
0.7424
1
0.7423
1
0.7423
1
0.7424
1
0.7424
1
M06-2X 0.7375
1
0.7375
1
0.7377
1
0.7377
1
0.7375
1
0.7375
1
PBEPBE 0.7514
1
0.7514
1
0.7504
1
0.7504
1
0.7514
1
0.7514
1
PBEPBEultrafine 0.7514
1
0.7514
1
0.7504
1
0.7504
1
0.7514
1
0.7514
1
PBE1PBE 0.7445
1
0.7445
1
0.7441
1
0.7441
1
0.7445
1
0.7445
1
HSEh1PBE 0.7444
1
0.7444
1
0.7439
1
0.7439
1
0.7444
1
0.7444
1
wB97X-D 1.1671
8
1.2276
7
1.1515
8
1.2090
7
1.1631
8
1.1631
8
Moller Plesset perturbation MP2 1.1756
27
1.1865
26
1.1687
27
1.1928
27
1.1877
28
1.1714
27
MP2=FULL 0.7384
1
0.7384
1
0.7373
1
0.7373
1
0.7384
1
0.7384
1
MP3 0.7427
1
0.7427
1
0.7415
1
0.7415
1
0.7427
1
0.7427
1
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
Configuration interaction CID 0.7465
1
0.7465
1
0.7461
1
0.7461
1
0.7465
1
0.7465
1
CISD 0.7469
1
0.7469
1
0.7465
1
0.7465
1
0.7469
1
0.7469
1
Quadratic configuration interaction QCISD 0.7469
1
0.7469
1
0.7465
1
0.7465
1
0.7469
1
0.7469
1
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
CCSD 0.7469
1
0.7469
1
0.7465
1
0.7465
1
0.7469
1
0.7469
1
CCSD=FULL 0.7469
1
0.7469
1
0.7465
1
0.7465
1
0.7469
1
0.7469
1
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.