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Release 19April 2018
NIST Standard Reference Database 101
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III.G.1.a.

Comparison of levels of theory for O-N


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 1.2144
54
PM3 1.2564
72
PM6 1.2514
131
composite G2 1.2760
104
G3 1.2537
115
G3B3 1.2893
126
G3MP2 1.1600
10
G4 1.2764
130
CBS-Q 1.2515
98

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 cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ Sadlej_pVTZ
hartree fock HF 1.3132
116
1.2900
115
1.2904
114
1.2637
115
1.2506
134
1.2537
121
1.2291
71
1.2470
121
1.2207
115
1.2219
110
1.2106
52
1.1149
1
1.2238
124
1.2335
143
1.2489
121
1.2496
114
1.2413
41
1.2246
105
1.2546
105
1.2498
36
1.1434
3
1.1529
3
1.1495
3
1.1845
2
1.1782
2
1.1554
4
ROHF 1.3254
10
1.2997
20
1.3005
20
1.2244
16
1.2552
23
1.2592
20
1.2640
20
1.2534
20
1.2579
19
1.2991
10
1.1735
2
1.1149
1
1.1837
10
1.1748
2
1.2540
20
1.2552
20
1.2584
19
1.2635
19
1.2595
19
1.2580
19
      1.1206
2
1.1138
1
 
density functional LSDA 1.3496
114
1.3126
105
1.3127
111
1.2896
107
1.2552
109
1.2557
106
1.2555
106
1.2492
109
1.2499
106
1.2495
106
1.1263
3
1.1446
1
1.2445
55
1.1301
4
1.2520
106
1.2482
106
1.2066
12
1.2499
98
1.2414
58
1.2048
12
      1.1550
1
1.1458
1
 
BLYP 1.3809
111
1.3500
111
1.3488
102
1.3311
112
1.2823
137
1.2904
110
1.2888
111
1.2825
101
1.2847
112
1.2829
112
1.1768
4
1.1611
1
1.2834
58
1.1737
5
1.2863
112
1.2831
112
1.1613
1
1.3389
73
1.2485
32
1.1609
1
      1.2121
2
1.2010
2
 
B1B95 1.3419
113
1.3142
100
1.3123
115
1.2917
114
1.2530
111
1.2540
111
1.2536
111
1.2481
111
1.2482
111
1.2475
114
1.1534
4
1.1381
1
1.2489
57
1.1493
5
1.2503
111
1.2457
114
1.1930
14
1.2482
103
1.2406
88
1.1902
14
      1.1959
2
1.2322
1
 
B3LYP 1.3914
121
1.3233
121
1.3241
121
1.3056
120
1.2961
121
1.2679
115
1.2663
117
1.2614
117
1.2591
78
1.2602
120
1.3374
48
1.1446
1
1.2678
125
1.2628
142
1.2636
117
1.2612
115
1.2433
35
1.2703
84
1.2699
119
1.2420
35
1.1664
3
1.1763
3
1.1700
3
1.2048
2
1.1950
2
1.1881
4
B3LYPultrafine 1.2401
1
1.3034
39
1.1949
1
1.1827
1
1.2655
111
1.2500
38
1.2490
61
1.2422
38
1.1483
1
1.1680
4
1.1608
4
1.1446
1
1.2530
42
1.1567
5
1.2578
49
1.2521
78
1.1445
1
1.2586
46
1.2776
125
1.1443
1
      1.2048
2
1.1950
2
 
B3PW91 1.3438
81
1.3164
116
1.3172
116
1.2953
115
1.2585
112
1.2584
112
1.2561
101
1.2514
112
1.2473
73
1.2527
112
1.1571
4
1.1421
1
1.2538
58
1.1534
5
1.2544
112
1.2518
112
1.1421
1
1.3060
73
1.2360
49
1.1418
1
      1.1995
2
1.1894
2
 
mPW1PW91 1.3391
81
1.3130
112
1.3130
82
1.2907
115
1.2544
111
1.2547
112
1.2533
113
1.2476
113
1.2471
115
1.2481
112
1.1541
4
1.1390
1
1.2498
58
1.1503
5
1.2509
112
1.2437
94
1.1390
1
1.2934
97
1.2441
53
1.1387
1
      1.1983
2
1.1897
2
 
M06-2X 1.3329
58
1.3115
58
1.3133
136
1.2886
57
1.2514
116
1.2513
57
1.2516
57
1.2463
57
1.2461
57
1.2434
71
1.1534
4
1.1358
1
1.2475
57
1.1482
5
1.2479
57
1.2436
71
1.1356
1
1.2474
51
1.2410
63
1.1354
1
      1.1989
2
1.1940
2
 
PBEPBE 1.3629
77
1.3377
112
1.3359
73
1.3124
72
1.2766
111
1.2765
111
1.2764
111
1.2712
111
1.2713
111
1.2706
111
1.3540
48
1.1569
1
1.2702
57
1.2712
142
1.2751
108
1.2704
111
1.2154
14
1.2676
55
1.2655
67
1.2113
14
      1.2028
2
1.1931
2
1.1961
4
PBEPBEultrafine 1.2557
1
1.3159
39
1.2142
1
1.1973
1
1.2727
94
1.2536
38
1.2529
38
1.2457
38
1.1606
1
1.1789
4
1.1705
4
1.1568
1
1.2576
42
1.1683
5
1.2652
49
1.2624
49
1.1572
1
1.2645
46
1.2606
46
1.1568
1
      1.2028
2
1.1930
2
 
PBE1PBE 1.3384
55
1.3089
49
1.3101
55
1.2891
54
1.2604
119
1.2512
54
1.2511
54
1.2447
54
1.2448
54
1.2456
54
1.1542
4
1.1394
1
1.2470
54
1.1505
5
1.2468
54
1.2449
54
1.1394
1
1.2477
51
1.2430
49
1.1392
1
      1.1973
2
1.1888
2
 
HSEh1PBE 1.3412
58
1.3158
119
1.3121
58
1.2912
57
1.2532
116
1.2530
57
1.2615
118
1.2468
57
1.2469
57
1.2474
57
1.1541
4
1.1392
1
1.2492
57
1.1503
5
1.2489
57
1.2555
118
1.1392
1
1.2480
51
1.2433
49
1.1390
1
      1.1972
2
1.1883
2
 
TPSSh 1.3063
17
1.3195
43
1.3211
43
1.3008
42
1.2703
134
1.2600
42
1.2693
134
1.2494
42
1.1897
16
1.2652
119
1.1643
4
  1.2521
42
1.1604
5
1.2531
42
1.2635
134
1.1758
8
1.2519
39
1.2482
39
1.1744
8
      1.2049
2
1.1933
2
 
wB97X-D 1.3248
30
1.2896
30
1.2999
139
1.2714
29
1.2620
138
1.2383
29
1.2621
138
1.2309
29
1.2571
138
1.2330
29
1.1556
4
  1.2577
138
1.1512
5
1.2612
138
1.2563
138
1.2239
18
1.2352
29
1.2558
138
1.2232
18
      1.2021
2
1.1944
2
 
B97D3 1.3045
11
1.3048
126
1.2508
11
1.2110
10
1.2657
125
1.1816
10
1.2653
125
1.1692
10
1.2606
125
1.1736
10
1.2622
141
  1.1677
10
1.1643
5
1.1750
10
1.2589
125
1.1542
6
1.1724
10
1.2648
124
1.1525
6
      1.2019
2
1.1912
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 cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ Sadlej_pVTZ
Moller Plesset perturbation MP2 1.3558
80
1.3483
122
1.3490
122
1.3390
115
1.2799
134
1.2808
121
1.2886
113
1.2693
137
1.2659
115
1.2600
99
1.1638
4
1.1362
1
1.2783
126
1.2667
142
1.2742
121
1.2651
98
1.2420
22
1.2766
82
1.2609
82
1.2411
21
1.1741
3
1.1743
4
1.1678
4
1.2088
2
1.2007
2
1.1941
4
MP2=FULL 1.3552
79
1.3450
96
1.3477
84
1.3404
83
1.2763
115
1.2779
100
1.2795
104
1.2642
115
1.2636
73
1.2580
87
1.1617
4
1.1354
1
1.2727
58
1.1591
5
1.2689
96
1.2587
96
1.2394
22
1.2727
67
1.2517
76
1.2383
21
1.1708
3
1.1738
4
1.1663
4
1.2081
2
1.1964
2
1.1932
4
ROMP2 1.4374
17
1.3284
15
1.3401
17
1.3216
17
1.2592
17
1.2591
17
1.2619
17
1.2357
14
1.2360
14
1.2377
14
1.1566
1
1.1566
1
1.2391
11
1.1581
1
1.2433
14
1.2348
11
1.1792
4
1.2567
15
1.2156
7
1.1780
4
      1.1707
1
1.1594
1
 
MP3 1.1402
1
1.1392
1
1.1392
1
1.1348
1
1.2580
111
1.1410
1
1.2633
134
1.1308
1
1.1308
1
1.1346
1
1.1510
4
1.1300
1
1.2414
42
1.1470
5
1.2436
42
1.2368
42
1.1287
1
1.1391
1
1.1312
1
1.1287
1
      1.2005
2
1.1908
2
 
MP3=FULL   1.2974
30
1.2979
30
1.2854
29
1.2624
134
1.2428
29
1.2623
130
1.2286
29
1.2288
29
1.2285
29
1.1489
4
  1.2408
42
1.1459
5
1.2430
42
1.2326
42
  1.2366
27
1.2211
27
        1.1999
2
1.1860
2
 
MP4 1.3257
4
1.3873
76
1.3675
4
1.3649
4
1.2914
88
1.1476
1
1.1478
1
1.2466
4
1.2825
68
1.1896
4
1.1398
3
1.1413
1
1.2889
49
1.1444
4
1.2852
49
1.2721
71
1.1406
1
1.2898
44
1.2686
35
1.1405
1
      1.1467
1
1.1420
1
 
MP4=FULL 1.1603
1
1.3798
50
1.1441
1
1.1396
1
1.2837
45
1.1474
1
1.1476
1
1.1394
1
1.2780
49
1.1435
1
1.1379
3
1.1406
1
1.1390
1
1.1431
4
1.2845
49
1.2736
49
1.1397
1
1.2888
44
1.2688
39
1.1396
1
      1.1464
1
1.1403
1
 
B2PLYP 1.3419
39
1.3180
39
1.3193
39
1.3046
38
1.2744
102
1.2580
38
1.2593
38
1.2495
38
1.2497
38
1.2508
55
1.1667
4
1.1518
1
1.2543
38
1.1625
5
1.2525
38
1.2670
110
1.1514
1
1.2550
35
1.2510
52
1.1514
1
      1.2170
2
1.2085
2
 
B2PLYP=FULL 1.3419
39
1.3100
39
1.3192
39
1.3046
38
1.2557
38
1.2576
38
1.2569
38
1.2491
38
1.2493
38
1.2487
38
1.1659
4
1.1511
1
1.2540
38
1.1621
5
1.2523
38
1.2490
38
1.1508
1
1.2547
35
1.2478
35
1.1507
1
      1.2167
2
1.2067
2
 
B2PLYP=FULLultrafine 1.3369
31
1.3146
31
1.3157
31
1.3015
30
1.2633
68
1.2540
30
1.2551
30
1.2449
30
1.2451
30
1.2449
30
1.1659
4
  1.2498
30
1.1620
5
1.2483
30
1.2452
30
  1.2532
30
1.2461
30
        1.2167
2
1.2067
2
 
Configuration interaction CID 1.1651
1
1.3115
80
1.3145
72
1.2967
71
1.2541
102
1.2855
2
1.2848
2
1.2370
72
1.1302
1
1.1566
4
1.1484
4
1.1283
1
1.1297
1
1.1432
5
1.2122
5
1.2041
5
1.1268
1
1.1382
1
1.1295
1
1.1267
1
      1.1991
2
1.1888
2
 
CISD   1.3166
80
1.3196
72
1.3016
71
1.2560
102
1.4332
1
1.2892
2
1.2397
71
1.1355
1
1.1583
4
1.1515
4
1.1325
1
1.1352
1
1.1460
5
1.2161
5
1.2072
5
1.1308
1
1.1435
1
1.1337
1
1.1307
1
      1.2040
2
1.1930
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 cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ Sadlej_pVTZ
Quadratic configuration interaction QCISD 1.2852
5
1.3392
112
1.3540
74
1.3360
79
1.2676
101
1.2727
83
1.2706
86
1.2542
93
1.2575
91
1.2526
82
1.1656
4
1.1504
1
1.2644
57
1.1626
5
1.2617
84
1.2516
85
1.1481
1
1.2690
54
1.2515
63
1.1481
1
      1.1682
1
1.2081
2
 
QCISD(T) 1.2532
1
1.2239
1
1.2239
1
1.2042
1
1.2728
74
1.1763
1
1.1759
1
1.2511
34
1.1818
4
1.1625
1
1.1383
3
1.1567
1
1.2746
55
1.1410
4
1.2741
66
1.2642
61
1.1554
1
1.2766
55
1.2639
46
1.1557
1
      1.1709
1
1.1594
1
 
QCISD(T)=FULL         1.2649
37
  1.2670
37
      1.1359
3
    1.1397
4
1.2572
37
1.2449
34
1.2191
15
1.2630
34
1.2415
31
1.2258
15
      1.1702
1
1.1536
1
 
QCISD(TQ) 1.2683
1
1.2368
1
1.2368
1
1.2129
1
1.2290
19
1.1806
1
1.2174
16
1.1636
1
1.1636
1
1.1649
1
1.1364
3
1.1573
1
1.1651
1
1.1372
3
1.2202
19
1.1905
14
1.1855
7
1.2123
16
1.1872
11
1.1829
3
           
QCISD(TQ)=FULL         1.2151
16
  1.2275
14
      1.1338
3
    1.1108
2
1.2166
14
1.2093
11
1.1661
8
1.2106
15
1.1797
10
1.1071
2
           
Coupled Cluster CCD 1.2601
5
1.3304
82
1.3339
74
1.3144
79
1.2603
109
1.2641
79
1.2650
79
1.2503
80
1.2458
71
1.2445
69
1.1547
4
1.1324
1
1.2539
57
1.1512
5
1.2534
82
1.2465
70
1.1310
1
1.2561
60
1.2396
50
1.1309
1
  1.1644
2
1.1563
2
1.2663
1
1.2542
1
 
CCSD 1.2552
1
1.2170
1
1.2170
1
1.2001
1
1.2621
94
1.2247
2
1.2229
2
1.2086
3
1.2100
2
1.2414
53
1.1619
4
1.1453
1
1.2575
50
1.1585
5
1.2621
63
1.2508
75
1.2291
19
1.2632
47
1.2486
61
1.1972
13
    1.1462
1
1.2731
1
1.2614
1
 
CCSD=FULL 1.2551
1
1.2169
1
1.2169
1
1.1999
1
1.2618
63
1.1660
1
1.1654
1
1.1501
1
1.1501
1
1.2391
52
1.1593
4
1.1431
1
1.2562
49
1.1571
5
1.2573
49
1.2436
63
1.2253
17
1.2618
46
1.2399
59
1.1781
11
      1.2721
1
1.2543
1
 
CCSD(T) 1.2555
1
1.1029
1
1.2183
1
1.1999
1
1.2734
87
1.2595
38
1.1987
9
1.2488
34
1.1849
12
1.1830
9
1.1355
3
1.1511
1
1.2717
55
1.1385
4
1.2722
66
1.2546
63
1.2310
19
1.2728
57
1.2578
45
1.2329
18
  1.1809
4
1.1736
4
1.1637
1
1.1531
1
 
CCSD(T)=FULL 1.2554
1
1.2183
1
1.2183
1
1.1998
1
1.2803
61
1.1682
1
1.1677
1
1.1536
1
1.1536
1
1.1550
1
1.1334
3
1.1494
1
1.2706
54
1.1372
4
1.2700
60
1.2586
51
1.2335
18
1.2783
47
1.2541
39
1.2331
16
  1.1803
4
1.1720
4
1.1631
1
1.1488
1
 
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 cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ 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 1.1845
2
1.1782
2
  1.1554
4
1.3121
120
1.2707
113
1.2808
116
1.2655
115
1.3006
122
1.3016
120
ROHF 1.1206
2
1.1138
1
      1.1454
1
  1.1358
1
1.2022
1
1.2020
1
density functional LSDA 1.1550
1
1.1458
1
    1.2222
1
1.1867
1
1.2169
1
1.1779
1
1.2014
1
1.2013
1
BLYP 1.2121
2
1.2010
2
    1.2324
1
1.1954
1
1.2277
1
1.1872
1
1.2209
1
1.2211
1
B1B95 1.1959
2
1.2322
1
    1.3035
48
1.2621
48
1.1955
1
1.1598
1
1.1891
1
1.1892
1
B3LYP 1.2048
2
1.1950
2
  1.1881
4
1.3269
119
1.2841
112
1.3236
119
1.2792
114
1.3157
119
1.3161
117
B3LYPultrafine 1.2048
2
1.1950
2
    1.2120
1
1.1783
1
1.2078
1
1.1699
1
1.1990
1
1.1991
1
B3PW91 1.1995
2
1.1894
2
    1.2065
1
1.1738
1
1.2020
1
1.1651
1
1.1941
1
1.1942
1
mPW1PW91 1.1983
2
1.1897
2
    1.2019
1
1.1700
1
1.1976
1
1.1613
1
1.1898
1
1.1899
1
M06-2X 1.1989
2
1.1940
2
    1.1913
1
1.1623
1
1.1859
1
1.1517
1
1.1850
1
1.1850
1
PBEPBE 1.2028
2
1.1931
2
  1.1961
4
1.2242
1
1.1885
1
1.2194
1
1.1802
1
1.2136
1
1.2137
1
PBEPBEultrafine 1.2028
2
1.1930
2
    1.2242
1
1.1885
1
1.2194
1
1.1802
1
1.2136
1
1.2137
1
PBE1PBE 1.1973
2
1.1888
2
    1.2018
1
1.1699
1
1.1975
1
1.1613
1
1.1901
1
1.1902
1
HSEh1PBE 1.1972
2
1.1883
2
    1.2026
1
1.1705
1
1.1983
1
1.1619
1
1.1904
1
1.1905
1
TPSSh 1.2049
2
1.1933
2
               
wB97X-D 1.2021
2
1.1944
2
    1.2925
30
1.2566
29
1.2889
30
1.2517
29
1.2787
30
1.2786
30
B97D3 1.2019
2
1.1912
2
               
Moller Plesset perturbation MP2 1.2088
2
1.2007
2
  1.1941
4
1.3592
120
1.2973
113
1.3526
116
1.2942
115
1.3536
122
1.3536
122
MP2=FULL 1.2081
2
1.1964
2
  1.1932
4
1.1393
1
1.1496
1
1.1364
1
1.1463
1
1.1337
1
1.1336
1
ROMP2 1.1707
1
1.1594
1
    1.2405
1
1.1957
1
1.2335
1
1.1875
1
1.2278
1
1.2277
1
MP3 1.2005
2
1.1908
2
    1.1442
1
1.1498
1
1.1414
1
1.1455
1
1.1377
1
1.1377
1
MP3=FULL 1.1999
2
1.1860
2
               
MP4 1.1467
1
1.1420
1
    1.1505
1
1.1543
1
1.1465
1
1.1511
1
1.1429
1
1.1428
1
MP4=FULL 1.1464
1
1.1403
1
    1.1505
1
1.1543
1
1.1465
1
1.1511
1
1.1428
1
1.1427
1
B2PLYP 1.2170
2
1.2085
2
    1.2215
1
1.1865
1
1.2174
1
1.1783
1
1.2127
1
1.2128
1
B2PLYP=FULL 1.2167
2
1.2067
2
    1.2215
1
1.1865
1
1.2174
1
1.1783
1
1.2127
1
1.2127
1
B2PLYP=FULLultrafine 1.2167
2
1.2067
2
               
Configuration interaction CID 1.1991
2
1.1888
2
    1.1462
1
1.1498
1
1.1429
1
1.1451
1
1.1389
1
1.1388
1
CISD 1.2040
2
1.1930
2
    1.1982
1
1.1571
1
1.1860
1
1.1516
1
1.1778
1
1.1773
1
Quadratic configuration interaction QCISD 1.1682
1
1.2081
2
    1.2412
1
1.1916
1
1.2342
1
1.1839
1
1.2286
1
1.2285
1
QCISD(T) 1.1709
1
1.1594
1
    1.2370
1
1.1959
1
1.2296
1
1.1877
1
1.2219
1
1.2216
1
QCISD(T)=FULL 1.1702
1
1.1536
1
               
QCISD(TQ)         1.2322
1
1.2028
1
1.2417
1
1.1938
1
1.2343
1
1.2336
1
Coupled Cluster CCD 1.2663
1
1.2542
1
    1.1458
1
1.1507
1
1.1425
1
1.1467
1
1.1387
1
1.1387
1
CCSD 1.2731
1
1.2614
1
    1.2342
1
1.1862
1
1.2263
1
1.1771
1
1.2195
1
1.2193
1
CCSD=FULL 1.2721
1
1.2543
1
    1.2342
1
1.1862
1
1.2263
1
1.1771
1
1.2194
1
1.2190
1
CCSD(T) 1.1637
1
1.1531
1
    1.2362
1
1.1897
1
1.2281
1
1.1802
1
1.2202
1
1.2196
1
CCSD(T)=FULL 1.1631
1
1.1488
1
    1.2362
1
1.1897
1
1.2281
1
1.1802
1
1.2201
1
1.2194
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.