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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 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 1.2134
54
PM3 1.2477
59
PM6 1.2519
130
composite G2 1.2744
104
G3 1.2523
115
G3B3 1.2879
126
G3MP2 1.1640
8
G4 1.2750
131
CBS-Q 1.2499
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 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-pVTZ Sadlej_pVTZ
hartree fock HF 1.3134
114
1.2892
114
1.2886
115
1.2627
115
1.2493
135
1.2523
121
1.2267
71
1.2457
121
1.2193
115
1.2205
110
1.2112
51
1.1149
1
1.2307
127
1.2477
121
1.2471
116
1.2469
39
1.2231
105
1.2547
104
1.2568
34
1.1434
3
1.1529
3
1.1495
3
1.1157
1
1.1554
4
ROHF 1.3254
10
1.2990
19
1.2998
19
1.2206
15
1.2556
22
1.2599
19
1.2650
19
1.2542
19
1.2590
18
1.2991
10
1.1129
1
1.1149
1
1.1775
9
1.2546
19
1.2561
19
1.2596
18
1.2647
18
1.2609
18
1.2594
18
         
density functional LSDA 1.3502
122
1.3152
119
1.3153
119
1.2920
116
1.2550
116
1.2554
113
1.2553
113
1.2490
116
1.2496
113
1.2492
113
1.1446
1
1.1446
1
1.2526
56
1.2517
113
1.2480
113
1.2066
12
1.2499
105
1.2445
57
1.2048
12
         
SVWN 1.2459
1
1.3145
119
1.1982
1
1.1851
1
1.2640
117
1.2570
55
1.2637
119
1.2511
55
1.2512
55
1.2509
55
1.1446
1
1.1446
1
1.2552
79
1.2528
55
1.2503
55
1.1453
1
1.2517
49
1.2453
47
1.1448
1
      1.1458
1
 
BLYP 1.3822
109
1.3479
112
1.3473
101
1.3291
112
1.2809
138
1.2878
112
1.2871
111
1.2806
101
1.2829
112
1.2811
112
1.1611
1
1.1611
1
1.2870
56
1.2846
112
1.2814
112
1.1613
1
1.3399
72
1.2554
29
1.1609
1
      1.1620
1
 
B1B95 1.3439
112
1.3132
113
1.3133
113
1.2919
113
1.2531
110
1.2541
110
1.2538
110
1.2483
110
1.2484
110
1.2476
113
1.1381
1
1.1381
1
1.2522
55
1.2504
110
1.2459
113
1.2038
13
1.2485
102
1.2427
86
1.2007
13
         
B3LYP 1.3931
119
1.3223
120
1.3231
120
1.3037
120
1.2934
123
1.2656
117
1.2648
117
1.2599
117
1.2567
78
1.2587
120
1.3452
46
1.1446
1
1.2664
126
1.2621
117
1.2589
117
1.2483
33
1.2673
86
1.2685
119
1.2473
33
1.1664
3
1.1763
3
1.1700
3
1.1454
1
1.1881
4
B3LYPultrafine 1.2401
1
1.3116
36
1.1949
1
1.1827
1
1.2639
111
1.2541
36
1.2517
59
1.2464
36
1.1483
1
1.1512
1
1.1446
1
1.1446
1
1.2574
40
1.2615
47
1.2544
76
1.1445
1
1.2627
44
1.2761
126
1.1443
1
      1.1454
1
 
B3PW91 1.3453
79
1.3152
115
1.3161
115
1.2934
115
1.2569
112
1.2569
112
1.2544
101
1.2498
112
1.2449
73
1.2512
112
1.1421
1
1.1421
1
1.2571
56
1.2529
112
1.2502
112
1.1421
1
1.3070
72
1.2395
47
1.1418
1
      1.1428
1
 
mPW1PW91 1.3406
79
1.3110
113
1.3116
81
1.2888
115
1.2522
113
1.2531
112
1.2518
113
1.2461
113
1.2456
115
1.2465
112
1.1390
1
1.1390
1
1.2531
56
1.2495
112
1.2419
94
1.1390
1
1.2942
96
1.2478
51
1.1387
1
      1.1397
1
 
M06-2X 1.3381
55
1.3174
55
1.2671
121
1.2922
55
1.2500
117
1.2544
55
1.2549
55
1.2496
55
1.2494
55
1.2459
69
1.1358
1
1.1358
1
1.2509
55
1.2511
55
1.2462
69
1.1356
1
1.2511
49
1.2439
61
1.1354
1
      1.1368
1
 
PBEPBE 1.3646
75
1.3364
111
1.3339
72
1.3093
72
1.2749
111
1.2748
111
1.2748
111
1.2696
111
1.2697
111
1.2837
111
1.3621
46
1.1569
1
1.2737
55
1.2734
108
1.2688
111
1.2266
13
1.2680
54
1.2674
67
1.2222
13
      1.1579
1
1.1961
4
PBEPBEultrafine 1.2557
1
1.3237
36
1.2142
1
1.1973
1
1.2726
93
1.2573
36
1.2569
36
1.2494
36
1.1606
1
1.1639
1
1.1568
1
1.1568
1
1.2616
40
1.2687
47
1.2661
47
1.1572
1
1.2685
44
1.2649
44
1.1568
1
      1.1578
1
 
PBE1PBE 1.3437
52
1.3162
52
1.3164
52
1.2927
52
1.2591
120
1.2544
52
1.2544
52
1.2480
52
1.2481
52
1.2488
52
1.1394
1
1.1394
1
1.2504
52
1.2500
52
1.2483
52
1.1394
1
1.2513
49
1.2469
47
1.1392
1
      1.1402
1
 
HSEh1PBE 1.3465
55
1.3149
119
1.3182
55
1.2947
55
1.2518
117
1.2561
55
1.2601
119
1.2500
55
1.2501
55
1.2506
55
1.1392
1
1.1392
1
1.2525
55
1.2520
55
1.2541
119
1.1392
1
1.2516
49
1.2472
47
1.1390
1
      1.1400
1
 
TPSSh 1.3194
13
1.3274
40
1.3290
40
1.3054
40
1.2689
135
1.2640
40
1.2679
135
1.2534
40
1.1930
13
1.2637
120
    1.2562
40
1.2570
40
1.2621
135
1.1783
5
1.2563
37
1.2528
37
1.1781
5
      1.1499
1
 
wB97X-D 1.3356
26
1.3016
26
1.2991
139
1.2793
26
1.2608
139
1.2456
26
1.2609
139
1.2385
26
1.2559
139
1.2406
26
    1.2565
139
1.2600
139
1.2551
139
1.2362
15
1.2428
26
1.2546
139
1.2359
15
      1.1404
1
 
B97D3 1.3331
6
1.3079
126
1.2746
6
1.2095
6
1.2715
126
1.1807
6
1.1738
6
1.1661
6
1.2666
126
1.1723
6
    1.1642
6
1.1725
6
1.1640
6
1.1229
2
1.1692
6
1.2637
125
1.1230
2
      1.1541
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 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-pVTZ Sadlej_pVTZ
Moller Plesset perturbation MP2 1.3591
78
1.3475
121
1.3482
121
1.3370
115
1.2786
135
1.2792
121
1.2864
113
1.2681
138
1.2644
115
1.2583
99
1.1362
1
1.1362
1
1.2769
127
1.2728
121
1.2633
98
1.2422
22
1.2736
84
1.2610
81
1.2405
21
1.1741
3
1.1743
4
1.1678
4
1.1370
1
1.1941
4
MP2=FULL 1.3570
77
1.3438
95
1.3479
83
1.3389
83
1.2748
115
1.2759
100
1.2777
104
1.2627
115
1.2612
73
1.2560
87
1.1354
1
1.1354
1
1.2761
56
1.2671
96
1.2568
96
1.2396
22
1.2727
66
1.2541
75
1.2458
19
1.1708
3
1.1738
4
1.1663
4
1.1352
1
1.1932
4
ROMP2 1.4374
17
1.3401
17
1.3401
17
1.3216
17
1.2592
17
1.2591
17
1.2618
17
1.2357
14
1.2360
14
1.2377
14
1.1566
1
1.1566
1
1.2391
11
1.2433
14
1.2348
11
1.1792
4
1.2567
15
1.2156
7
1.1780
4
         
MP3 1.1402
1
1.1392
1
1.1392
1
1.1348
1
1.2564
111
1.1410
1
1.2620
135
1.1308
1
1.1308
1
1.1346
1
1.1300
1
1.1300
1
1.2458
40
1.2477
40
1.2411
40
1.1287
1
1.1391
1
1.1312
1
1.1287
1
      1.1311
1
 
MP3=FULL   1.3114
26
1.3121
26
1.2944
26
1.2612
135
1.2505
26
1.2610
131
1.2364
26
1.2366
26
1.2362
26
    1.2451
40
1.2471
40
1.2368
40
  1.2447
24
1.2293
24
        1.1281
1
 
MP4 1.3257
4
1.3908
75
1.3675
4
1.3649
4
1.2914
88
1.1476
1
1.1478
1
1.2466
4
1.2825
68
1.1896
4
1.1413
1
1.1413
1
1.2930
48
1.2891
48
1.2722
72
1.1406
1
1.2941
43
1.2702
35
1.1405
1
      1.1420
1
 
MP4=FULL 1.1603
1
1.3819
48
1.1441
1
1.1396
1
1.2877
44
1.1474
1
1.1476
1
1.1394
1
1.2819
48
1.1435
1
1.1406
1
1.1406
1
1.1390
1
1.2884
48
1.2775
48
1.1397
1
1.2932
43
1.2737
38
1.1397
1
      1.1403
1
 
B2PLYP 1.3480
36
1.3262
36
1.3276
36
1.3095
36
1.2726
103
1.2621
36
1.2636
36
1.2538
36
1.2540
36
1.2536
53
1.1518
1
1.1518
1
1.2588
36
1.2567
36
1.2653
111
1.1514
1
1.2598
33
1.2543
50
1.1514
1
      1.1532
1
 
B2PLYP=FULL 1.3479
36
1.3174
36
1.3275
36
1.3094
36
1.2599
36
1.2618
36
1.2612
36
1.2534
36
1.2536
36
1.2529
36
1.1511
1
1.1511
1
1.2586
36
1.2564
36
1.2534
36
1.1508
1
1.2595
33
1.2528
33
1.1507
1
      1.1518
1
 
B2PLYP=FULLultrafine 1.3467
27
1.3281
27
1.3293
27
1.3104
27
1.2782
68
1.2614
27
1.2627
27
1.2525
27
1.2527
27
1.2524
27
    1.2579
27
1.2557
27
1.2531
27
  1.2611
27
1.2544
27
        1.1518
1
 
Configuration interaction CID 1.1651
1
1.3101
79
1.3130
71
1.2936
71
1.2530
101
1.2855
2
1.2848
2
1.2367
71
1.1077
2
1.1566
4
1.1283
1
1.1283
1
1.1297
1
1.2803
2
1.2735
2
1.1268
1
1.1382
1
1.1295
1
1.1267
1
      1.1294
1
 
CISD   1.3157
79
1.3187
71
1.2984
71
1.2542
102
1.4332
1
1.2892
2
1.2373
71
1.1104
2
1.1583
4
1.1325
1
1.1325
1
1.1352
1
1.2846
2
1.2768
2
1.1308
1
1.1435
1
1.1337
1
        1.1336
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 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-pVTZ Sadlej_pVTZ
Quadratic configuration interaction QCISD 1.2854
5
1.3378
111
1.3555
72
1.3359
78
1.2656
101
1.2725
82
1.2704
85
1.2540
92
1.2573
90
1.2523
81
1.1504
1
1.1504
1
1.2678
55
1.2618
83
1.2513
84
1.1481
1
1.2725
52
1.2542
61
1.1481
1
      1.1527
1
 
QCISD(T) 1.2532
1
1.2239
1
1.2239
1
1.2042
1
1.2728
74
1.1763
1
1.1759
1
1.2585
32
1.1818
4
1.1625
1
1.1567
1
1.1567
1
1.2783
54
1.2771
65
1.2674
60
1.1554
1
1.2802
54
1.2682
45
1.1556
1
      1.1594
1
 
QCISD(T)=FULL         1.2699
36
  1.2720
36
            1.2622
36
1.2503
33
1.2301
14
1.2685
33
1.2474
30
1.2374
14
      1.1536
1
 
QCISD(TQ) 1.2683
1
1.2368
1
1.2368
1
1.2129
1
1.2370
18
1.1806
1
1.2262
15
1.1636
1
1.1636
1
1.1649
1
1.1573
1
1.1573
1
1.1651
1
1.2281
18
1.2000
13
1.2100
5
1.2211
15
1.1992
10
1.2425
2
         
QCISD(TQ)=FULL         1.2238
15
  1.2385
13
            1.2273
13
1.2200
11
1.1810
7
1.2199
14
1.1926
9
1.1526
1
         
Coupled Cluster CCD 1.2601
5
1.3291
81
1.3359
72
1.3144
78
1.2587
109
1.2640
78
1.2649
78
1.2502
79
1.2456
70
1.2443
68
1.1324
1
1.1324
1
1.2573
55
1.2537
81
1.2491
68
1.1310
1
1.2591
58
1.2431
48
1.1309
1
  1.1644
2
1.1563
2
   
CCSD 1.2552
1
1.2170
1
1.2170
1
1.2001
1
1.2618
93
1.1667
1
1.1662
1
1.1784
2
1.1510
1
1.2442
51
1.1453
1
1.1453
1
1.2612
48
1.2650
61
1.2531
73
1.2373
17
1.2672
45
1.2515
59
1.2045
11
    1.1462
1
   
CCSD=FULL 1.2551
1
1.2169
1
1.2169
1
1.1999
1
1.2643
61
1.1660
1
1.1654
1
1.1501
1
1.1501
1
1.2420
50
1.1431
1
1.1431
1
1.2600
47
1.2609
47
1.2463
61
1.2345
15
1.2659
44
1.2428
57
1.1833
9
         
CCSD(T) 1.2555
1
1.1029
1
1.2183
1
1.1999
1
1.2734
87
1.2641
37
1.2025
8
1.2542
33
1.1844
11
1.1978
7
1.1511
1
1.1511
1
1.2754
54
1.2751
65
1.2546
63
1.2402
18
1.2762
56
1.2578
45
1.2428
17
  1.1809
4
1.1736
4
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
1.1494
1
1.1494
1
1.2743
53
1.2732
59
1.2586
51
1.2435
17
1.2783
47
1.2541
39
1.2444
15
  1.1803
4
1.1720
4
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 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-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 1.3104
121
1.2681
115
1.2799
115
1.2639
115
1.3000
121
1.2999
121
ROHF   1.1454
1
  1.1358
1
1.2022
1
1.2020
1
density functional LSDA 1.2222
1
1.1867
1
1.2169
1
1.1779
1
1.2014
1
1.2013
1
SVWN 1.2222
1
1.1867
1
1.2169
1
1.1779
1
1.2014
1
1.2013
1
BLYP 1.2324
1
1.1954
1
1.2277
1
1.1872
1
1.2209
1
1.2211
1
B1B95 1.2984
51
1.2579
51
1.1955
1
1.1598
1
1.1891
1
1.1892
1
B3LYP 1.3252
120
1.2817
114
1.3220
120
1.2775
114
1.3140
120
1.3144
118
B3LYPultrafine 1.2120
1
1.1783
1
1.2078
1
1.1699
1
1.1990
1
1.1991
1
B3PW91 1.2065
1
1.1738
1
1.2020
1
1.1651
1
1.1941
1
1.1942
1
mPW1PW91 1.2019
1
1.1700
1
1.1976
1
1.1613
1
1.1898
1
1.1899
1
M06-2X 1.1913
1
1.1623
1
1.1859
1
1.1517
1
1.1850
1
1.1850
1
PBEPBE 1.2242
1
1.1885
1
1.2194
1
1.1802
1
1.2136
1
1.2137
1
PBEPBEultrafine 1.2242
1
1.1885
1
1.2194
1
1.1802
1
1.2136
1
1.2137
1
PBE1PBE 1.2018
1
1.1699
1
1.1975
1
1.1613
1
1.1901
1
1.1902
1
HSEh1PBE 1.2026
1
1.1705
1
1.1983
1
1.1619
1
1.1904
1
1.1905
1
wB97X-D 1.3031
26
1.2637
26
1.2997
26
1.2592
26
1.2894
26
1.2894
26
Moller Plesset perturbation MP2 1.3575
121
1.2949
115
1.3516
115
1.2925
115
1.3527
121
1.3527
121
MP2=FULL 1.1393
1
1.1496
1
1.1364
1
1.1463
1
1.1337
1
1.1336
1
ROMP2 1.2405
1
1.1957
1
1.2335
1
1.1875
1
1.2278
1
1.2277
1
MP3 1.1442
1
1.1498
1
1.1414
1
1.1455
1
1.1377
1
1.1377
1
MP4 1.1505
1
1.1543
1
1.1465
1
1.1511
1
1.1429
1
1.1428
1
MP4=FULL 1.1505
1
1.1543
1
1.1465
1
1.1511
1
1.1428
1
1.1427
1
B2PLYP 1.2215
1
1.1865
1
1.2174
1
1.1783
1
1.2127
1
1.2128
1
B2PLYP=FULL 1.2215
1
1.1865
1
1.2174
1
1.1783
1
1.2127
1
1.2127
1
Configuration interaction CID 1.1462
1
1.1498
1
1.1429
1
1.1451
1
1.1389
1
1.1388
1
CISD 1.1982
1
1.1571
1
1.1860
1
1.1516
1
1.1778
1
1.1773
1
Quadratic configuration interaction QCISD 1.2412
1
1.1916
1
1.2342
1
1.1839
1
1.2286
1
1.2285
1
QCISD(T) 1.2370
1
1.1959
1
1.2296
1
1.1877
1
1.2219
1
1.2216
1
QCISD(TQ) 1.2322
1
1.2028
1
1.2417
1
1.1938
1
1.2343
1
1.2336
1
Coupled Cluster CCD 1.1458
1
1.1507
1
1.1425
1
1.1467
1
1.1387
1
1.1387
1
CCSD 1.2342
1
1.1862
1
1.2263
1
1.1771
1
1.2195
1
1.2193
1
CCSD=FULL 1.2342
1
1.1862
1
1.2263
1
1.1771
1
1.2194
1
1.2190
1
CCSD(T) 1.2362
1
1.1897
1
1.2281
1
1.1802
1
1.2201
1
1.2196
1
CCSD(T)=FULL 1.2362
1
1.1897
1
1.2281
1
1.1802
1
1.2200
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.