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Release 17bSeptember 2015
NIST Standard Reference Database 101
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III.G.1.a.

Comparison of levels of theory for N-O


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 1.2094
42
PM3 1.2454
47
PM6 1.2556
112
composite G2 1.2796
93
G3 1.2545
106
G3B3 1.2891
117
G3MP2 1.2001
4
G4 1.2782
116
CBS-Q 1.2526
89

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 Sadlej_pVTZ
hartree fock HF 1.3155
103
1.2892
104
1.2899
104
1.2632
105
1.2524
121
1.2546
112
1.2272
62
1.2478
112
1.2206
104
1.2205
101
1.2112
51
1.1149
1
1.2327
112
1.2498
112
1.2495
107
1.2496
37
1.2234
99
1.2572
98
1.2554
33
1.1434
3
1.1529
3
1.1495
3
1.1554
4
ROHF 1.3238
17
1.2942
23
1.2949
23
1.2276
17
1.2469
26
1.2492
23
1.2533
23
1.2429
23
1.2556
20
1.2628
17
1.1129
1
1.1149
1
1.2022
2
1.2436
23
1.2442
23
1.2540
19
1.2550
20
1.2508
20
1.2537
19
       
density functional LSDA 1.3490
110
1.3127
110
1.3128
110
1.2919
104
1.2545
104
1.2544
104
1.2546
104
1.2489
104
1.2490
104
1.2483
104
1.1446
1
1.1446
1
1.2726
36
1.2510
104
1.2473
104
1.1987
16
1.2497
99
1.2476
46
1.1973
16
       
SVWN 1.2459
1
1.3157
104
1.1982
1
1.1851
1
1.2689
100
1.2742
36
1.2675
104
1.2705
36
1.2706
36
1.2685
36
1.1446
1
1.1446
1
1.2552
79
1.2707
36
1.2699
36
1.1453
1
1.2724
33
1.2677
31
1.1448
1
       
BLYP 1.3812
97
1.3464
102
1.3455
91
1.3312
101
1.2838
125
1.2884
102
1.2879
101
1.2814
91
1.2853
100
1.2818
102
1.1611
1
1.1611
1
1.3105
36
1.2853
102
1.2824
102
1.1613
1
1.3717
55
1.2794
14
1.1609
1
       
B1B95 1.3428
103
1.3125
104
1.3127
104
1.2908
104
1.2517
104
1.2528
104
1.2526
104
1.2471
104
1.2471
104
1.2469
104
1.1381
1
1.1381
1
1.2687
36
1.2492
104
1.2451
104
1.2037
18
1.2472
99
1.2408
76
1.2062
17
       
B3LYP 1.3971
109
1.3229
112
1.3238
112
1.3041
112
1.2971
111
1.2662
109
1.2658
109
1.2606
109
1.2593
68
1.2591
112
1.3523
44
1.1446
1
1.2694
112
1.2627
109
1.2595
109
1.2490
32
1.2690
81
1.2690
115
1.2446
33
1.1664
3
1.1763
3
1.1700
3
1.1881
4
B3LYPultrafine 1.2401
1
1.3308
17
1.1949
1
1.1827
1
1.2641
100
1.2719
17
1.2566
42
1.2644
17
1.1483
1
1.1512
1
1.1446
1
1.1446
1
1.2797
21
1.2808
28
1.2602
59
1.1445
1
1.2839
28
1.2794
114
1.1443
1
       
B3PW91 1.3439
67
1.3139
105
1.3149
105
1.2933
105
1.2553
105
1.2562
104
1.2531
94
1.2493
105
1.2462
61
1.2502
102
1.1421
1
1.1421
1
1.2749
36
1.2517
105
1.2488
105
1.1421
1
1.3241
60
1.2482
32
1.1418
1
       
mPW1PW91 1.3411
68
1.3114
104
1.3142
70
1.2907
104
1.2525
104
1.2535
103
1.2522
104
1.2465
104
1.2471
104
1.2480
101
1.1390
1
1.1390
1
1.2729
37
1.2500
103
1.2431
84
1.1390
1
1.3113
80
1.2678
35
1.1387
1
       
M06-2X 1.3492
36
1.3340
36
1.2629
107
1.3086
36
1.2506
102
1.2690
36
1.2697
36
1.2645
36
1.2645
36
1.2527
52
1.1358
1
1.1358
1
1.2664
36
1.2660
36
1.2532
52
1.1356
1
1.2673
33
1.2516
47
1.1354
1
       
PBEPBE 1.3628
64
1.3363
100
1.3352
60
1.3139
60
1.2755
102
1.2766
100
1.2769
100
1.2718
100
1.2718
100
1.2857
102
1.3693
44
1.1569
1
1.2956
36
1.2757
97
1.2697
102
1.2248
18
1.2899
37
1.2822
52
1.2210
18
      1.1961
4
PBEPBEultrafine 1.2557
1
1.3405
17
1.2142
1
1.1973
1
1.2793
76
1.2766
17
1.2777
17
1.2696
17
1.1606
1
1.1639
1
1.1568
1
1.1568
1
1.2884
21
1.2917
28
1.2903
28
1.1572
1
1.2942
28
1.2915
28
1.1568
1
       
PBE1PBE 1.3548
33
1.3349
33
1.3349
33
1.3113
33
1.2610
105
1.2702
33
1.2710
33
1.2646
33
1.2647
33
1.2648
33
1.1394
1
1.1394
1
1.2675
33
1.2664
33
1.2651
33
1.1394
1
1.2686
33
1.2652
31
1.1392
1
       
HSEh1PBE 1.3577
36
1.3174
102
1.3365
36
1.3126
36
1.2539
100
1.2715
36
1.2638
102
1.2663
36
1.2664
36
1.2661
36
1.1392
1
1.1392
1
1.2693
36
1.2681
36
1.2578
102
1.1392
1
1.2690
33
1.2657
31
1.1390
1
       
TPSSh   1.3569
20
1.3601
20
1.3340
20
1.2702
120
1.2921
20
1.2702
120
1.2851
20
  1.2668
110
    1.2901
20
1.2879
20
1.2646
120
  1.2909
20
1.2895
20
         
wB97X-D 1.3727
9
1.3616
9
1.2988
127
1.3333
9
1.2624
127
1.2974
9
1.2978
9
1.2916
9
1.2576
127
1.2923
9
    1.2940
9
1.2923
9
1.2568
127
1.2967
7
1.2953
9
1.2563
127
1.2962
7
       
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 Sadlej_pVTZ
Moller Plesset perturbation MP2 1.3633
64
1.3483
112
1.3491
112
1.3369
106
1.2810
120
1.2794
112
1.2886
103
1.2706
123
1.2644
106
1.2581
90
1.1362
1
1.1362
1
1.2800
112
1.2728
112
1.2634
90
1.2667
15
1.2729
78
1.2608
75
1.2655
14
1.1741
3
1.1743
4
1.1678
4
1.1941
4
MP2=FULL 1.3626
63
1.3445
86
1.3498
72
1.3399
72
1.2747
106
1.2760
91
1.2792
94
1.2643
105
1.2656
61
1.2559
78
1.1354
1
1.1354
1
1.2967
37
1.2667
87
1.2569
87
1.2640
15
1.2814
53
1.2577
63
1.2797
12
1.1708
3
1.1738
4
1.1663
4
1.1932
4
ROMP2 1.4434
18
1.3588
16
1.3588
16
1.3366
16
1.2584
19
1.2584
19
1.2604
19
1.2356
16
1.2357
16
1.2429
13
1.1566
1
1.1566
1
1.2910
4
1.2426
16
1.2339
13
1.1962
7
1.2476
16
1.2159
14
1.1995
9
       
MP3 1.1402
1
1.1392
1
1.1392
1
1.1348
1
1.2563
100
1.1410
1
1.2629
120
1.1308
1
1.1308
1
1.1346
1
1.1300
1
1.1300
1
1.2660
21
1.2676
21
1.2613
21
1.1287
1
1.1391
1
1.1312
1
1.1287
1
       
MP3=FULL   1.3812
9
1.3833
9
1.3597
9
1.2622
120
1.3057
9
1.2619
116
1.2909
9
1.2911
9
1.2908
9
    1.2720
20
1.2735
20
1.2631
20
  1.3093
7
1.2931
7
         
MP4 1.3257
4
1.3952
63
1.3675
4
1.3649
4
1.2890
78
1.1476
1
1.1478
1
1.2466
4
1.2817
56
1.1896
4
1.1413
1
1.1413
1
1.3145
28
1.3088
28
1.2752
58
1.1406
1
1.3139
26
1.2949
18
1.1405
1
       
MP4=FULL 1.1603
1
1.3984
28
1.1441
1
1.1396
1
1.3046
24
1.1474
1
1.1476
1
1.1394
1
1.3007
28
1.1435
1
1.1406
1
1.1406
1
1.1390
1
1.3081
28
1.2979
28
1.1397
1
1.3129
26
1.2955
22
1.1397
1
       
B2PLYP 1.3541
17
1.3452
17
1.3482
17
1.3283
17
1.2739
88
1.2802
17
1.2832
17
1.2716
17
1.2718
17
1.2596
36
1.1518
1
1.1518
1
1.2784
17
1.2740
17
1.2667
96
1.1514
1
1.2810
17
1.2618
36
1.1514
1
       
B2PLYP=FULL 1.3541
17
1.3380
17
1.3481
17
1.3282
17
1.2793
17
1.2799
17
1.2823
17
1.2712
17
1.2712
17
1.2719
17
1.1511
1
1.1511
1
1.2782
17
1.2738
17
1.2735
17
1.1508
1
1.2808
17
1.2756
17
1.1507
1
       
B2PLYP=FULLultrafine 1.3781
10
1.3817
10
1.3849
10
1.3605
10
1.2927
51
1.3074
10
1.3108
10
1.2983
10
1.2984
10
1.2996
10
    1.3072
10
1.3005
10
1.3032
10
  1.3097
10
1.3058
10
         
Configuration interaction CID 1.1651
1
1.3129
65
1.3169
57
1.2968
58
1.2523
91
1.2855
2
1.2848
2
1.2371
59
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
       
CISD   1.3290
66
1.3317
59
1.2989
59
1.2535
92
1.4332
1
1.2892
2
1.2373
59
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
         
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 Sadlej_pVTZ
Quadratic configuration interaction QCISD 1.2854
5
1.3374
100
1.3611
59
1.3383
67
1.2640
92
1.2747
70
1.2689
76
1.2525
83
1.2560
81
1.2505
72
1.1504
1
1.1504
1
1.2839
36
1.2602
74
1.2495
75
1.1481
1
1.2878
36
1.2615
47
1.1481
1
       
QCISD(T) 1.2532
1
1.2239
1
1.2239
1
1.2042
1
1.2742
64
1.1763
1
1.1759
1
1.2842
12
1.1818
4
1.1625
1
1.1567
1
1.1567
1
1.2957
34
1.2780
53
1.2681
48
1.1554
1
1.2838
43
1.2780
34
1.1556
1
       
QCISD(T)=FULL         1.2956
16
  1.2992
16
            1.2869
16
1.2787
16
1.2767
6
1.2973
16
1.2789
13
1.2933
6
       
QCISD(TQ) 1.2683
1
1.2368
1
1.2368
1
1.2129
1
1.2528
9
1.1806
1
1.2328
6
1.1636
1
1.1636
1
1.1649
1
1.1573
1
1.1573
1
1.1651
1
1.2436
9
1.1881
4
1.1557
1
1.2266
6
1.1858
3
1.1560
1
       
QCISD(TQ)=FULL         1.2393
5
  1.2422
5
            1.2276
5
1.2313
3
  1.2392
4
1.1839
1
         
Coupled Cluster CCD 1.2601
5
1.3330
68
1.3419
59
1.3179
66
1.2573
100
1.2647
67
1.2655
67
1.2507
68
1.2452
59
1.2419
59
1.1324
1
1.1324
1
1.2730
36
1.2555
69
1.2476
59
1.1310
1
1.2595
49
1.2504
40
1.1309
1
  1.1644
2
1.1563
2
 
CCSD 1.2552
1
1.2170
1
1.2170
1
1.2001
1
1.2586
81
1.1667
1
1.1662
1
1.1784
2
1.1510
1
1.2494
33
1.1453
1
1.1453
1
1.2796
28
1.2785
41
1.2593
55
1.2684
9
1.2858
28
1.2590
44
1.2100
3
    1.1462
1
 
CCSD=FULL 1.2551
1
1.2169
1
1.2169
1
1.1999
1
1.2713
44
1.1660
1
1.1654
1
1.1501
1
1.1501
1
1.2481
33
1.1431
1
1.1431
1
1.2788
28
1.2790
28
1.2537
44
1.2735
8
1.2849
28
1.2538
45
1.1603
2
       
CCSD(T) 1.2555
1
1.1029
1
1.2183
1
1.1999
1
1.2763
71
1.2759
17
1.1483
2
1.2747
13
1.1576
5
1.1563
1
1.1511
1
1.1511
1
1.2925
34
1.2743
55
1.2540
54
1.2704
12
1.2766
47
1.2652
35
1.2767
10
  1.1809
4
1.1736
4
 
CCSD(T)=FULL 1.2554
1
1.2183
1
1.2183
1
1.1998
1
1.2880
46
1.1682
1
1.1677
1
1.1536
1
1.1536
1
1.1550
1
1.1494
1
1.1494
1
1.2916
34
1.2871
40
1.2735
36
1.2797
11
1.2961
32
1.2736
24
1.2888
9
  1.1803
4
1.1720
4
 
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 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 1.3126
112
1.2708
106
1.2800
106
1.2666
106
1.3027
112
1.3025
112
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 1.3267
110
1.2830
104
1.3227
112
1.2779
106
1.3149
112
1.3154
110
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 1.3554
9
1.3158
9
1.3527
9
1.3123
9
1.3430
9
1.3430
9
Moller Plesset perturbation MP2 1.3573
112
1.2967
105
1.3512
106
1.2932
106
1.3528
112
1.3528
112
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.