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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 1.2057
29
PM3 1.2967
79
PM6 1.2558
109
composite G2 1.3042
86
G3 1.2620
94
G3B3 1.2877
110
G4 1.2776
106
CBS-Q 1.2656
78

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 1.3176
96
1.2909
95
1.2915
95
1.2567
93
1.2370
220
1.2641
103
1.2338
97
1.2577
103
1.2272
97
1.2285
92
1.2119
54
1.1149
1
1.2288
110
1.2593
103
1.2605
98
1.2407
31
1.2321
90
1.2700
89
1.2575
24
1.1434
3
1.1529
3
1.1495
3
1.1554
4
ROHF 1.3233
16
1.2883
22
1.2890
22
1.2194
16
1.2452
25
1.2475
22
1.2518
22
1.2411
22
1.2541
19
1.2618
16
1.1129
1
1.1149
1
1.1168
1
1.2418
22
1.2425
22
1.2525
18
1.2535
19
1.2492
19
1.2523
18
       
density functional LSDA 1.3484
102
1.3082
105
1.3083
105
1.2888
99
1.2515
99
1.2514
99
1.2516
99
1.2463
99
1.2463
99
1.2451
99
1.1446
1
1.1446
1
1.2832
20
1.2482
99
1.2441
99
1.1930
15
1.2464
94
1.2396
33
1.1924
15
       
SVWN 1.2459
1
1.3132
99
1.1982
1
1.1851
1
1.2676
95
1.2816
20
1.2657
99
1.2814
20
1.2814
20
1.2753
20
1.1446
1
1.1446
1
1.1474
1
1.2794
20
1.2791
20
1.1453
1
1.2819
17
1.2774
15
1.1448
1
       
BLYP 1.3786
91
1.3473
97
1.3384
86
1.3267
96
1.2919
97
1.2842
97
1.2834
96
1.2769
86
1.2808
94
1.2781
94
1.1611
1
1.1611
1
1.3234
20
1.2822
96
1.2780
97
1.1613
1
1.3678
53
1.1621
1
1.1609
1
       
B1B95 1.3418
95
1.3071
96
1.3073
96
1.2868
98
1.2472
96
1.2485
96
1.2482
96
1.2429
96
1.2429
96
1.2431
95
1.1381
1
1.1381
1
1.2732
20
1.2451
96
1.2403
96
1.1984
17
1.2428
90
1.2352
35
1.2011
16
       
B3LYP 1.3947
104
1.3166
103
1.3170
103
1.2985
103
1.2930
107
1.2600
103
1.2595
103
1.2546
103
1.2518
54
1.2541
100
1.3407
49
1.1446
1
1.2656
110
1.2569
103
1.2528
103
1.2314
24
1.2601
72
1.2425
60
1.2299
24
1.1664
3
1.1763
3
1.1700
3
1.1881
4
B3LYPultrafine 1.2401
1
1.1949
1
1.1949
1
1.1827
1
1.2582
94
1.1587
1
1.2420
26
1.1483
1
1.1483
1
1.1512
1
1.1446
1
1.1446
1
1.2902
5
1.2905
12
1.2550
46
1.1445
1
1.2925
12
1.2779
104
1.1443
1
       
B3PW91 1.3431
54
1.3087
97
1.3092
97
1.2890
97
1.2509
97
1.2518
96
1.2479
86
1.2452
97
1.2394
48
1.2455
94
1.1421
1
1.1421
1
1.2807
20
1.2476
97
1.2439
97
1.1421
1
1.3278
53
1.1429
1
1.1418
1
       
mPW1PW91 1.3389
54
1.3045
95
1.3064
59
1.2834
97
1.2466
95
1.2477
94
1.2462
95
1.2407
95
1.2402
97
1.2406
94
1.1390
1
1.1390
1
1.2742
20
1.2443
94
1.2348
75
1.1390
1
1.3133
69
1.2653
18
1.1387
1
       
M06-2X 1.3585
20
1.3368
20
1.3372
20
1.3121
20
1.2480
95
1.2707
20
1.2714
20
1.2664
20
1.2665
20
1.2649
20
1.1358
1
1.1358
1
1.2683
20
1.2683
20
1.2657
20
1.1356
1
1.2688
17
1.2648
15
1.1354
1
       
PBEPBE 1.3615
51
1.3301
97
1.3244
51
1.3059
51
1.2716
97
1.2716
97
1.2717
97
1.2669
97
1.2670
97
1.2836
94
1.3510
52
1.1569
1
1.3080
20
1.2708
94
1.2656
97
1.2197
17
1.2961
21
1.2735
42
1.2163
17
      1.1961
4
PBEPBEultrafine 1.2557
1
1.2142
1
1.2142
1
1.1973
1
1.2734
98
1.1707
1
1.1691
1
1.1606
1
1.1606
1
1.1639
1
1.1568
1
1.1568
1
1.3143
5
1.3090
12
1.3061
12
1.1572
1
1.3109
12
1.3077
12
1.1568
1
       
PBE1PBE 1.3655
17
1.3390
17
1.3390
17
1.3196
17
1.2592
104
1.2739
17
1.2749
17
1.2694
17
1.2695
17
1.2679
17
1.1394
1
1.1394
1
1.2719
17
1.2712
17
1.2685
17
1.1394
1
1.2727
17
1.2687
15
1.1392
1
       
HSEh1PBE 1.3683
20
1.3404
20
1.3410
20
1.3207
20
1.2506
95
1.2756
20
1.2767
20
1.2717
20
1.2717
20
1.2698
20
1.1392
1
1.1392
1
1.2743
20
1.2734
20
1.2707
20
1.1392
1
1.2734
17
1.2694
15
1.1390
1
       
TPSSh   1.3969
4
1.3969
4
1.3878
4
1.2677
113
1.3348
4
1.2676
113
1.3335
4
        1.3339
4
1.3362
4
1.2616
113
  1.3334
4
1.3292
4
         
Moller Plesset perturbation MP2 1.3603
50
1.3423
100
1.3426
100
1.3284
94
1.2947
130
1.2742
100
1.2832
183
1.2631
99
1.2589
94
1.2487
66
1.1362
1
1.1362
1
1.2749
110
1.2678
100
1.2512
104
1.2391
6
1.2604
63
1.2602
32
1.2295
5
1.1741
3
1.1743
4
1.1678
4
1.1905
4
MP2=FULL 1.3575
50
1.3358
74
1.3410
59
1.3292
59
1.2647
118
1.2691
79
1.2720
82
1.2590
93
1.2589
44
1.2496
46
1.1354
1
1.1354
1
1.2961
20
1.2590
75
1.2484
86
1.2367
6
1.2662
37
1.2514
29
1.2712
3
1.1708
3
1.1738
4
1.1663
4
 
ROMP2 1.4569
15
1.3464
13
1.3464
13
1.3141
13
1.2464
16
1.2464
16
1.2460
16
1.2199
13
1.2200
13
1.2225
10
1.1566
1
1.1566
1
1.1623
1
1.2258
13
1.2057
10
1.1803
6
1.2209
13
1.2102
13
1.1887
8
       
MP3 1.1402
1
1.1392
1
1.1392
1
1.1348
1
1.2520
92
1.1410
1
1.2601
113
1.1308
1
1.1308
1
1.1346
1
1.1300
1
1.1300
1
1.2631
5
1.2691
5
1.2592
5
1.1287
1
1.1391
1
1.1312
1
1.1287
1
       
MP3=FULL         1.2595
113
  1.2590
109
          1.2954
4
1.3016
4
1.2865
4
               
MP4 1.3257
4
1.3983
47
1.3675
4
1.3649
4
1.2827
63
1.1476
1
1.1478
1
1.2466
4
1.2757
40
1.1896
4
1.1413
1
1.1413
1
1.3201
12
1.3161
12
1.2648
49
1.1406
1
1.3254
12
1.2999
4
1.1405
1
       
MP4=FULL 1.1603
1
1.4150
12
1.1441
1
1.1396
1
1.2984
8
1.1474
1
1.1476
1
1.1394
1
1.3085
12
1.1435
1
1.1406
1
1.1406
1
1.1390
1
1.3155
12
1.3027
12
1.1397
1
1.3245
12
1.3021
9
1.1397
1
       
B2PLYP         1.2732
71
                  1.2635
85
               
B2PLYP=FULLultrafine         1.2877
44
                                   
Configuration interaction CID 1.1651
1
1.3221
56
1.3281
48
1.2888
46
1.2474
81
1.2639
5
1.2641
5
1.2288
50
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   1.3396
57
1.3440
50
1.2901
47
1.2477
84
1.2962
4
1.2892
2
1.2306
47
1.1104
2
1.1583
4
1.1325
1
1.1325
1
1.1352
1
1.2611
5
1.2768
2
1.1308
1
1.1435
1
1.1337
1
         
Quadratic configuration interaction QCISD 1.2854
5
1.3312
89
1.3564
47
1.3324
55
1.2608
81
1.2701
58
1.2623
65
1.2467
72
1.2507
70
1.2465
41
1.1504
1
1.1504
1
1.2863
20
1.2530
60
1.2408
51
1.1481
1
1.2881
20
1.2758
15
1.1481
1
       
QCISD(T) 1.2532
1
1.2239
1
1.2239
1
1.2042
1
1.2654
49
1.1763
1
1.1759
1
1.1887
2
1.1818
4
1.1625
1
1.1567
1
1.1567
1
1.2996
18
1.2738
37
1.2601
32
1.1554
1
1.2771
30
1.2698
18
1.1556
1
       
QCISD(TQ) 1.2683
1
1.2368
1
1.2368
1
1.2129
1
1.1806
1
1.1806
1
1.1801
1
1.1636
1
1.1636
1
1.1649
1
1.1573
1
1.1573
1
1.1651
1
1.1706
1
1.1605
1
1.1557
1
1.1749
1
1.1611
1
1.1560
1
       
Coupled Cluster CCD 1.2601
5
1.3272
56
1.3366
47
1.3129
57
1.2547
92
1.2592
55
1.2602
58
1.2458
59
1.2372
47
1.2375
44
1.1324
1
1.1324
1
1.2743
20
1.2469
59
1.2464
43
1.1310
1
1.2510
36
1.2495
24
1.1309
1
  1.1644
2
1.1563
2
 
CCSD 1.2552
1
1.2170
1
1.2170
1
1.2001
1
1.2504
67
1.1667
1
1.1662
1
1.1784
2
1.1510
1
1.1517
1
1.1453
1
1.1453
1
1.2833
12
1.2802
25
1.2701
23
1.2531
2
1.2893
12
1.2764
12
1.1433
1
       
CCSD=FULL 1.2551
1
1.2169
1
1.2169
1
1.1999
1
1.2905
12
1.1660
1
1.1654
1
1.1501
1
1.1501
1
1.1501
1
1.1431
1
1.1431
1
1.2825
12
1.2841
12
1.2704
12
1.2507
2
1.2884
12
1.2703
12
1.1410
1
       
CCSD(T) 1.2555
1
1.2203
4
1.2183
1
1.1999
1
1.2663
62
1.2181
7
1.1790
5
1.1865
3
1.1702
7
1.1563
1
1.1511
1
1.1511
1
1.2960
18
1.2679
40
1.2379
45
1.2525
5
1.2681
34
1.2567
25
1.2493
4
  1.1809
4
1.1736
4
 
CCSD(T)=FULL 1.2554
1
1.2183
1
1.2183
1
1.1998
1
1.2810
31
1.1682
1
1.1677
1
1.1536
1
1.1536
1
1.1550
1
1.1494
1
1.1494
1
1.2951
18
1.2849
25
1.2672
21
1.2783
4
1.2950
19
1.2685
14
1.2830
3
  1.1803
4
1.1720
4
 

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 1.3225
103
1.2814
100
1.2878
97
1.2771
100
1.3006
100
1.3005
100
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 1.2997
54
1.2596
56
1.1955
1
1.1598
1
1.1891
1
1.1892
1
B3LYP 1.3212
101
1.2776
98
1.3172
103
1.2726
100
1.3097
103
1.3101
101
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
Moller Plesset perturbation MP2 1.3510
100
1.2921
96
1.3438
94
1.2884
97
1.3458
100
1.3458
100
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
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.