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III.G.1.a.

Comparison of levels of theory for N-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 1.1844
16
PM3 1.4151
49
PM6 1.3018
51
composite G2 1.2471
45
G3 1.2565
51
G3B3 1.3125
52
G4 1.3297
50
CBS-Q 1.2167
34

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 aug-cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ Sadlej_pVTZ
hartree fock HF 1.3649
51
1.2882
51
1.2883
51
1.2721
51
1.3322
117
1.2562
51
1.2987
51
1.2536
51
1.2962
51
1.2957
51
1.3430
36
1.0665
1
1.2721
52
1.2562
51
1.2417
49
1.1070
17
1.2571
51
1.2459
48
1.1007
14
1.0762
1
1.0760
1
1.1380
6
1.1296
6
1.0846
2
ROHF 1.1479
1
0.8926
5
0.8926
5
0.8436
4
0.9559
7
0.8862
5
0.8859
5
0.8812
5
0.7198
3
1.0720
1
1.1576
1
  0.5416
2
0.8857
5
0.8788
5
0.7167
3
0.7244
3
0.7176
3
0.7167
3
         
density functional LSDA 1.4271
50
1.3661
50
1.3660
50
1.3529
50
1.3353
50
1.3352
50
1.3338
50
1.3305
50
1.3306
50
1.3313
50
1.0944
1
1.0944
1
1.1728
8
1.3349
50
1.3272
50
1.1230
2
1.3353
49
1.1518
9
1.1229
2
1.1319
1
1.1319
1
     
SVWN 1.1890
1
1.3308
46
1.1181
1
1.1229
1
1.3172
44
1.1838
8
1.3084
46
1.1762
8
1.1761
8
1.1792
8
1.0944
1
1.0944
1
1.0962
1
1.1833
8
1.1726
8
1.0939
1
1.1702
7
1.1604
7
1.0937
1
1.1319
1
1.1319
1
     
BLYP 1.4644
51
1.3936
51
1.3075
34
1.3385
51
1.3151
48
1.3175
51
1.3161
51
1.2710
34
1.3549
51
1.3551
51
1.1031
1
1.1031
1
1.1864
8
1.3195
50
1.3094
51
1.1022
1
1.4134
32
1.1030
1
1.1021
1
1.1400
1
1.1400
1
     
B1B95 1.4378
50
1.3642
50
1.3641
50
1.3484
51
1.3299
50
1.3316
50
1.3308
50
1.3284
50
1.3283
50
1.3282
50
1.1084
2
1.0878
1
1.1663
8
1.3315
50
1.3233
50
1.1321
3
1.3307
49
1.1870
16
1.1209
3
1.1165
1
1.1164
1
     
B3LYP 1.4351
51
1.3277
47
1.3284
51
1.3133
51
1.3366
51
1.3363
51
1.2931
51
1.2905
51
1.2280
22
1.2862
45
1.3892
31
1.0912
1
1.3026
52
1.3362
51
1.2800
48
1.1290
14
1.2289
26
1.1952
23
1.1265
14
1.1217
1
1.1217
1
1.1608
6
1.1500
6
1.1218
2
B3LYPultrafine 1.1807
1
1.1127
1
1.1127
1
1.1184
1
1.3445
48
1.1055
1
1.3996
11
1.0954
1
1.0954
1
1.0988
1
1.0912
1
1.0912
1
1.4415
4
1.1812
8
1.2651
22
1.0902
1
1.1684
7
1.3282
49
1.0901
1
         
B3PW91 1.3269
23
1.3242
51
1.3243
51
1.3079
51
1.2846
49
1.2885
51
1.2494
34
1.2850
51
1.2245
22
1.3276
51
1.0910
1
1.0910
1
1.1702
8
1.2881
51
1.2819
51
1.0901
1
1.3848
32
1.0910
1
1.0901
1
1.1215
1
1.1214
1
     
mPW1PW91 1.3154
23
1.3191
51
1.2516
23
1.3439
51
1.2812
48
1.3288
51
1.2830
51
1.2806
51
1.3230
51
1.3231
51
1.0888
1
1.0888
1
1.1567
7
1.2836
51
1.2179
28
1.0880
1
1.3444
38
1.1467
8
1.0879
1
1.1178
1
1.1178
1
     
M06-2X 1.2396
8
1.1930
8
1.1938
8
1.1839
8
1.3025
50
1.1728
8
1.1713
8
1.1678
8
1.1676
8
1.1686
8
1.0862
1
1.0862
1
1.1536
7
1.1727
8
1.1645
8
1.0854
1
1.1615
7
1.1533
7
1.0853
1
1.1105
1
1.1102
1
     
PBEPBE 1.3402
23
1.3848
51
1.2810
21
1.2714
21
1.3496
51
1.3494
51
1.3480
51
1.3455
51
1.3455
51
1.3436
49
1.3840
34
1.1031
1
1.1727
7
1.3535
49
1.3424
51
1.1530
3
1.1792
7
1.1959
16
1.1446
3
1.1395
1
1.1396
1
    1.1319
2
PBEPBEultrafine 1.1954
1
1.1273
1
1.1273
1
1.1303
1
1.3646
56
1.1168
1
1.1162
1
1.1072
1
1.1072
1
1.1109
1
1.1031
1
1.1031
1
1.4557
4
1.1934
8
1.1841
8
1.1024
1
1.1800
7
1.1713
7
1.1022
1
         
PBE1PBE 1.2494
8
1.1969
8
1.1969
8
1.1892
8
1.3027
52
1.1772
8
1.1754
8
1.1716
8
1.1714
8
1.1732
8
1.0898
1
1.0898
1
1.1574
7
1.1768
8
1.1682
8
1.0889
1
1.1649
7
1.1566
7
1.0889
1
1.1188
1
1.1188
1
     
HSEh1PBE 1.2500
8
1.1954
8
1.1962
8
1.1890
8
1.3056
46
1.1771
8
1.1752
8
1.1714
8
1.1712
8
1.1730
8
1.0894
1
1.0894
1
1.1570
7
1.1766
8
1.1679
8
1.0885
1
1.1646
7
1.1562
7
1.0885
1
1.1187
1
1.1187
1
     
TPSSh   1.4803
5
1.4803
5
1.4651
5
1.3411
50
1.4482
5
1.3407
50
1.4423
5
        1.5645
3
1.4479
5
1.3353
50
  1.4909
4
1.4812
4
           
Moller Plesset perturbation MP2 1.3418
22
1.3649
51
1.3652
51
1.3480
51
1.3498
57
1.3081
51
1.3756
111
1.3012
51
1.2992
48
1.2987
46
1.1131
1
1.1131
1
1.3117
52
1.3502
51
1.2780
41
1.0258
9
1.2500
26
1.1861
16
1.0237
9
1.1588
1
1.1600
1
1.1759
8
1.1619
8
1.1557
2
MP2=FULL 1.3416
22
1.2970
28
1.2994
23
1.2873
23
1.3465
55
1.2676
33
1.2692
34
1.2997
51
1.2409
22
1.2381
22
1.1111
1
1.1111
1
1.1915
8
1.2525
28
1.2492
29
1.0234
9
1.2211
20
1.1605
11
0.9935
7
1.1545
1
1.1547
1
1.1751
8
1.1598
8
 
ROMP2 0.8456
3
0.7794
3
0.7794
3
0.7813
3
0.7694
3
0.7694
3
0.7693
3
0.7647
3
0.7647
3
0.5722
2
    0.5711
2
0.7703
3
0.7621
3
  0.7719
3
1.1470
1
           
MP3 1.1757
1
1.1088
1
1.1088
1
1.1149
1
1.2847
47
1.1057
1
1.3603
49
1.0949
1
1.0949
1
1.0961
1
1.0895
1
1.0895
1
1.4389
4
1.4557
4
1.4392
4
1.0865
1
1.1067
1
1.0899
1
1.0867
1
  1.1109
1
     
MP3=FULL         1.3323
50
  1.3323
49
          1.5542
3
1.5716
3
1.5504
3
                 
MP4 1.2530
3
1.2415
19
1.1403
1
1.1470
1
1.2579
26
1.1282
1
1.1285
1
1.2260
3
1.2575
20
1.3190
6
1.1131
1
1.1131
1
1.1847
7
1.1944
7
1.2402
17
1.1102
1
1.1957
7
1.1834
7
1.1104
1
1.1571
1
1.1580
1
     
MP4=FULL 1.1903
1
1.2278
7
1.1402
1
1.1469
1
1.1922
7
1.1275
1
1.1278
1
1.1182
1
1.1875
7
1.1155
1
1.1112
1
1.1112
1
1.1144
1
1.1936
7
1.1791
7
1.1079
1
1.1948
7
1.1774
7
1.1080
1
1.1527
1
1.1525
1
     
B2PLYP 1.5021
5
1.4330
5
1.4330
5
1.4293
5
1.3541
43
1.4150
5
1.4867
4
1.4081
5
1.4079
5
1.4087
5
1.0992
1
1.0992
1
1.4026
5
1.4152
5
1.3737
46
1.0978
1
1.4505
4
1.4379
4
1.0978
1
         
B2PLYP=FULL 1.5791
4
1.5101
4
1.5101
4
1.5041
4
1.4900
4
1.4899
4
1.4863
4
1.4837
4
1.4834
4
1.4833
4
    1.4778
4
1.4905
4
1.4771
4
  1.5624
3
1.5488
3
           
B2PLYP=FULLultrafine         1.4099
29
                                     
Configuration interaction CID 1.2613
4
1.2393
22
1.2189
20
1.2112
20
1.2366
33
1.1040
1
1.1036
1
1.1942
22
1.1713
4
1.2386
6
1.0870
1
1.0870
1
1.0894
1
1.1033
1
1.0873
1
1.0838
1
1.1045
1
1.0873
1
1.0840
1
1.1024
1
1.1023
1
     
CISD 1.2621
4
1.2498
21
1.2231
20
1.2152
20
1.2359
31
  1.1053
1
1.1902
20
1.1730
4
1.2403
6
1.0886
1
1.0886
1
1.0912
1
1.1050
1
1.0890
1
1.0854
1
1.1060
1
1.0889
1
1.0855
1
1.1037
1
1.1035
1
     
Quadratic configuration interaction QCISD 1.3379
7
1.3123
35
1.2387
18
1.2588
20
1.2507
32
1.2525
22
1.2359
25
1.2258
25
1.2430
27
1.2014
17
1.0975
1
1.0975
1
1.1529
6
1.2390
22
1.1852
18
1.0942
1
1.1686
8
0.9506
6
1.0943
1
1.1195
1
1.1195
1
     
QCISD(T) 1.1900
1
1.1278
1
1.1278
1
1.1339
1
1.2386
22
1.1925
2
1.1919
2
1.2296
4
1.3185
5
1.1836
2
1.1040
1
1.1040
1
1.1737
7
1.1865
11
1.1738
11
1.1008
1
1.1856
9
1.1710
9
1.1010
1
1.1331
1
1.1336
1
     
QCISD(T)=FULL         1.1287
2
  1.1287
2
1.1297
1
          1.1284
2
1.1108
2
1.1081
2
1.1300
2
1.1099
2
1.1082
2
    1.1276
2
1.1109
2
 
QCISD(TQ) 1.1939
1
1.1267
1
1.1267
1
1.1334
1
1.1197
1
1.1197
1
1.1195
1
1.1090
1
1.1090
1
1.1092
1
1.1030
1
1.1030
1
1.1046
1
1.1190
1
1.1033
1
1.0997
1
1.1210
1
1.1034
1
1.1000
1
         
Coupled Cluster CCD 1.3237
7
1.2525
21
1.2325
20
1.2468
21
1.2877
34
1.2254
21
1.2248
21
1.2233
24
1.1969
18
1.1949
18
1.0944
1
1.0944
1
1.1617
7
1.2366
22
1.1929
16
1.0911
1
1.1616
10
1.0204
9
1.0913
1
1.1157
1
1.1159
1
1.1928
4
1.1790
4
 
CCSD 1.1891
1
1.1212
1
1.1212
1
1.1281
1
1.2303
23
1.1846
2
1.1839
2
1.2220
4
1.1688
4
1.1752
2
1.0964
1
1.0964
1
1.1642
7
1.1941
9
1.1731
8
0.9178
5
1.1760
7
1.1621
7
0.9179
5
1.1176
1
1.1177
1
     
CCSD=FULL 1.1890
1
1.1211
1
1.1211
1
1.1280
1
1.1616
6
1.1129
1
1.1126
1
1.1022
1
1.1022
1
1.1009
1
1.0946
1
1.0946
1
1.1508
6
1.1769
7
1.1467
6
0.9158
5
1.1752
7
1.1443
6
0.9159
5
1.1144
1
1.1138
1
     
CCSD(T) 1.1899
1
1.1400
2
1.1272
1
1.1335
1
1.2417
23
1.2197
5
1.1573
5
1.2111
5
1.2853
6
1.1832
2
1.1035
2
1.1035
1
1.1730
7
1.1975
18
1.2055
21
0.9891
7
1.1754
14
1.1601
14
0.9867
7
1.1320
1
1.1325
1
1.1728
7
1.1587
7
 
CCSD(T)=FULL 1.1898
1
1.1270
1
1.1270
1
1.1333
1
1.1792
15
1.1191
1
1.1189
1
1.1087
2
1.1087
1
1.1074
1
1.1017
1
1.1017
1
1.1723
7
1.1803
13
1.1662
12
0.9869
7
1.1698
9
1.1586
10
0.9663
6
1.1285
1
1.1283
1
1.1720
7
1.1569
7
 

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 1.2915
51
1.2976
50
1.2877
51
1.2896
50
1.2809
51
1.2810
51
density functional LSDA 1.1611
1
1.1432
1
1.1491
1
1.1219
1
1.1381
1
1.1381
1
SVWN 1.1611
1
1.1432
1
1.1491
1
1.1219
1
1.1381
1
1.1381
1
BLYP 1.1629
1
1.1440
1
1.1513
1
1.1220
1
1.1486
1
1.1491
1
B1B95 1.4130
36
1.3963
36
1.1708
2
1.1445
2
1.1663
2
1.1665
2
B3LYP 1.3351
51
1.3379
50
1.3308
51
1.3302
50
1.3221
51
1.3214
50
B3LYPultrafine 1.1488
1
1.1320
1
1.1376
1
1.1099
1
1.1333
1
1.1336
1
B3PW91 1.1465
1
1.1306
1
1.1351
1
1.1088
1
1.1307
1
1.1309
1
mPW1PW91 1.1433
1
1.1278
1
1.1320
1
1.1060
1
1.1276
1
1.1279
1
M06-2X 1.1375
1
1.1240
1
1.1243
1
1.0998
1
1.1239
1
1.1240
1
PBEPBE 1.1602
1
1.1424
1
1.1485
1
1.1212
1
1.1454
1
1.1457
1
PBEPBEultrafine 1.1602
1
1.1424
1
1.1485
1
1.1212
1
1.1454
1
1.1457
1
PBE1PBE 1.1438
1
1.1284
1
1.1326
1
1.1069
1
1.1282
1
1.1285
1
HSEh1PBE 1.1443
1
1.1288
1
1.1332
1
1.1074
1
1.1282
1
1.1285
1
Moller Plesset perturbation MP2 1.3796
51
1.3530
50
1.3721
51
1.3461
50
1.3665
51
1.3667
51
MP2=FULL 1.1959
1
1.1598
1
1.1814
1
1.1378
1
1.1754
1
1.1752
1
MP3 1.1492
1
1.1338
1
1.1341
1
1.1110
1
1.1292
1
1.1288
1
MP4 1.1824
1
1.1551
1
1.1718
1
1.1344
1
1.1647
1
1.1650
1
MP4=FULL 1.1824
1
1.1551
1
1.1718
1
1.1344
1
1.1646
1
1.1647
1
B2PLYP 1.1637
1
1.1411
1
1.1518
1
1.1191
1
1.1469
1
1.1471
1
Configuration interaction CID 1.1524
1
1.1314
1
1.1381
1
1.1087
1
1.1331
1
1.1329
1
CISD 1.1542
1
1.1330
1
1.1399
1
1.1103
1
1.1349
1
1.1347
1
Quadratic configuration interaction QCISD 1.1653
1
1.1425
1
1.1510
1
1.1202
1
1.1457
1
1.1454
1
QCISD(T) 1.1695
1
1.1477
1
1.1559
1
1.1260
1
1.1500
1
1.1498
1
QCISD(TQ) 1.1700
1
1.1479
1
1.1559
1
1.1258
1
1.1502
1
1.1500
1
Coupled Cluster CCD 1.1619
1
1.1394
1
1.1475
1
1.1170
1
1.1422
1
1.1420
1
CCSD 1.1639
1
1.1414
1
1.1497
1
1.1191
1
1.1443
1
1.1441
1
CCSD=FULL 1.1639
1
1.1414
1
1.1497
1
1.1191
1
1.1442
1
1.1439
1
CCSD(T) 1.1692
1
1.1473
1
1.1556
1
1.1255
1
1.1497
1
1.1495
1
CCSD(T)=FULL 1.1692
1
1.1473
1
1.1556
1
1.1255
1
1.1495
1
1.1493
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.