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III.G.1.a.

Comparison of levels of theory for N-H


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 1.0430
74
PM3 1.0942
213
PM6 1.1197
248
composite G2 1.0779
227
G3 1.0548
251
G3B3 1.0607
275
G4 1.0335
262
CBS-Q 1.0580
192
molecular mechanics DREIDING 1.0119
8

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 1.0451
245
1.0230
266
1.0170
248
1.0094
248
1.0716
614
1.0118
252
1.0543
262
1.0097
252
1.0117
250
1.0108
250
1.0222
164
1.0920
24
1.1310
273
1.0176
252
1.0097
246
1.0256
93
1.0142
249
1.0153
259
1.0413
87
0.9902
4
1.0225
4
1.0142
4
1.0033
6
ROHF 1.0529
6
1.1510
17
1.1599
16
1.2123
11
1.1147
22
1.1496
16
1.1481
16
1.1461
16
1.2085
11
1.0120
6
1.0222
1
  1.5506
4
1.1562
16
1.1461
16
1.2490
9
1.2122
11
1.2052
11
1.3207
7
       
density functional LSDA 1.0807
255
1.0494
261
1.0493
263
1.0405
262
1.0440
262
1.0427
262
1.0424
257
1.0411
261
1.0413
260
1.0386
252
1.0205
3
1.0204
3
1.0646
50
1.0454
257
1.0397
261
1.0325
14
1.0412
249
1.0559
71
1.0341
10
       
SVWN 1.0636
3
1.1447
233
1.0210
3
1.0071
3
1.1421
227
1.0677
50
1.1382
227
1.0656
50
1.0658
50
1.0657
50
1.0205
3
1.0204
3
1.0193
3
1.0729
50
1.0641
50
1.0201
3
1.0694
49
1.0666
47
1.0200
3
       
BLYP 1.1052
241
1.0482
252
1.0524
208
1.0388
246
1.0407
251
1.0390
252
1.0380
248
1.0400
208
1.0369
246
1.0531
250
1.0220
3
1.0218
3
1.0641
50
1.0449
248
1.0339
250
1.0214
3
1.0563
147
1.0218
3
1.0210
3
       
B1B95 1.0982
243
1.0619
258
1.0589
254
1.0533
259
1.0527
252
1.0549
258
1.0384
258
1.0496
253
1.0500
253
1.0538
253
1.0102
3
1.0100
3
1.0519
50
1.0598
257
1.0506
255
1.0301
22
1.0553
251
1.0387
89
1.0298
15
       
B3LYP 1.0727
244
1.0389
264
1.0372
246
1.0282
248
1.0427
268
1.0293
252
1.0315
263
1.0273
248
1.0426
120
1.0439
248
1.0404
138
1.0584
20
1.1440
275
1.0448
252
1.0262
235
1.0556
89
1.0372
172
1.0535
175
1.0473
82
1.0062
4
1.0485
4
1.0370
4
1.0198
6
B3LYPultrafine 1.0624
3
1.1124
17
1.0217
3
1.0059
3
1.0751
257
1.0180
3
1.0519
52
1.0148
3
1.0157
3
1.0172
3
1.0135
3
1.1235
17
1.0079
15
1.0916
32
1.0788
109
1.0128
3
1.0859
32
1.0316
254
1.0124
3
       
B3PW91 1.0848
112
1.0359
248
1.0360
246
1.0270
246
1.0298
245
1.0280
250
1.0305
208
1.0262
250
1.0416
120
1.0425
250
1.0129
3
1.0127
3
1.0550
50
1.0337
250
1.0249
246
1.0122
3
1.0472
145
1.0128
3
1.0121
3
       
mPW1PW91 1.0832
125
1.0337
247
1.0468
138
1.0404
252
1.0277
248
1.0809
250
1.0254
250
1.0241
250
1.0249
249
1.0405
250
1.0111
3
1.0110
3
1.0531
50
1.0317
250
1.0300
173
1.0106
3
1.0490
192
1.0521
52
1.0104
3
       
M06-2X 1.0905
51
1.0627
51
1.0627
51
1.0548
51
1.1287
246
1.0563
51
1.0561
51
1.0547
51
1.0550
51
1.0546
51
1.0124
3
1.0123
3
1.0547
50
1.0615
51
1.0531
51
1.0114
3
1.0582
50
1.0555
48
1.0112
3
       
PBEPBE 1.0952
117
1.0493
261
1.0624
132
1.0513
132
1.0419
264
1.0377
251
1.0391
265
1.0357
252
1.0362
249
1.0832
243
1.0487
142
1.0632
20
1.0642
50
1.0442
239
1.0341
251
1.0434
22
1.0615
78
1.0478
126
1.0441
20
      1.0280
6
PBEPBEultrafine 1.0740
3
1.1004
21
1.0330
3
1.0125
3
1.0593
284
1.0262
3
1.0991
22
1.0231
3
1.0240
3
1.0258
3
1.0218
3
1.1046
21
1.0157
15
1.1011
32
1.0907
32
1.0215
3
1.0948
32
1.1034
48
1.0213
3
       
PBE1PBE 1.0986
44
1.0686
44
1.0686
44
1.0610
44
1.1240
253
1.0642
44
1.0622
44
1.0606
44
1.0615
44
1.0614
44
1.0121
3
1.0120
3
1.0606
44
1.0681
44
1.0596
44
1.0117
3
1.0639
44
1.0617
42
1.0116
3
       
HSEh1PBE 1.0934
51
1.0618
51
1.0618
51
1.0544
51
1.1307
238
1.0559
51
1.0554
51
1.0539
51
1.0546
51
1.0545
51
1.0119
3
1.0118
3
1.0541
50
1.0614
51
1.0526
51
1.0113
3
1.0581
50
1.0550
48
1.0112
3
       
TPSSh   1.0201
17
1.0201
17
1.0134
17
1.1243
262
1.0140
17
1.1232
262
1.0125
17
        1.0084
12
1.0199
17
1.1198
262
  1.0157
17
1.0107
15
         
Moller Plesset perturbation MP2 1.0821
113
1.0398
272
1.0347
249
1.0298
251
1.0702
316
1.0254
252
1.0599
541
1.0250
240
1.0268
250
1.0527
182
1.0150
5
1.0649
18
1.1413
277
1.0345
252
1.0642
240
1.0704
43
1.0390
170
1.0496
120
1.0738
40
1.0060
4
1.0349
7
1.0225
7
1.0222
6
MP2=FULL 1.0813
111
1.0413
178
1.0451
145
1.0404
143
1.0399
294
1.0280
204
1.0276
207
1.0244
245
1.0402
118
1.0374
121
1.0093
3
1.0105
3
1.0535
50
1.0400
177
1.0406
182
1.0671
43
1.0461
87
1.0430
71
1.0729
39
1.0036
4
1.0341
7
1.0213
7
 
ROMP2 1.3834
7
1.3513
7
1.3513
7
1.3477
7
1.3060
8
1.3009
8
1.2986
8
1.2992
8
1.3016
8
1.2993
8
    1.5620
4
1.3135
8
1.2968
8
1.0659
1
1.3099
8
1.0611
2
1.0669
1
       
MP3 1.0647
3
1.0202
3
1.0202
3
1.0104
3
1.0292
247
1.0115
3
1.1148
266
1.0102
3
1.0129
3
1.0125
3
1.0097
3
1.0102
3
1.0074
15
1.0185
15
1.0059
15
1.0082
3
1.0194
3
1.0105
3
1.0083
3
       
MP3=FULL         1.1219
261
  1.1031
250
          1.0035
12
1.0126
12
0.9990
12
               
MP4 1.0735
10
1.0520
116
1.0213
9
1.0140
6
1.0414
139
1.0148
3
1.0140
3
1.0219
19
1.0471
89
1.0201
8
1.0139
3
1.0146
3
1.0880
30
1.1101
26
1.0457
81
1.0128
3
1.1069
26
1.0983
26
1.0133
3
       
MP4=FULL 1.0677
3
1.1016
28
1.0248
3
1.0139
3
1.1063
26
1.0138
3
1.0130
3
1.0141
3
1.1006
26
1.0141
3
1.0124
3
1.0134
3
1.0140
3
1.1092
26
1.0948
26
1.0107
3
1.0951
30
1.0843
30
1.0112
3
       
B2PLYP 1.0344
6
1.0162
6
1.0162
6
1.0120
6
1.1588
190
1.0078
6
1.0094
6
1.0067
6
1.0077
6
1.0067
6
    1.0070
6
1.0138
6
1.1272
222
  1.0119
6
1.0043
4
         
B2PLYP=FULL 1.0344
6
1.0162
6
1.0162
6
1.0120
6
1.0103
6
1.0075
6
1.0091
6
1.0066
6
1.0075
6
1.0063
6
    1.0070
6
1.0136
6
1.0050
6
  1.0117
6
1.0037
4
         
B2PLYP=FULLultrafine         1.0892
144
                                   
Configuration interaction CID 1.0719
9
1.0437
134
1.0434
134
1.0369
133
1.0276
204
1.0101
7
1.0092
7
1.0258
147
1.0448
15
1.0124
8
1.0076
3
1.0080
3
1.0090
3
1.0200
7
1.0136
13
1.0060
3
1.0174
3
1.0082
3
1.0062
3
       
CISD 1.0637
17
1.0441
145
1.0441
134
1.0377
134
1.0283
203
1.0095
6
1.0097
7
1.0308
133
1.0452
15
1.0128
8
1.0082
3
1.0086
3
1.0097
3
1.0204
7
1.0144
13
1.0066
3
1.0180
3
1.0089
3
1.0068
3
       
Quadratic configuration interaction QCISD 1.0784
14
1.0685
209
1.0470
139
1.0415
132
1.0383
178
1.0333
142
1.0345
136
1.0312
162
1.0379
124
1.0461
85
1.0119
3
1.0123
3
1.0596
46
1.0532
146
1.0416
92
1.0103
3
1.0601
54
1.0525
56
1.0107
3
       
QCISD(T) 1.0703
3
1.0320
5
1.0264
3
1.0150
3
1.0846
116
1.0278
19
1.0271
19
1.0255
28
1.0254
8
1.0233
5
1.0138
3
1.0144
3
1.0605
47
1.0600
82
1.0509
73
1.0125
3
1.0658
56
1.0659
50
1.0129
3
       
QCISD(TQ) 1.0705
3
1.0260
3
1.0260
3
1.0152
3
1.0218
3
1.0156
3
1.0146
3
1.0148
3
1.0173
3
1.0161
3
1.0137
3
1.0143
3
1.0144
3
1.0273
3
1.0141
3
1.0123
3
1.0239
3
1.0148
3
1.0127
3
       
Coupled Cluster CCD 1.0783
14
1.0482
146
1.0462
129
1.0394
130
1.0559
210
1.0327
140
1.0330
136
1.0326
144
1.0435
93
1.0434
88
1.0139
8
1.0114
3
1.0537
50
1.0510
152
1.0380
97
1.0094
3
1.0534
73
1.0470
70
1.0097
3
  1.0368
3
1.0232
3
 
CCSD 1.0703
3
1.0294
5
1.0243
3
1.0138
3
1.0812
109
1.0263
19
1.0236
22
1.0245
25
1.0269
6
1.0213
5
1.0116
3
1.0121
3
1.0989
26
1.0624
59
1.0493
59
1.1389
17
1.0945
30
1.0974
26
1.3229
7
       
CCSD=FULL 1.0702
3
1.0241
3
1.0241
3
1.0137
3
1.0906
31
1.0129
3
1.0120
3
1.0128
3
1.0146
3
1.0128
3
1.0100
3
1.0110
3
1.0823
31
1.0929
31
1.0823
29
1.0768
16
1.0890
32
1.0969
25
1.1855
6
       
CCSD(T) 1.0703
3
1.0802
18
1.0263
3
1.0150
3
1.0492
133
1.0256
29
1.0677
23
1.0256
27
1.0275
9
1.0233
5
1.0199
4
1.1533
7
1.0649
43
1.0608
81
1.0472
81
1.1109
26
1.0573
71
1.0779
56
1.0290
23
  1.0388
7
1.0253
7
 
CCSD(T)=FULL 1.0703
3
1.0259
3
1.0259
3
1.0149
3
1.0601
74
1.0144
3
1.0135
3
1.0144
3
1.0164
3
1.0143
3
1.0120
3
1.0130
3
1.0646
43
1.0690
52
1.0511
56
1.1085
26
1.0672
48
1.0655
41
1.1366
20
  1.0381
7
1.0241
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 1.0157
248
1.0184
248
1.0125
248
1.0193
252
1.0155
252
1.0118
248
density functional LSDA 1.0198
3
1.0353
3
1.0199
3
1.0316
3
1.0115
3
1.0114
3
SVWN 1.0198
3
1.0353
3
1.0199
3
1.0316
3
1.0115
3
1.0114
3
BLYP 1.0225
3
1.0342
3
1.0194
3
1.0289
3
1.0177
3
1.0180
3
B1B95 1.0439
178
1.0447
163
1.0194
10
1.0226
10
1.0197
10
1.0198
10
B3LYP 1.0362
247
1.0376
247
1.0318
246
1.0332
246
1.0345
250
1.0317
246
B3LYPultrafine 1.0144
3
1.0253
3
1.0111
3
1.1514
7
1.0088
3
1.0090
3
B3PW91 1.0111
3
1.0226
3
1.0087
3
1.0183
3
1.0064
3
1.0066
3
mPW1PW91 1.0091
3
1.0203
3
1.0065
3
1.0160
3
1.0047
3
1.0049
3
M06-2X 1.0065
3
1.0184
3
1.0018
3
1.0137
3
1.0058
3
1.0059
3
PBEPBE 1.0183
3
1.0312
3
1.0162
3
1.0266
3
1.0149
3
1.0152
3
PBEPBEultrafine 1.0181
3
1.0312
3
1.0162
3
1.0266
3
1.0149
3
1.0152
3
PBE1PBE 1.0096
3
1.0211
3
1.0071
3
1.0168
3
1.0056
3
1.0058
3
HSEh1PBE 1.0099
3
1.0214
3
1.0074
3
1.0170
3
1.0054
3
1.0056
3
Moller Plesset perturbation MP2 1.0387
250
1.0373
245
1.0343
252
1.0361
252
1.0380
256
1.0349
252
MP2=FULL 1.0209
3
1.0244
3
1.0159
3
1.0186
3
1.0159
3
1.0159
3
MP3 1.0221
3
1.0251
3
1.0162
3
1.0184
3
1.0161
3
1.0161
3
MP4 1.0246
3
1.0282
3
1.0197
3
1.0223
3
1.0190
3
1.0190
3
MP4=FULL 1.0246
3
1.0282
3
1.0197
3
1.0223
3
1.0188
3
1.0188
3
Configuration interaction CID 1.0222
3
1.0243
3
1.0164
3
1.0177
3
1.0161
3
1.0161
3
CISD 1.0223
3
1.0246
3
1.0167
3
1.0181
3
1.0163
3
1.0163
3
Quadratic configuration interaction QCISD 1.0253
3
1.0280
3
1.0199
3
1.0216
3
1.0194
3
1.0194
3
QCISD(T) 1.0260
3
1.0291
3
1.0209
3
1.0229
3
1.0202
3
1.0202
3
QCISD(TQ) 1.0264
3
1.0295
3
1.0211
3
1.0231
3
1.0206
3
1.0206
3
Coupled Cluster CCD 1.0250
3
1.0275
3
1.0194
3
1.0210
3
1.0190
3
1.0191
3
CCSD 1.0254
3
1.0279
3
1.0199
3
1.0215
3
1.0194
3
1.0195
3
CCSD=FULL 1.0254
3
1.0279
3
1.0199
3
1.0215
3
1.0193
3
1.0193
3
CCSD(T) 1.0260
3
1.0291
3
1.0209
3
1.0229
3
1.0202
3
1.0202
3
CCSD(T)=FULL 1.0260
3
1.0291
3
1.0209
3
1.0229
3
1.0201
3
1.0201
3
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.