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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 H-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 1.0446
198
PM3 1.1050
195
PM6 1.0360
343
composite G2 1.0745
307
G3 1.0560
339
G3B3 1.0300
353
G3MP2 1.2319
27
G4 1.0442
349
CBS-Q 1.0423
288
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 daug-cc-pVTZ Sadlej_pVTZ
hartree fock HF 1.0586
329
1.0346
349
1.0303
338
1.0223
340
1.0140
357
1.0243
336
1.0151
215
1.0219
336
1.0236
338
1.0229
338
1.0549
150
1.1105
20
1.0209
350
1.0295
336
1.0220
330
1.0010
135
1.0262
333
1.0262
337
1.0104
122
0.9902
4
1.0225
4
1.0142
4
0.9985
3
1.0033
6
ROHF 1.0277
4
1.0213
35
1.0250
29
1.0106
24
1.0140
33
1.0109
29
1.0058
29
1.0057
29
1.0046
29
0.9951
4
    1.0062
20
1.0154
29
1.0047
29
1.0027
22
1.0059
25
1.0008
25
1.0013
20
         
density functional LSDA 1.0747
345
1.0612
344
1.0610
346
1.0355
348
1.0381
344
1.0535
343
1.0530
342
1.0350
343
1.0516
345
1.0497
339
1.0205
3
1.0204
3
1.0328
167
1.0566
338
1.0502
342
1.0280
13
1.0526
330
1.0318
185
1.0277
9
      1.0209
3
 
SVWN 1.0636
3
1.0534
335
1.0210
3
1.0071
3
1.0469
325
1.0358
165
1.0477
326
1.0336
165
1.0335
169
1.0334
169
1.0205
3
1.0204
3
1.0626
222
1.0403
165
1.0320
165
1.0201
3
1.0359
164
1.0318
162
1.0200
3
      1.0209
3
 
BLYP 1.0997
329
1.0609
338
1.0650
300
1.0513
338
1.0459
375
1.0512
336
1.0504
332
1.0523
298
1.0488
334
1.0488
338
1.0220
3
1.0218
3
1.0324
164
1.0565
332
1.0462
334
1.0214
3
1.0637
212
1.0376
99
1.0210
3
      1.0217
3
 
B1B95 1.0645
336
1.0308
341
1.0281
337
1.0221
342
1.0216
333
1.0238
339
1.0221
339
1.0181
334
1.0185
338
1.0214
338
1.0102
3
1.0100
3
1.0200
165
1.0277
338
1.0188
336
1.0228
18
1.0199
327
1.0169
227
1.0232
12
      1.0098
3
 
B3LYP 1.0853
330
1.0513
344
1.0501
334
1.0411
338
1.0277
340
1.0418
334
1.0434
338
1.0397
330
1.0517
233
1.0414
350
1.0681
126
1.0694
16
1.0353
350
1.0287
334
1.0389
317
1.0256
123
1.0496
262
1.0333
340
1.0181
115
1.0062
4
1.0485
4
1.0370
4
1.0132
3
1.0198
6
B3LYPultrafine 1.0624
3
1.0525
125
1.0217
3
1.0059
3
1.0518
337
1.0332
107
1.0406
145
1.0301
107
1.0157
3
1.0172
3
1.0135
3
1.1235
17
1.0268
126
1.0334
147
1.0248
215
1.0128
3
1.0282
147
1.0424
341
1.0124
3
      1.0132
3
 
B3PW91 1.0952
225
1.0485
338
1.0487
336
1.0397
338
1.0423
329
1.0403
334
1.0430
298
1.0383
334
1.0502
235
1.0384
338
1.0129
3
1.0127
3
1.0227
167
1.0454
334
1.0371
330
1.0122
3
1.0542
210
1.0258
109
1.0121
3
      1.0130
3
 
mPW1PW91 1.0924
238
1.0464
337
1.0577
246
1.0373
340
1.0400
332
1.0793
334
1.0376
334
1.0362
334
1.0366
337
1.0364
338
1.0111
3
1.0110
3
1.0209
167
1.0434
334
1.0422
265
1.0106
3
1.0420
292
1.0196
169
1.0104
3
      1.0110
3
 
M06-2X 1.0629
170
1.0345
170
1.0444
308
1.0249
170
1.0384
335
1.0252
166
1.0244
166
1.0232
166
1.0232
170
1.0221
190
1.0124
3
1.0123
3
1.0228
165
1.0296
166
1.0207
186
1.0114
3
1.0250
165
1.0204
183
1.0112
3
      1.0119
3
 
PBEPBE 1.1070
223
1.0619
338
1.0466
230
1.0360
232
1.0536
338
1.0498
333
1.0508
339
1.0477
334
1.0478
335
1.0706
329
1.0754
130
1.0731
16
1.0318
165
1.0371
325
1.0460
333
1.0353
18
1.0368
189
1.0331
217
1.0360
16
      1.0220
3
1.0280
6
PBEPBEultrafine 1.0740
3
1.0610
125
1.0330
3
1.0125
3
1.0603
290
1.0408
107
1.0501
126
1.0380
107
1.0240
3
1.0258
3
1.0218
3
1.1237
17
1.0347
126
1.0415
147
1.0326
147
1.0215
3
1.0361
147
1.0425
155
1.0213
3
      1.0221
3
 
PBE1PBE 1.0656
163
1.0338
163
1.0339
163
1.0247
163
1.0373
336
1.0265
159
1.0239
159
1.0224
159
1.0230
163
1.0231
163
1.0121
3
1.0120
3
1.0225
159
1.0295
159
1.0215
159
1.0117
3
1.0250
159
1.0211
157
1.0116
3
      1.0122
3
 
HSEh1PBE 1.0656
170
1.0478
339
1.0329
170
1.0242
170
1.0377
327
1.0244
166
1.0358
335
1.0219
166
1.0225
170
1.0225
170
1.0119
3
1.0118
3
1.0219
165
1.0291
166
1.0366
335
1.0113
3
1.0244
165
1.0204
163
1.0112
3
      1.0118
3
 
TPSSh 1.0729
45
1.0414
135
1.0414
135
1.0311
135
1.0398
345
1.0308
131
1.0379
345
1.0279
131
1.0257
45
1.0404
303
    1.0282
126
1.0358
131
1.0350
345
1.0211
14
1.0306
131
1.0263
129
1.0211
14
      1.0158
3
 
wB97X-D 1.0787
82
1.0438
82
1.0452
371
1.0350
82
1.0389
367
1.0358
78
1.0341
367
1.0324
78
1.0357
371
1.0326
82
    1.0317
367
1.0354
367
1.0339
367
1.0149
29
1.0344
78
1.0334
367
1.0128
29
      1.0112
3
 
B97D3 1.0803
21
1.0509
324
1.0500
21
1.0407
21
1.0436
320
1.0424
17
1.0427
17
1.0401
17
1.0400
324
1.0347
21
    1.0406
17
1.0466
17
1.0390
17
1.0252
9
1.0431
17
1.0387
316
1.0252
9
      1.0174
3
 
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 1.0924
226
1.0518
350
1.0481
335
1.0431
339
1.0472
368
1.0378
336
1.0256
344
1.0416
365
1.0386
338
1.0211
289
1.0150
5
1.0797
14
1.0336
354
1.0464
336
1.0191
282
1.0162
91
1.0513
262
1.0271
240
1.0153
88
1.0060
4
1.0349
7
1.0225
7
1.0121
3
1.0222
6
MP2=FULL 1.0930
222
1.0549
272
1.0332
243
1.0284
243
1.0275
334
1.0408
294
1.0404
298
1.0370
330
1.0494
234
1.0209
246
1.0093
3
1.0105
3
1.0218
167
1.0521
269
1.0177
255
1.0136
91
1.0271
202
1.0181
212
1.0136
85
1.0036
4
1.0341
7
1.0213
7
1.0092
3
1.0215
6
ROMP2 1.0941
21
1.0426
21
1.0426
21
1.0322
21
1.0305
21
1.0250
21
1.0178
21
1.0209
21
1.0233
21
1.0248
21
    1.0211
19
1.0326
21
1.0184
21
  1.0231
23
             
MP3 1.0647
3
1.0202
3
1.0202
3
1.0104
3
1.0418
331
1.0115
3
1.0316
346
1.0102
3
1.0129
3
1.0125
3
1.0097
3
1.0102
3
1.0233
123
1.0330
123
1.0213
123
1.0082
3
1.0194
3
1.0105
3
1.0083
3
      1.0104
3
 
MP3=FULL   1.0447
82
1.0447
82
1.0381
82
1.0371
344
1.0311
78
1.0259
330
1.0301
78
1.0300
82
1.0286
82
    1.0228
123
1.0319
123
1.0187
122
  1.0355
77
1.0145
69
        1.0074
3
 
MP4 1.0735
10
1.0375
205
1.0213
9
1.0140
6
1.0302
225
1.0148
3
1.0140
3
1.0219
19
1.0247
187
1.0201
8
1.0139
3
1.0146
3
1.0268
142
1.0362
137
1.0229
173
1.0128
3
1.0333
133
1.0275
121
1.0133
3
      1.0152
3
 
MP4=FULL 1.0677
3
1.0387
147
1.0248
3
1.0139
3
1.0338
134
1.0138
3
1.0130
3
1.0141
3
1.0272
144
1.0141
3
1.0124
3
1.0134
3
1.0140
3
1.0355
136
1.0214
125
1.0107
3
1.0323
137
1.0254
117
1.0112
3
      1.0121
3
 
B2PLYP 1.0701
128
1.0373
128
1.0373
128
1.0297
128
1.0472
298
1.0279
124
1.0269
131
1.0254
124
1.0260
130
1.0238
152
1.0117
3
1.0118
3
1.0256
124
1.0334
124
1.0345
313
1.0109
3
1.0292
124
1.0220
146
1.0109
3
      1.0119
3
 
B2PLYP=FULL 1.0701
128
1.0374
135
1.0373
128
1.0297
128
1.0300
131
1.0276
124
1.0266
131
1.0253
124
1.0259
128
1.0255
128
    1.0255
124
1.0331
124
1.0234
122
  1.0290
124
1.0234
121
        1.0111
3
 
B2PLYP=FULLultrafine 1.0783
85
1.0451
85
1.0450
85
1.0365
85
1.0309
209
1.0347
81
1.0331
81
1.0320
81
1.0320
85
1.0318
85
    1.0321
81
1.0397
81
1.0300
81
  1.0352
81
1.0294
81
        1.0111
3
 
Configuration interaction CID 1.0719
9
1.0295
234
1.0294
237
1.0233
237
1.0402
294
1.0101
7
1.0092
7
1.0142
244
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
      1.0082
3
 
CISD 1.0665
13
1.0306
245
1.0299
237
1.0237
237
1.0408
293
1.0095
6
1.0097
7
1.0164
232
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
      1.0089
3
 
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 1.0762
13
1.0736
299
1.0349
234
1.0286
230
1.0286
266
1.0214
236
1.0216
229
1.0449
252
1.0232
216
1.0219
206
1.0119
3
1.0123
3
1.0227
161
1.0369
244
1.0197
212
1.0103
3
1.0283
169
1.0153
181
1.0107
3
      1.0126
3
 
QCISD(T) 1.0703
3
1.0320
5
1.0264
3
1.0150
3
1.0517
215
1.0278
19
1.0271
19
1.0333
101
1.0212
7
1.0233
5
1.0138
3
1.0144
3
1.0250
160
1.0354
185
1.0229
168
1.0125
3
1.0319
161
1.0198
139
1.0129
3
      1.0150
3
 
QCISD(T)=FULL         1.0375
105
  1.0270
100
            1.0398
101
1.0241
96
1.0153
42
1.0364
100
1.0182
84
1.0177
32
      1.0119
3
 
QCISD(TQ) 1.0705
3
1.0260
3
1.0260
3
1.0152
3
1.0288
41
1.0156
3
1.0186
39
1.0148
3
1.0173
3
1.0161
3
1.0137
3
1.0143
3
1.0144
3
1.0309
43
1.0208
32
1.0228
13
1.0278
33
1.0222
21
1.0171
6
         
QCISD(TQ)=FULL         1.0288
40
  1.0197
36
            1.0294
44
1.0182
32
1.0207
13
1.0264
35
1.0192
21
1.0153
6
         
Coupled Cluster CCD 1.0763
13
1.0355
242
1.0332
227
1.0272
229
1.0617
299
1.0207
234
1.0204
230
1.0206
238
1.0229
196
1.0218
190
1.0158
5
1.0114
3
1.0215
162
1.0358
250
1.0193
198
1.0094
3
1.0282
175
1.0152
168
1.0097
3
  1.0368
3
1.0232
3
1.0117
3
 
CCSD 1.0703
3
1.0294
5
1.0243
3
1.0138
3
1.0284
221
1.0263
19
1.0223
26
1.0245
25
1.0220
5
1.0254
129
1.0116
3
1.0121
3
1.0247
140
1.0323
171
1.0192
190
1.0138
62
1.0304
139
1.0157
142
1.0173
25
      1.0124
3
 
CCSD=FULL 1.0702
3
1.0241
3
1.0241
3
1.0137
3
1.0295
166
1.0129
3
1.0135
7
1.0128
3
1.0146
3
1.0241
127
1.0100
3
1.0110
3
1.0237
143
1.0327
143
1.0177
161
1.0127
57
1.0296
142
1.0126
146
1.0160
22
      1.0093
3
 
CCSD(T) 1.0703
3
1.0971
13
1.0263
3
1.0150
3
1.0351
217
1.0333
106
1.0480
39
1.0331
103
1.0301
24
1.0298
22
1.0199
4
1.1533
7
1.0253
155
1.0358
179
1.0238
179
1.0187
70
1.0310
176
1.0266
142
1.0194
57
  1.0388
7
1.0253
7
1.0149
3
 
CCSD(T)=FULL 1.0703
3
1.0259
3
1.0259
3
1.0149
3
1.0339
169
1.0144
3
1.0135
3
1.0144
3
1.0164
3
1.0143
3
1.0120
3
1.0130
3
1.0234
148
1.0344
159
1.0218
144
1.0174
64
1.0309
155
1.0162
121
1.0203
43
  1.0381
7
1.0241
7
1.0118
3
 
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 1.0289
338
1.0309
336
1.0249
338
1.0300
340
1.0276
342
1.0250
338
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 1.0370
161
1.0367
152
1.0156
9
1.0187
9
1.0161
9
1.0162
9
B3LYP 1.0496
335
1.0502
333
1.0445
334
1.0453
332
1.0469
338
1.0450
334
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
wB97X-D 1.0424
82
1.0420
82
1.0357
82
1.0360
82
1.0375
82
1.0375
82
Moller Plesset perturbation MP2 1.0528
336
1.0499
334
1.0475
338
1.0470
340
1.0510
342
1.0488
338
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
B2PLYP 1.0153
3
1.0233
3
1.0114
3
1.0184
3
1.0100
3
1.0102
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.