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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 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 1.0688
138
PM3 1.1610
135
PM6 1.0382
281
composite G2 1.0945
253
G3 1.0704
284
G3B3 1.0359
300
G3MP2 1.2950
21
G4 1.0530
291
CBS-Q 1.0571
233
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 1.0685
274
1.0433
295
1.0386
283
1.0304
285
1.0190
303
1.0323
285
1.0623
165
1.0298
285
1.0320
283
1.0313
283
1.0473
150
1.1105
20
1.0277
294
1.0377
285
1.0301
279
1.0210
116
1.0342
282
1.0348
286
1.0347
104
0.9902
4
1.0225
4
1.0142
4
1.0033
6
ROHF 1.0529
6
1.0996
31
1.1026
30
1.1041
25
1.0833
33
1.0878
30
1.0821
30
1.0821
30
1.0983
25
1.0120
6
1.0222
1
  1.1287
18
1.0926
30
1.0812
30
1.1097
21
1.0978
25
1.0919
25
1.1194
19
       
density functional LSDA 1.0802
286
1.0702
288
1.0700
290
1.0402
289
1.0431
289
1.0619
291
1.0612
290
1.0399
288
1.0605
289
1.0587
281
1.0205
3
1.0204
3
1.0452
104
1.0650
286
1.0586
290
1.0325
14
1.0610
278
1.0425
125
1.0341
10
       
SVWN 1.0636
3
1.0605
274
1.0210
3
1.0071
3
1.0540
268
1.0487
104
1.0551
269
1.0462
104
1.0464
104
1.0467
104
1.0205
3
1.0204
3
1.0576
222
1.0535
104
1.0444
104
1.0201
3
1.0484
103
1.0443
101
1.0200
3
       
BLYP 1.1100
274
1.0702
283
1.0766
245
1.0600
283
1.0536
334
1.0595
285
1.0584
281
1.0625
247
1.0577
279
1.0576
283
1.0220
3
1.0218
3
1.0450
101
1.0654
281
1.0543
283
1.0214
3
1.0692
151
1.0255
36
1.0210
3
       
B1B95 1.0714
279
1.0365
284
1.0334
280
1.0274
285
1.0265
280
1.0290
286
1.0272
286
1.0231
281
1.0236
281
1.0272
281
1.0102
3
1.0100
3
1.0322
104
1.0334
285
1.0240
283
1.0301
22
1.0280
279
1.0248
175
1.0298
15
       
B3LYP 1.0952
277
1.0599
291
1.0588
281
1.0492
285
1.0325
289
1.0497
285
1.0515
288
1.0478
281
1.0686
179
1.0498
297
1.0591
126
1.0694
16
1.0415
296
1.0338
285
1.0474
268
1.0491
107
1.0620
212
1.0396
295
1.0421
99
1.0062
4
1.0485
4
1.0370
4
1.0198
6
B3LYPultrafine 1.0624
3
1.0577
60
1.0217
3
1.0059
3
1.0611
288
1.0235
46
1.0405
84
1.0194
46
1.0157
3
1.0172
3
1.0135
3
1.1235
17
1.0159
65
1.0507
86
1.0339
155
1.0128
3
1.0442
86
1.0505
287
1.0124
3
       
B3PW91 1.1155
169
1.0572
283
1.0575
281
1.0481
283
1.0507
278
1.0485
283
1.0526
247
1.0464
283
1.0675
179
1.0470
283
1.0129
3
1.0127
3
1.0351
104
1.0538
283
1.0453
279
1.0122
3
1.0600
149
1.0128
47
1.0121
3
       
mPW1PW91 1.1112
182
1.0551
282
1.0740
190
1.0456
285
1.0483
281
1.0949
283
1.0454
283
1.0443
283
1.0452
282
1.0450
283
1.0111
3
1.0110
3
1.0332
104
1.0518
283
1.0548
213
1.0106
3
1.0525
230
1.0318
106
1.0104
3
       
M06-2X 1.0778
105
1.0469
105
1.0520
249
1.0375
105
1.0453
279
1.0378
105
1.0363
105
1.0355
105
1.0359
105
1.0327
125
1.0124
3
1.0123
3
1.0349
104
1.0425
105
1.0304
125
1.0114
3
1.0374
104
1.0303
122
1.0112
3
       
PBEPBE 1.1271
169
1.0712
285
1.0573
176
1.0456
178
1.0621
289
1.0581
284
1.0588
290
1.0558
285
1.0565
282
1.0839
276
1.0666
130
1.0731
16
1.0442
104
1.0428
276
1.0541
284
1.0434
22
1.0479
130
1.0426
157
1.0441
20
      1.0280
6
PBEPBEultrafine 1.0740
3
1.0657
60
1.0330
3
1.0125
3
1.0724
231
1.0315
46
1.0519
65
1.0276
46
1.0240
3
1.0258
3
1.0218
3
1.1237
17
1.0240
65
1.0592
86
1.0491
86
1.0215
3
1.0524
86
1.0639
94
1.0213
3
       
PBE1PBE 1.0819
98
1.0480
98
1.0480
98
1.0387
98
1.0442
282
1.0406
98
1.0371
98
1.0362
98
1.0372
98
1.0377
98
1.0121
3
1.0120
3
1.0358
98
1.0439
98
1.0350
98
1.0117
3
1.0385
98
1.0345
96
1.0116
3
       
HSEh1PBE 1.0807
105
1.0517
279
1.0458
105
1.0369
105
1.0452
270
1.0373
105
1.0427
279
1.0345
105
1.0354
105
1.0358
105
1.0119
3
1.0118
3
1.0342
104
1.0422
105
1.0404
279
1.0113
3
1.0368
104
1.0328
102
1.0112
3
       
TPSSh   1.0333
70
1.0333
70
1.0222
70
1.0463
291
1.0218
70
1.0443
291
1.0184
70
  1.0464
264
    1.0175
65
1.0270
70
1.0414
291
  1.0202
70
1.0155
68
         
wB97X-D 1.0946
18
1.0433
18
1.0483
314
1.0279
18
1.0417
314
1.0281
18
1.0181
18
1.0212
18
1.0388
314
1.0265
18
    1.0182
18
1.0306
18
1.0366
314
1.0195
9
1.0182
18
1.0360
314
1.0125
9
       
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 1.1129
169
1.0606
295
1.0567
280
1.0511
284
1.0510
312
1.0456
285
1.0305
294
1.0455
309
1.0469
283
1.0272
234
1.0150
5
1.0797
14
1.0399
298
1.0545
285
1.0248
231
1.0483
72
1.0638
210
1.0364
185
1.0487
69
1.0060
4
1.0349
7
1.0225
7
1.0222
6
MP2=FULL 1.1139
165
1.0679
216
1.0417
187
1.0363
187
1.0326
283
1.0507
243
1.0498
246
1.0449
278
1.0662
177
1.0290
190
1.0093
3
1.0105
3
1.0338
104
1.0645
217
1.0246
203
1.0455
72
1.0361
139
1.0263
149
1.0484
66
1.0036
4
1.0341
7
1.0213
7
1.0215
6
ROMP2 1.2190
19
1.1657
19
1.1657
19
1.1544
19
1.1455
20
1.1400
20
1.1313
20
1.1350
20
1.1378
20
1.1393
20
    1.1584
16
1.1488
20
1.1321
20
1.0659
1
1.1386
20
1.0611
2
1.0669
1
       
MP3 1.0647
3
1.0202
3
1.0202
3
1.0104
3
1.0497
282
1.0115
3
1.0378
292
1.0102
3
1.0129
3
1.0125
3
1.0097
3
1.0102
3
1.0129
62
1.0241
62
1.0110
62
1.0082
3
1.0194
3
1.0105
3
1.0083
3
       
MP3=FULL   1.0445
18
1.0445
18
1.0313
18
1.0435
290
1.0222
18
1.0316
276
1.0180
18
1.0198
18
1.0215
18
    1.0121
62
1.0226
62
1.0079
62
  1.0195
18
1.0093
18
         
MP4 1.0735
10
1.0482
155
1.0213
9
1.0140
6
1.0385
176
1.0148
3
1.0140
3
1.0219
19
1.0377
134
1.0201
8
1.0139
3
1.0146
3
1.0444
80
1.0562
76
1.0352
124
1.0128
3
1.0531
73
1.0465
71
1.0133
3
       
MP4=FULL 1.0677
3
1.0572
82
1.0248
3
1.0139
3
1.0536
76
1.0138
3
1.0130
3
1.0141
3
1.0458
80
1.0141
3
1.0124
3
1.0134
3
1.0140
3
1.0554
76
1.0425
73
1.0107
3
1.0500
79
1.0458
67
1.0112
3
       
B2PLYP 1.0661
63
1.0286
63
1.0286
63
1.0200
63
1.0486
241
1.0180
63
1.0167
70
1.0149
63
1.0164
65
1.0157
87
1.0117
3
1.0118
3
1.0147
63
1.0237
63
1.0339
259
1.0109
3
1.0181
63
1.0123
85
1.0109
3
       
B2PLYP=FULL 1.0661
63
1.0296
70
1.0285
63
1.0200
63
1.0209
70
1.0177
63
1.0163
70
1.0148
63
1.0162
63
1.0164
63
    1.0147
63
1.0235
63
1.0127
63
  1.0179
63
1.0118
61
         
B2PLYP=FULLultrafine 1.0899
21
1.0411
21
1.0411
21
1.0274
21
1.0268
150
1.0246
21
1.0170
21
1.0192
21
1.0206
21
1.0233
21
    1.0176
21
1.0289
21
1.0160
21
  1.0189
21
1.0126
21
         
Configuration interaction CID 1.0719
9
1.0393
178
1.0390
181
1.0322
180
1.0505
243
1.0101
7
1.0092
7
1.0219
192
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 1.0665
13
1.0401
189
1.0397
181
1.0329
181
1.0512
242
1.0095
6
1.0097
7
1.0252
180
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
       
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 1.0784
14
1.0886
246
1.0441
180
1.0373
176
1.0355
217
1.0292
186
1.0292
180
1.0579
202
1.0328
163
1.0324
154
1.0119
3
1.0123
3
1.0360
100
1.0470
190
1.0292
158
1.0103
3
1.0406
108
1.0300
129
1.0107
3
       
QCISD(T) 1.0703
3
1.0320
5
1.0264
3
1.0150
3
1.0676
163
1.0278
19
1.0271
19
1.0249
44
1.0254
8
1.0233
5
1.0138
3
1.0144
3
1.0386
98
1.0482
131
1.0376
118
1.0125
3
1.0457
107
1.0417
97
1.0129
3
       
QCISD(T)=FULL         1.0275
46
  1.0174
42
            1.0295
43
1.0146
43
1.0186
22
1.0237
43
1.0142
39
1.0199
16
       
QCISD(TQ) 1.0705
3
1.0260
3
1.0260
3
1.0152
3
1.0320
28
1.0156
3
1.0199
26
1.0148
3
1.0173
3
1.0161
3
1.0137
3
1.0143
3
1.0144
3
1.0339
30
1.0214
23
1.0235
9
1.0280
24
1.0241
13
1.0171
6
       
QCISD(TQ)=FULL         1.0339
24
  1.0203
24
            1.0330
28
1.0188
23
1.0212
9
1.0271
23
1.0208
13
1.0153
6
       
Coupled Cluster CCD 1.0783
14
1.0445
188
1.0423
173
1.0354
174
1.0743
250
1.0285
184
1.0279
180
1.0282
188
1.0341
142
1.0335
137
1.0158
5
1.0114
3
1.0343
101
1.0453
196
1.0297
144
1.0094
3
1.0406
120
1.0326
120
1.0097
3
  1.0368
3
1.0232
3
 
CCSD 1.0703
3
1.0294
5
1.0243
3
1.0138
3
1.0370
167
1.0263
19
1.0223
26
1.0245
25
1.0269
6
1.0174
62
1.0116
3
1.0121
3
1.0441
77
1.0461
108
1.0294
128
1.0630
44
1.0485
81
1.0365
93
1.1460
17
       
CCSD=FULL 1.0702
3
1.0241
3
1.0241
3
1.0137
3
1.0429
105
1.0129
3
1.0135
7
1.0128
3
1.0146
3
1.0159
62
1.0100
3
1.0110
3
1.0410
82
1.0515
82
1.0312
100
1.0385
41
1.0470
83
1.0097
100
1.0822
16
       
CCSD(T) 1.0703
3
1.0971
13
1.0263
3
1.0150
3
1.0450
166
1.0265
45
1.0677
23
1.0249
43
1.0254
8
1.0233
5
1.0199
4
1.1533
7
1.0397
94
1.0492
126
1.0356
128
1.0636
53
1.0432
122
1.0507
100
1.0253
38
  1.0388
7
1.0253
7
 
CCSD(T)=FULL 1.0703
3
1.0259
3
1.0259
3
1.0149
3
1.0462
121
1.0144
3
1.0135
3
1.0144
3
1.0164
3
1.0143
3
1.0120
3
1.0130
3
1.0405
90
1.0489
101
1.0355
95
1.0681
47
1.0446
98
1.0382
86
1.0898
33
  1.0381
7
1.0241
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

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 1.0373
283
1.0394
281
1.0333
283
1.0390
285
1.0363
287
1.0333
283
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 1.0299
162
1.0293
153
1.0194
10
1.0226
10
1.0197
10
1.0198
10
B3LYP 1.0580
282
1.0588
280
1.0529
281
1.0539
279
1.0555
285
1.0534
281
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 1.0383
18
1.0379
18
1.0237
18
1.0251
18
1.0323
18
1.0323
18
Moller Plesset perturbation MP2 1.0610
281
1.0584
278
1.0557
283
1.0557
285
1.0594
287
1.0569
283
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.