National Institute of Standards and Technology
Computational Chemistry Comparison and Benchmark DataBase
Release 18October 2016
NIST Standard Reference Database 101
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III.G.1.a.

Comparison of levels of theory for H-P


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 1.3223
29
PM3 1.2732
29
PM6 1.4562
41
composite G2 1.3999
39
G3 1.3999
39
G3B3 1.4237
39
G3MP2 1.4029
3
G4 1.4224
41
CBS-Q 1.3999
39

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) 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
hartree fock HF 1.3871
35
1.4187
39
1.3990
39
1.4232
39
1.4002
41
1.4021
39
1.3986
26
1.4030
39
1.4045
36
1.4037
39
1.4079
14
1.4103
41
1.4162
39
1.4062
39
1.4027
34
1.4156
39
1.4049
36
1.4023
34
1.4029
21
1.4045
11
1.4176
3
1.4056
3
ROHF 1.3872
3
1.4137
6
1.3945
6
1.3984
3
1.4015
7
1.3977
6
1.3978
6
1.3985
6
1.3895
3
1.3876
3
    1.4113
6
1.4019
6
1.3883
3
1.4007
3
1.3907
3
1.3883
3
  1.4054
2
   
density functional LSDA 1.4254
39
1.4470
36
1.4337
36
1.4623
39
1.4358
39
1.4351
36
1.4345
36
1.4354
39
1.4344
36
1.4329
36
  1.4356
13
1.4463
36
1.4323
36
1.4261
12
1.4443
36
1.4299
26
1.4256
12
1.4322
11
1.4316
11
   
SVWN   1.4603
41
    1.4358
37
1.4337
13
1.4371
41
1.4332
13
1.4332
13
1.4320
13
  1.4416
29
1.4453
13
1.4309
13
  1.4429
13
1.4303
13
  1.4322
11
1.4316
11
   
BLYP 1.4337
35
1.4566
39
1.4335
39
1.4630
39
1.4371
41
1.4358
39
1.4348
39
1.4350
39
1.4334
36
1.4325
36
  1.4342
13
1.4478
39
1.4313
39
  1.4438
15
1.4168
5
  1.4315
11
1.4303
11
   
B1B95 1.4150
36
1.4231
36
1.4161
36
1.4405
36
1.4172
36
1.4177
36
1.4173
36
1.4182
36
1.4182
36
1.4169
36
  1.4183
13
1.4298
36
1.4166
36
1.4123
13
1.4279
36
1.4142
31
1.4116
13
1.4164
11
1.4158
11
   
B3LYP 1.4203
36
1.4424
39
1.4208
39
1.4484
39
1.4235
39
1.4232
39
1.4225
39
1.4226
39
1.4200
29
1.4214
39
1.4221
10
1.4274
41
1.4355
39
1.4207
39
1.4170
34
1.4332
39
1.4192
36
1.4165
34
1.4176
21
1.4194
11
1.4340
3
1.4187
3
B3LYPultrafine   1.4229
5
    1.4227
36
1.4092
5
1.4223
10
1.4086
5
      1.4220
12
1.4331
13
1.4218
25
  1.4307
13
1.4211
41
  1.4203
11
1.4195
11
   
B3PW91 1.4195
29
1.4425
39
1.4211
39
1.4466
39
1.4221
39
1.4223
39
1.4218
39
1.4232
39
1.4207
29
1.4214
39
  1.4238
13
1.4343
39
1.4219
39
  1.4323
15
1.4165
11
  1.4216
11
1.4210
11
   
mPW1PW91 1.4167
30
1.4392
39
1.4156
29
1.4419
36
1.4192
39
1.4196
39
1.4190
39
1.4207
39
1.4202
36
1.4184
36
  1.4214
13
1.4317
39
1.4199
39
  1.4313
23
1.4170
13
  1.4194
11
1.4189
11
   
M06-2X 1.4049
13
1.4254
13
1.4181
41
1.4326
13
1.4161
41
1.4127
13
1.4122
13
1.4108
13
1.4119
13
1.4126
18
  1.4144
13
1.4241
13
1.4115
18
  1.4230
13
1.4111
18
  1.4125
11
1.4121
11
   
PBEPBE 1.4325
29
1.4559
36
1.4312
26
1.4567
26
1.4354
36
1.4351
36
1.4343
36
1.4358
36
1.4350
36
1.4336
36
1.4377
8
1.4363
13
1.4468
36
1.4334
36
1.4274
13
1.4440
14
1.4349
24
1.4267
13
1.4343
11
1.4334
11
   
PBEPBEultrafine   1.4360
5
    1.4377
25
1.4213
5
1.4213
5
1.4219
5
      1.4355
12
1.4459
13
1.4323
13
  1.4434
13
1.4315
13
  1.4343
11
1.4335
11
   
PBE1PBE 1.4155
13
1.4176
13
1.4176
13
1.4408
13
1.4225
41
1.4182
13
1.4185
13
1.4200
13
1.4205
13
1.4191
13
  1.4235
13
1.4315
13
1.4197
13
  1.4301
13
1.4191
13
  1.4216
11
1.4210
11
   
HSEh1PBE 1.4161
13
1.4430
41
1.4178
13
1.4414
13
1.4229
41
1.4194
13
1.4230
41
1.4200
13
1.4205
13
1.4193
13
  1.4236
13
1.4319
13
1.4237
41
  1.4304
13
1.4190
13
  1.4215
11
1.4209
11
   
TPSSh 1.4027
3
1.4335
12
1.4136
12
1.4365
12
1.4217
41
1.4145
12
1.4215
41
1.4166
12
1.4002
3
1.4215
39
  1.4196
12
1.4281
12
1.4226
41
1.3966
3
1.4263
12
1.4151
12
1.3965
3
1.4187
11
1.4181
11
   
wB97X-D 1.4002
3
1.4065
3
1.4205
40
1.4094
3
1.4213
40
1.3965
3
1.4210
40
1.3975
3
1.4218
40
1.3976
3
  1.4249
40
1.4219
40
1.4210
40
1.3961
3
1.4091
3
1.4204
40
1.3961
3
       
B97D3   1.4501
37
    1.4347
37
      1.4333
37
              1.4306
37
         
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) 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
Moller Plesset perturbation MP2 1.4078
29
1.4362
39
1.4099
39
1.4433
39
1.4184
42
1.4049
39
1.4046
39
1.4181
42
1.4076
36
1.4095
39
  1.4149
41
1.4233
39
1.4106
39
1.4074
22
1.4249
39
1.4106
37
1.4048
18
1.4087
24
1.4102
11
1.4228
3
1.4090
3
MP2=FULL 1.4073
29
1.4364
39
1.4071
26
1.4389
26
1.4136
39
1.4040
39
1.4034
39
1.4136
39
1.4053
29
1.4054
31
  1.4099
13
1.4218
39
1.4045
31
1.4020
22
1.4252
21
1.4032
32
1.3973
17
1.4045
24
1.4047
11
1.4221
3
1.4065
3
ROMP2 1.4016
3
1.4058
3
1.3927
3
1.4129
3
1.3953
3
1.3874
3
1.3876
3
1.3952
3
  1.3945
3
    1.4058
3
1.3947
3
1.3925
3
1.4083
3
1.3954
3
1.3931
3
       
MP3         1.4169
36
  1.4109
41
        1.4095
12
1.4209
12
1.4085
12
        1.4114
11
1.4119
11
   
MP3=FULL   1.4124
3
1.3948
3
1.4191
3
1.4219
41
1.3859
3
1.4086
37
1.3976
3
1.3903
3
1.3918
3
  1.4092
12
1.4193
12
1.4044
12
  1.4070
3
1.3907
3
  1.4070
11
1.4064
11
   
MP4 1.4199
1
1.4441
32
    1.4204
38
    1.4294
14
1.4090
26
    1.4141
13
1.4256
13
1.4176
38
  1.4278
13
1.4135
13
  1.4153
11
1.4157
11
   
MP4=FULL   1.4423
13
    1.4186
13
      1.4093
13
      1.4238
13
1.4089
13
  1.4259
13
1.4084
13
  1.4110
11
1.4102
11
   
B2PLYP 1.4037
6
1.4242
6
1.4041
6
1.4303
6
1.4184
34
1.4050
6
1.4084
9
1.4074
6
1.4065
6
1.4105
11
  1.4103
6
1.4189
6
1.4198
34
  1.4196
6
1.4107
11
  1.4148
4
1.4152
4
   
B2PLYP=FULL 1.4037
6
1.4285
9
1.4041
6
1.4303
6
1.4105
9
1.4047
6
1.4078
9
1.4074
6
1.4063
6
1.4060
6
  1.4102
6
1.4185
6
1.4054
6
  1.4191
6
1.4053
6
  1.4136
4
1.4133
4
   
B2PLYP=FULLultrafine 1.3994
3
1.4074
3
1.3935
3
1.4133
3
1.4178
16
1.3936
3
1.3937
3
1.3960
3
1.3959
3
1.3957
3
  1.3997
3
1.4077
3
1.3948
3
  1.4087
3
1.3950
3
         
Configuration interaction CID   1.4351
26
1.4093
26
1.4421
26
1.4157
39
    1.4158
39
          1.4160
6
        1.4073
11
1.4074
11
   
CISD   1.4397
32
1.4098
26
1.4430
26
1.4161
39
    1.4128
26
          1.4167
6
        1.4077
11
1.4077
11
   
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) 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
Quadratic configuration interaction QCISD 1.4224
1
1.4480
39
1.4241
32
1.4482
26
1.4218
39
1.4075
32
1.4075
38
1.4224
39
1.4120
35
1.4108
31
  1.4133
13
1.4278
39
1.4137
34
  1.4264
13
1.4134
18
  1.4146
12
1.4143
11
   
QCISD(T)         1.4234
39
1.4164
6
1.4161
6
1.4265
19
      1.4154
13
1.4284
32
1.4155
32
  1.4285
26
1.4159
23
  1.4162
11
1.4166
11
   
QCISD(T)=FULL         1.4100
5
  1.3972
5
          1.4146
5
1.4009
5
1.3896
3
1.4181
5
1.4011
5
  1.4114
3
1.4107
3
   
Coupled Cluster CCD 1.4219
1
1.4438
32
1.4135
26
1.4482
26
1.4210
39
1.4065
32
1.4059
32
1.4213
39
1.4078
26
1.4091
26
  1.4122
13
1.4270
39
1.4127
32
  1.4254
26
1.4129
23
  1.4129
11
1.4133
11
1.4272
3
1.4130
3
CCSD         1.4215
39
1.4152
6
1.4149
6
1.4921
14
  1.4092
11
  1.4131
13
1.4272
19
1.4142
21
1.4082
11
1.4262
13
1.4132
18
1.4057
9
1.4137
11
1.4139
11
   
CCSD=FULL         1.4195
18
        1.4125
8
  1.4128
13
1.4227
13
1.4085
18
1.4028
11
1.4244
13
1.4078
18
1.4008
7
1.4093
11
1.4084
11
   
CCSD(T)         1.4226
28
1.4123
19
1.4161
6
1.4264
19
      1.4153
13
1.4283
32
1.4150
31
1.4075
16
1.4285
26
1.4159
23
1.4067
15
1.4110
16
1.4165
11
1.4301
3
1.4157
3
CCSD(T)=FULL         1.4191
20
            1.4150
13
1.4258
16
1.4105
16
1.4021
16
1.4269
13
1.4092
13
1.4109
9
1.4125
12
1.4110
11
1.4294
3
1.4134
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) 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

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 1.4346
39
1.4193
39
1.4348
39
1.4199
39
1.4209
39
1.4182
39
density functional B1B95 1.4677
11
1.4464
14
       
B3LYP 1.4606
39
1.4398
39
1.4607
39
1.4394
39
1.4470
39
1.4407
39
wB97X-D 1.4221
3
1.4135
3
1.4256
3
1.4134
3
1.4106
3
1.4062
3
Moller Plesset perturbation MP2 1.4562
39
1.4341
39
1.4549
39
1.4328
39
1.4384
39
1.4349
39
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.