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Comparison of levels of theory for P-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 1.3237
30
PM3 1.2757
30
PM6 1.4562
42
composite G2 1.4001
40
G3 1.4001
40
G3B3 1.4262
40
G3MP2 1.3896
7
G4 1.4225
42
CBS-Q 1.4000
40

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 Def2TZVPP 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 1.3870
36
1.4190
40
1.3991
40
1.4234
40
1.4003
42
1.4023
40
1.3990
27
1.4031
40
1.4046
37
1.4038
40
1.4079
14
1.4104
42
1.3966
43
1.4163
40
1.4063
40
1.4027
34
1.4157
40
1.4050
37
1.4023
34
1.4029
21
1.3960
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
       
density functional LSDA 1.4252
40
1.4557
24
1.4338
37
1.4624
40
1.4359
40
1.4351
37
1.4346
37
1.4354
40
1.4344
37
1.4330
37
1.4278
3
1.4324
21
1.4285
3
1.4463
37
1.4324
37
1.4261
12
1.4443
37
1.4301
30
1.4256
12
1.4266
15
1.4224
11
   
BLYP 1.4335
36
1.4568
40
1.4335
40
1.4632
40
1.4371
42
1.4358
40
1.4349
40
1.4351
40
1.4335
37
1.4326
37
1.4278
3
1.4308
21
1.4284
3
1.4478
40
1.4314
40
  1.4396
20
1.4187
13
  1.4244
15
1.4192
11
   
B1B95 1.4148
37
  1.4162
37
1.4407
37
1.4173
37
1.4178
37
1.4174
37
1.4183
37
1.4182
37
1.4169
37
1.4136
3
1.4157
21
1.4144
3
1.4298
37
1.4167
37
1.4123
13
1.4279
37
1.4143
32
1.4116
13
1.4107
15
1.4066
11
   
B3LYP 1.4202
37
1.4426
40
1.4209
40
1.4486
40
1.4236
40
1.4232
40
1.4226
40
1.4227
40
1.4202
30
1.4215
40
1.4221
10
1.4274
42
1.4094
43
1.4355
40
1.4207
40
1.4170
34
1.4333
40
1.4193
37
1.4165
34
1.4176
21
1.4095
11
1.4340
3
1.4187
3
B3LYPultrafine   1.4257
13
    1.4229
37
1.4112
13
1.4180
18
1.4107
13
  1.4224
3
1.4177
3
1.4195
20
1.4184
3
1.4298
21
1.4190
30
  1.4280
21
1.4211
42
  1.4141
15
1.4095
11
   
B3PW91 1.4192
30
1.4427
40
1.4212
40
1.4467
40
1.4222
40
1.4224
40
1.4219
40
1.4233
40
1.4208
30
1.4215
40
1.4185
3
1.4211
21
1.4194
3
1.4344
40
1.4219
40
  1.4286
20
1.4134
16
  1.4157
15
1.4115
11
   
mPW1PW91 1.4164
31
1.4394
40
1.4158
30
1.4421
37
1.4193
40
1.4196
40
1.4191
40
1.4208
40
1.4203
37
1.4185
37
1.4164
3
1.4189
21
1.4174
3
1.4318
40
1.4199
40
  1.4285
28
1.4145
21
  1.4137
15
1.4097
11
   
M06-2X 1.4019
21
1.4228
21
1.4124
43
1.4295
21
1.4162
42
1.4104
21
1.4101
21
1.4086
21
1.4099
21
1.4100
23
1.4111
3
1.4124
21
1.4115
3
1.4216
21
1.4090
23
  1.4209
21
1.4088
23
  1.4074
15
1.4039
11
   
PBEPBE 1.4323
30
1.4561
37
1.4318
30
1.4578
30
1.4355
37
1.4352
37
1.4344
37
1.4359
37
1.4351
37
1.4337
37
1.4355
11
1.4329
21
1.4199
43
1.4468
37
1.4335
37
1.4274
13
1.4407
22
1.4318
29
1.4267
13
1.4277
15
1.4230
11
   
PBEPBEultrafine   1.4387
13
    1.4343
30
1.4231
13
1.4231
13
1.4238
13
  1.4337
3
1.4296
3
1.4323
20
1.4305
3
1.4420
21
1.4288
21
  1.4402
21
1.4283
21
  1.4278
15
1.4230
11
   
PBE1PBE 1.4114
21
  1.4147
21
1.4370
21
1.4225
42
1.4154
21
1.4160
21
1.4173
21
1.4179
21
1.4164
21
1.4184
3
1.4209
21
1.4194
3
1.4284
21
1.4170
21
  1.4275
21
1.4166
21
  1.4159
15
1.4119
11
   
HSEh1PBE 1.4120
21
1.4432
42
1.4149
21
1.4375
21
1.4230
42
1.4166
21
1.4230
42
1.4173
21
1.4179
21
1.4165
21
1.4183
3
1.4209
21
1.4194
3
1.4288
21
1.4237
42
  1.4278
21
1.4165
21
  1.4157
15
1.4116
11
   
TPSSh 1.4051
11
1.4298
20
1.4107
20
1.4327
20
1.4217
42
1.4117
20
1.4215
42
1.4139
20
1.4078
11
1.4215
40
1.4161
3
1.4172
20
1.4170
3
1.4250
20
1.4225
42
1.4025
10
1.4239
20
1.4128
20
1.4025
10
1.4126
15
1.4084
11
   
wB97X-D 1.4021
11
1.4182
11
1.4205
41
1.4210
11
1.4213
41
1.4043
11
1.4210
41
1.4051
11
1.4217
41
1.4046
11
1.4136
3
1.4248
41
1.4144
3
1.4221
41
1.4209
41
1.4016
10
1.4163
11
1.4204
41
1.4015
10
1.3951
4
1.3954
4
   
B97D3 1.4187
8
1.4503
38
1.4171
8
1.4387
8
1.4347
38
1.4181
8
1.4315
38
1.4189
8
1.4333
38
1.4167
8
1.4140
43
1.4216
8
1.4253
3
1.4300
8
1.4313
38
1.4122
7
1.4293
8
1.4306
38
1.4121
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) TZVP Def2TZVPP 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 1.4076
30
1.4364
40
1.4100
40
1.4435
40
1.4185
43
1.4051
40
1.4047
40
1.4181
43
1.4078
37
1.4096
40
1.4093
3
1.4150
42
1.4010
43
1.4234
40
1.4107
40
1.4077
25
1.4250
40
1.4107
38
1.4055
21
1.4087
24
1.4014
11
1.4228
3
1.4090
3
MP2=FULL 1.4071
30
1.4366
40
1.4077
30
1.4401
30
1.4138
40
1.4041
40
1.4035
40
1.4137
40
1.4055
30
1.4056
32
1.4075
3
1.4076
21
1.4062
3
1.4219
40
1.4047
32
1.4023
25
1.4220
26
1.4034
33
1.3982
20
1.4045
24
1.3960
11
1.4221
3
1.4065
3
ROMP2 1.4016
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
1.3892
4
1.3898
4
   
MP3         1.4170
37
  1.4109
42
      1.4120
3
1.4078
20
1.4112
3
1.4189
20
1.4068
20
        1.4060
15
1.4031
11
   
MP3=FULL   1.4241
11
1.4020
11
1.4309
11
1.4219
42
1.3934
11
1.4086
38
1.4055
11
1.3976
11
1.3984
11
1.4100
3
1.4075
20
1.4086
3
1.4173
20
1.4028
20
  1.4144
11
1.3973
11
  1.4017
15
1.3976
11
   
MP4 1.4199
1
1.4445
33
    1.4206
39
    1.4294
14
1.4097
30
  1.4146
3
1.4116
21
1.4139
3
1.4226
21
1.4177
39
  1.4252
21
1.4113
21
  1.4093
15
1.4062
11
   
MP4=FULL   1.4383
21
    1.4158
21
      1.4067
21
  1.4130
3
  1.4116
3
1.4209
21
1.4065
21
  1.4234
21
1.4056
20
  1.4051
15
1.4009
11
   
B2PLYP 1.4028
14
1.4237
14
1.4041
14
1.4296
14
1.4184
35
1.4048
14
1.4048
14
1.4070
14
1.4063
14
1.4072
16
1.4126
3
1.4099
14
1.4129
3
1.4187
14
1.4197
35
  1.4193
14
1.4074
16
  1.4037
8
1.4040
8
   
B2PLYP=FULL 1.4027
14
1.4233
14
1.4041
14
1.4297
14
1.4069
14
1.4045
14
1.4043
14
1.4071
14
1.4061
14
1.4056
14
1.4121
3
1.4098
14
1.4122
3
1.4183
14
1.4051
14
  1.4188
14
1.4050
14
  1.4025
8
1.4023
8
   
B2PLYP=FULLultrafine 1.4013
11
1.4190
11
1.4013
11
1.4249
11
1.4136
21
1.4014
11
1.4014
11
1.4039
11
1.4033
11
1.4027
11
1.4122
3
1.4069
11
1.4122
3
1.4153
11
1.4022
11
  1.4160
11
1.4021
11
  1.3914
4
1.3913
4
   
Configuration interaction CID   1.4366
30
1.4101
30
1.4435
30
1.4157
40
    1.4158
40
    1.4097
3
  1.4091
3
1.4254
3
1.4160
6
        1.4025
15
1.4000
11
   
CISD   1.4399
33
1.4106
30
1.4444
30
1.4161
40
    1.4137
30
    1.4104
3
  1.4097
3
1.4262
3
1.4167
6
        1.4029
15
1.4004
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 Def2TZVPP 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
1.4482
40
1.4241
33
1.4498
30
1.4219
40
1.4077
33
1.4077
39
1.4225
40
1.4121
36
1.4110
32
1.4142
3
1.4112
21
1.4133
3
1.4279
40
1.4138
35
  1.4243
21
1.4105
23
  1.4090
16
1.4051
11
   
QCISD(T)         1.4235
40
1.4164
6
1.4161
6
1.4223
24
    1.4161
3
1.4130
21
1.4148
3
1.4285
33
1.4157
33
  1.4294
30
1.4166
27
  1.4103
15
1.4071
11
   
QCISD(T)=FULL         1.4119
13
  1.3987
13
      1.4145
3
  1.4125
3
1.4166
13
1.4027
13
1.3958
10
1.4197
13
1.4025
13
1.3977
7
1.3992
7
1.3987
7
   
QCISD(TQ)         1.4110
7
  1.3988
7
      1.4163
3
  1.4150
3
1.4179
7
1.4061
7
1.4041
7
1.4209
7
1.4070
7
         
QCISD(TQ)=FULL         1.4110
7
  1.3977
7
      1.4147
3
  1.4127
3
1.4163
7
1.4022
7
1.3987
7
1.4191
7
1.4017
7
         
Coupled Cluster CCD 1.4219
1
1.4441
33
1.4143
30
1.4496
30
1.4211
40
1.4067
33
1.4061
33
1.4214
40
1.4086
30
1.4097
30
1.4131
3
1.4102
21
1.4124
3
1.4271
40
1.4129
33
  1.4262
30
1.4135
27
  1.4073
15
1.4043
11
1.4272
3
1.4130
3
CCSD         1.4216
40
1.4152
6
1.4149
6
1.4921
14
  1.4059
16
1.4140
3
1.4111
21
1.4132
3
1.4238
24
1.4114
26
1.4059
18
1.4242
21
1.4104
23
1.4043
16
1.4080
15
1.4048
11
   
CCSD=FULL         1.4162
23
        1.4065
13
1.4121
3
1.4107
21
1.4106
3
1.4203
21
1.4057
23
1.4004
18
1.4224
21
1.4047
22
1.3983
14
1.4037
15
1.3994
11
   
CCSD(T)         1.4201
33
1.4085
24
1.4160
7
1.4222
24
1.4163
4
1.4167
4
1.4161
3
1.4129
21
1.4152
3
1.4284
33
1.4150
31
1.4088
19
1.4293
30
1.4165
27
1.4083
18
1.4110
16
1.4070
11
1.4301
3
1.4157
3
CCSD(T)=FULL         1.4178
25
          1.4144
3
1.4126
21
1.4124
3
1.4222
21
1.4074
21
1.4034
19
1.4246
21
1.4065
20
1.4106
12
1.4069
16
1.4017
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 Def2TZVPP 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)
daug-cc-pVDZ daug-cc-pVTZ daug-cc-pVQZ Sadlej_pVTZ CEP-31G CEP-31G* CEP-121G CEP-121G* LANL2DZ SDD
hartree fock HF         1.4347
40
1.4194
40
1.4350
40
1.4200
40
1.4210
40
1.4184
40
density functional B1B95         1.4677
11
1.4464
14
       
B3LYP         1.4607
40
1.4399
40
1.4608
40
1.4395
40
1.4471
40
1.4409
40
wB97X-D         1.4332
11
1.4206
11
1.4361
11
1.4208
11
1.4216
11
1.4162
11
Moller Plesset perturbation MP2         1.4564
40
1.4342
40
1.4551
40
1.4329
40
1.4385
40
1.4351
40
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.