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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 1.3223
38
PM3 1.2785
36
PM6 1.4603
49
composite G2 1.4017
33
G3 1.4017
33
G3B3 1.4281
42
G3MP2 1.3873
10
G4 1.4256
49
CBS-Q 1.4016
33

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 aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
hartree fock HF 1.3926
44
1.4266
47
1.4031
47
1.4305
47
1.4040
49
1.4061
47
1.4050
37
1.4072
47
1.4090
45
1.4074
47
1.4103
24
1.4141
49
1.4205
47
1.4099
47
1.4069
42
1.4199
47
1.4091
45
1.4066
42
1.4017
24
1.3960
11
1.4176
3
1.4056
3
1.3996
6
1.4276
14
1.4097
50
ROHF 1.3872
3
1.4445
10
1.4130
10
1.4516
8
1.4159
11
1.4159
10
1.4153
10
1.4176
10
1.4218
8
1.3876
3
1.4166
8
1.4264
8
1.4315
10
1.4197
10
1.4182
8
1.4337
8
1.4211
8
1.4180
8
1.3934
3
        1.4337
8
1.4211
8
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
1.4463
37
1.4324
37
1.4261
12
1.4443
37
1.4301
30
1.4256
12
1.4252
18
1.4224
11
    1.4241
6
   
BLYP 1.4379
44
1.4620
47
1.4371
47
1.4682
47
1.4409
49
1.4395
47
1.4388
47
1.4390
47
1.4379
45
1.4367
45
1.4364
14
1.4371
32
1.4519
47
1.4351
47
  1.4466
31
1.4297
24
  1.4229
18
1.4192
11
    1.4228
6
1.4562
14
1.4402
14
B1B95 1.4184
45
1.4247
14
1.4198
45
1.4462
45
1.4210
45
1.4213
45
1.4211
45
1.4220
45
1.4219
45
1.4204
45
1.4215
13
1.4216
32
1.4338
45
1.4204
45
1.4120
13
1.4321
45
1.4189
40
1.4114
13
1.4093
18
1.4066
11
    1.4092
6
1.4386
14
1.4252
14
B3LYP 1.4243
45
1.4479
47
1.4244
47
1.4536
47
1.4271
47
1.4268
47
1.4262
47
1.4265
47
1.4256
38
1.4249
47
1.4251
21
1.4308
49
1.4395
47
1.4242
47
1.4212
42
1.4373
47
1.4233
45
1.4207
42
1.4161
24
1.4095
11
1.4340
3
1.4187
3
1.4127
6
1.4443
14
1.4295
14
B3LYPultrafine   1.4409
24
    1.4270
45
1.4219
24
1.4243
29
1.4218
24
  1.4304
14
1.4256
14
1.4260
31
1.4362
32
1.4225
41
  1.4346
32
1.4244
49
  1.4127
18
1.4095
11
    1.4127
6
1.4443
14
1.4295
14
B3PW91 1.4238
38
1.4478
47
1.4246
47
1.4516
47
1.4256
47
1.4258
47
1.4254
47
1.4269
47
1.4260
38
1.4248
47
1.4263
14
1.4268
32
1.4382
47
1.4253
47
  1.4348
31
1.4214
27
  1.4143
18
1.4115
11
    1.4142
6
1.4431
14
1.4303
14
mPW1PW91 1.4208
39
1.4446
47
1.4208
38
1.4480
45
1.4227
47
1.4230
47
1.4226
47
1.4244
47
1.4242
45
1.4222
45
1.4242
14
1.4246
32
1.4355
47
1.4233
47
  1.4327
39
1.4200
32
  1.4124
18
1.4097
11
    1.4123
6
1.4406
14
1.4282
14
M06-2X 1.4089
32
1.4315
32
1.4156
50
1.4382
32
1.4195
49
1.4161
32
1.4160
32
1.4148
32
1.4159
32
1.4152
34
1.4148
49
1.4186
32
1.4281
32
1.4144
34
  1.4274
32
1.4142
34
  1.4063
18
1.4039
11
    1.4067
6
1.4368
14
1.4227
14
PBEPBE 1.4367
38
1.4619
45
1.4368
38
1.4650
38
1.4395
45
1.4391
45
1.4386
45
1.4401
45
1.4392
45
1.4375
45
1.4377
24
1.4387
32
1.4511
45
1.4374
45
1.4274
13
1.4466
33
1.4353
40
1.4267
13
1.4263
18
1.4230
11
    1.4257
6
1.4553
14
1.4422
14
PBEPBEultrafine   1.4534
24
    1.4375
41
1.4338
24
1.4339
24
1.4348
24
  1.4426
14
1.4383
14
1.4385
31
1.4479
32
1.4345
32
  1.4464
32
1.4340
32
  1.4264
18
1.4230
11
    1.4257
6
1.4553
14
1.4422
14
PBE1PBE 1.4180
32
1.4286
14
1.4202
32
1.4450
32
1.4256
49
1.4210
32
1.4217
32
1.4231
32
1.4235
32
1.4216
32
1.4263
14
1.4266
32
1.4344
32
1.4225
32
  1.4336
32
1.4222
32
  1.4146
18
1.4119
11
    1.4143
6
1.4425
14
1.4303
14
HSEh1PBE 1.4186
32
1.4480
49
1.4204
32
1.4456
32
1.4260
49
1.4221
32
1.4262
49
1.4231
32
1.4236
32
1.4217
32
1.4262
14
1.4267
32
1.4348
32
1.4267
49
  1.4340
32
1.4221
32
  1.4144
18
1.4116
11
    1.4142
6
1.4429
14
1.4303
14
TPSSh 1.4190
22
1.4392
31
1.4168
31
1.4419
31
1.4245
49
1.4179
31
1.4244
49
1.4205
31
1.4200
22
1.4244
47
1.4239
14
1.4236
31
1.4316
31
1.4254
49
1.4154
21
1.4307
31
1.4189
31
1.4153
21
1.4113
18
1.4084
11
    1.4115
6
1.4403
14
1.4278
14
wB97X-D 1.4150
22
1.4356
22
1.4234
48
1.4384
22
1.4241
48
1.4164
22
1.4240
48
1.4173
22
1.4247
48
1.4160
22
1.4215
14
1.4278
48
1.4279
48
1.4238
48
1.4140
21
1.4289
22
1.4233
48
1.4139
21
1.3986
7
1.3954
4
    1.4099
6
1.4386
14
1.4256
14
B97D3 1.4338
19
1.4568
45
1.4294
19
1.4566
19
1.4376
45
1.4305
19
1.4349
45
1.4317
19
1.4365
45
1.4286
19
1.4182
50
1.4397
45
1.4437
19
1.4343
45
1.4257
18
1.4428
19
1.4335
45
1.4255
18
1.4119
3
      1.4192
6
1.4500
14
1.4313
49
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 aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Moller Plesset perturbation MP2 1.4130
38
1.4425
47
1.4136
47
1.4493
47
1.4212
50
1.4082
47
1.4080
47
1.4212
50
1.4115
45
1.4127
47
1.4157
14
1.4179
49
1.4270
47
1.4140
47
1.4105
35
1.4286
47
1.4142
45
1.4096
31
1.4074
27
1.4014
11
1.4228
3
1.4090
3
1.4043
6
1.4347
14
1.4194
14
MP2=FULL 1.4129
38
1.4427
47
1.4129
38
1.4485
38
1.4174
47
1.4073
47
1.4068
47
1.4177
47
1.4103
38
1.4099
40
1.4141
14
1.4130
32
1.4254
47
1.4091
40
1.4052
35
1.4258
36
1.4075
40
1.4029
31
1.4032
27
1.3960
11
1.4221
3
1.4065
3
1.4016
6
1.4329
14
1.4145
14
ROMP2 1.4584
5
1.4514
5
1.4514
5
1.5117
5
1.4553
5
1.4431
5
1.4440
5
1.4585
5
1.4474
5
1.4467
5
1.4456
5
1.4529
5
1.4667
5
1.4502
5
1.3925
3
1.4689
5
    1.3928
7
1.3898
4
      1.4688
5
1.4506
5
MP3         1.4213
45
  1.4133
49
      1.4181
14
1.4138
31
1.4252
31
1.4126
31
        1.4048
18
1.4031
11
    1.4063
6
1.4394
11
1.4236
11
MP3=FULL   1.4423
22
1.4137
22
1.4488
22
1.4248
49
1.4041
22
1.4115
46
1.4183
22
1.4083
22
1.4086
22
1.4166
14
1.4135
31
1.4236
31
1.4085
31
  1.4261
22
1.4074
21
  1.4005
18
1.3976
11
    1.4103
3
1.4376
11
1.4187
11
MP4 1.4199
1
1.4521
41
    1.4246
47
    1.4294
14
1.4147
39
  1.4213
14
1.4170
32
1.4284
32
1.4207
46
  1.4311
32
1.4165
31
  1.4080
18
1.4062
11
    1.4092
6
1.4423
11
1.4269
11
MP4=FULL   1.4474
32
    1.4218
32
      1.4119
32
  1.4198
14
  1.4267
32
1.4118
31
  1.4293
32
1.4122
28
  1.4038
18
1.4009
11
    1.4068
6
1.4404
11
1.4219
11
B2PLYP 1.4141
25
1.4375
25
1.4134
25
1.4433
25
1.4222
42
1.4138
25
1.4140
25
1.4168
25
1.4155
25
1.4149
27
1.4203
14
1.4193
25
1.4287
25
1.4230
42
  1.4291
25
1.4153
27
  1.4030
11
1.4040
8
    1.4079
6
1.4389
14
1.4241
14
B2PLYP=FULL 1.4141
25
1.4377
25
1.4134
25
1.4434
25
1.4165
25
1.4135
25
1.4136
25
1.4169
25
1.4153
25
1.4142
25
1.4199
14
1.4191
25
1.4282
25
1.4140
25
  1.4286
25
1.4137
25
  1.4018
11
1.4023
8
    1.4072
6
1.4383
14
1.4228
14
B2PLYP=FULLultrafine 1.4149
22
1.4371
22
1.4133
22
1.4428
22
1.4219
49
1.4132
22
1.4133
22
1.4166
22
1.4151
22
1.4139
22
1.4199
14
1.4189
22
1.4337
49
1.4192
49
  1.4285
22
1.4184
49
  1.3950
7
1.3913
4
    1.4072
6
1.4383
14
1.4228
14
Configuration interaction CID   1.4460
38
1.4157
38
1.4526
38
1.4196
47
    1.4200
47
    1.4160
14
  1.4334
14
1.4190
16
        1.4012
18
1.4000
11
    1.4030
6
1.4375
11
1.4213
11
CISD   1.4482
40
1.4163
38
1.4539
38
1.4200
47
    1.4200
38
    1.4169
14
  1.4345
14
1.4198
16
        1.4016
18
1.4004
11
    1.4034
6
1.4385
11
1.4222
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 aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Quadratic configuration interaction QCISD 1.4224
1
1.4551
47
1.4263
40
1.4595
38
1.4258
47
1.4119
40
1.4114
46
1.4267
47
1.4159
43
1.4155
40
1.4210
14
1.4172
32
1.4316
47
1.4178
42
  1.4306
32
1.4157
34
  1.4077
19
1.4051
11
    1.4083
6
1.4426
11
1.4265
11
QCISD(T)         1.4291
44
1.4164
6
1.4161
6
1.4293
31
    1.4301
11
1.4208
29
1.4350
37
1.4216
37
  1.4369
35
1.4218
35
  1.4090
18
1.4071
11
    1.4103
6
1.4564
8
1.4393
8
QCISD(T)=FULL         1.4258
21
  1.4111
21
      1.4286
11
  1.4300
21
1.4147
21
1.3980
14
1.4330
21
1.4140
20
1.4143
15
1.3989
10
1.3987
7
    1.4079
6
1.4544
8
1.4335
8
QCISD(TQ)         1.4311
15
  1.4170
15
      1.4405
8
  1.4372
15
1.4236
15
1.4068
8
1.4450
12
1.4289
12
1.4256
1
          1.4569
8
1.4596
5
QCISD(TQ)=FULL         1.4359
12
  1.4201
12
      1.4391
8
  1.4403
12
1.4241
12
1.4015
8
1.4430
12
1.4228
12
1.4203
1
          1.4764
5
1.4255
1
Coupled Cluster CCD 1.4219
1
1.4519
40
1.4197
38
1.4583
38
1.4248
47
1.4107
40
1.4102
40
1.4254
47
1.4135
38
1.4143
38
1.4195
14
1.4159
32
1.4306
47
1.4169
40
  1.4316
38
1.4168
37
  1.4061
18
1.4043
11
1.4272
3
1.4130
3
1.4075
6
1.4411
11
1.4251
11
CCSD         1.4255
47
1.4177
16
1.4177
16
1.4688
24
1.4230
11
1.4131
27
1.4208
14
1.4170
32
1.4286
34
1.4155
36
1.4122
29
1.4305
32
1.4154
33
1.4041
20
1.4068
18
1.4048
11
    1.4081
6
1.4425
11
1.4264
11
CCSD=FULL         1.4220
34
        1.4133
24
1.4190
14
1.4166
32
1.4265
32
1.4109
34
1.4082
26
1.4287
32
1.4099
33
1.4105
19
1.4024
18
1.3994
11
    1.4053
6
1.4406
11
1.4212
11
CCSD(T)         1.4271
37
1.4141
31
1.4248
14
1.4292
31
1.4293
12
1.4292
12
1.4300
11
1.4207
29
1.4349
37
1.4215
36
1.4166
27
1.4368
34
1.4217
34
1.4166
26
1.4097
19
1.4070
11
1.4301
3
1.4157
3
1.4102
6
1.4564
8
1.4392
8
CCSD(T)=FULL         1.4270
35
          1.4216
14
1.4186
32
1.4284
32
1.4131
32
1.4095
30
1.4309
32
1.4123
31
1.4145
23
1.4055
19
1.4017
11
1.4294
3
1.4134
3
1.4078
6
1.4429
11
1.4236
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 aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ

average calculated bond lengths (Å)
Methods with effective core potentials (select basis sets)
CEP-31G CEP-31G* CEP-121G CEP-121G* LANL2DZ SDD cc-pVTZ-PP aug-cc-pVTZ-PP Def2TZVPP
hartree fock HF 1.4416
47
1.4236
47
1.4408
47
1.4242
47
1.4277
47
1.4255
47
    1.4007
50
ROHF                 1.4174
8
density functional LSDA                 1.4285
3
BLYP                 1.4367
14
B1B95 1.4677
11
1.4464
14
            1.4222
14
B3LYP 1.4655
47
1.4438
47
1.4652
47
1.4433
47
1.4519
47
1.4461
47
    1.4138
50
B3LYPultrafine                 1.4261
14
B3PW91                 1.4270
14
mPW1PW91                 1.4250
14
M06-2X                 1.4196
14
PBEPBE                 1.4247
50
PBEPBEultrafine                 1.4389
14
PBE1PBE                 1.4271
14
HSEh1PBE                 1.4271
14
TPSSh                 1.4246
14
wB97X-D 1.4508
22
1.4337
22
1.4518
22
1.4340
22
1.4390
22
1.4332
22
    1.4223
14
B97D3                 1.4320
14
Moller Plesset perturbation MP2 1.4619
47
1.4384
47
1.4598
47
1.4370
47
1.4438
47
1.4408
47
    1.4048
50
MP2=FULL                 1.4125
14
ROMP2                 1.4442
5
MP3                 1.4172
14
MP3=FULL                 1.4149
14
MP4                 1.4051
6
MP4=FULL                 1.4180
14
B2PLYP                 1.4205
14
B2PLYP=FULL                 1.4197
14
B2PLYP=FULLultrafine                 1.4198
14
Configuration interaction CID                 1.4152
14
CISD                 1.4160
14
Quadratic configuration interaction QCISD                 1.4200
14
QCISD(T)                 1.4286
11
QCISD(T)=FULL                 1.4264
11
QCISD(TQ)                 1.4289
11
QCISD(TQ)=FULL                 1.4366
8
Coupled Cluster CCD                 1.4187
14
CCSD                 1.4198
14
CCSD=FULL                 1.4174
14
CCSD(T)                 1.4287
11
CCSD(T)=FULL                 1.4197
14
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.