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III.G.1.a.

Comparison of levels of theory for H-Be


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 1.4094
7
PM3 1.3349
13
PM6 1.3926
11
composite G2 1.4015
8
G3 1.3880
10
G3B3 1.3968
12
G4 1.4149
9
CBS-Q 1.4056
12

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-pCVDZ cc-pCVTZ
hartree fock HF 1.3680
12
1.4189
12
1.4189
12
1.4152
12
1.4025
14
1.4017
12
1.3953
12
1.4060
12
1.4030
12
1.4017
12
1.3340
6
1.3962
12
1.4102
12
1.4047
9
1.3995
12
1.4246
9
1.3994
12
1.3977
12
1.3399
5
1.3336
5
ROHF 1.3003
2
1.4735
6
1.4735
6
1.4668
6
1.4449
6
1.4457
6
1.4449
6
1.4601
6
1.4566
6
1.3411
2
1.3391
2
1.4691
5
1.4609
6
1.4588
6
1.4789
5
1.4595
6
1.4572
6
1.4790
5
1.3508
1
1.3422
1
density functional LSDA 1.3827
12
1.4147
12
1.4147
12
1.4130
12
1.4056
12
1.4050
12
1.3992
12
1.4022
12
1.4004
12
1.4019
12
  1.4211
7
1.4134
12
1.3979
12
  1.4042
12
1.4197
7
  1.3704
1
1.3568
1
SVWN   1.4147
12
    1.4056
12
1.4211
7
1.3993
12
1.4240
7
1.4222
7
1.4208
7
    1.4327
7
1.4210
7
  1.4277
7
1.4197
7
  1.3704
1
1.3568
1
BLYP 1.3878
11
1.4034
12
1.4157
10
1.4151
10
1.3956
12
1.3943
12
1.3998
10
1.4039
10
1.3898
12
1.3915
12
  1.4102
7
1.4007
12
1.3985
7
  1.3421
6
    1.3591
1
1.3468
1
B1B95 1.3751
12
1.4000
12
1.4000
12
1.3987
12
1.3928
12
1.3921
12
1.3862
12
1.3901
12
1.3879
12
1.3894
12
  1.4082
7
1.3988
12
1.3860
12
1.3774
2
1.3895
12
1.3986
9
1.3654
2
1.3554
1
1.3441
1
B3LYP 1.3738
12
1.3969
12
1.3969
12
1.4084
10
1.3895
12
1.3883
12
1.3829
12
1.3985
10
1.4017
9
1.3858
12
1.3313
6
1.3831
12
1.4073
10
1.3991
9
1.3794
12
1.4027
9
1.3789
12
1.3776
12
1.3369
5
1.3285
5
B3LYPultrafine   1.3595
1
    1.3895
12
1.3478
1
1.3478
1
1.3463
1
      1.3461
1
1.4152
7
1.4056
7
  1.4102
7
1.3983
9
  1.3533
1
1.3411
1
B3PW91 1.3985
9
1.4032
12
1.4150
10
1.4145
10
1.3951
12
1.3945
12
1.3988
10
1.4055
10
1.4088
9
1.3922
12
  1.4115
7
1.4131
7
1.4005
7
  1.3434
6
    1.3590
1
1.3478
1
mPW1PW91 1.3890
10
1.4022
12
1.4196
9
1.4009
12
1.3942
12
1.3936
12
1.3875
12
1.3934
12
1.3908
12
1.3912
12
  1.4112
7
1.4188
9
1.4062
9
  1.3941
10
1.4114
7
  1.3583
1
1.3478
1
M06-2X 1.4002
7
1.4103
7
1.4103
7
1.4124
7
1.3914
12
1.4065
7
1.4068
7
1.4107
7
1.4063
7
1.4054
7
  1.4028
7
1.4141
7
1.4048
7
  1.4092
7
1.4030
7
  1.3544
1
1.3430
1
PBEPBE 1.4085
9
1.4120
12
1.4298
9
1.4298
9
1.4035
12
1.4027
12
1.3967
12
1.4014
12
1.3990
12
1.3999
12
1.3445
6
1.4191
7
1.4099
12
1.3964
12
1.3897
2
1.4240
7
1.4178
7
1.3771
2
1.3683
1
1.3560
1
PBEPBEultrafine   1.3742
1
    1.3978
10
1.3624
1
1.3623
1
1.3613
1
      1.3610
1
1.4294
7
1.4193
7
  1.4240
7
1.4178
7
  1.3683
1
1.3560
1
PBE1PBE 1.4043
7
1.4204
7
1.4204
7
1.4184
7
1.3964
12
1.4125
7
1.4126
7
1.4179
7
1.4151
7
1.4128
7
  1.4130
7
1.4235
7
1.4147
7
  1.4186
7
1.4134
7
  1.3608
1
1.3492
1
HSEh1PBE 1.4044
7
1.4201
7
1.4201
7
1.4182
7
1.3963
12
1.4122
7
1.4125
7
1.4175
7
1.4147
7
1.4125
7
  1.4126
7
1.4232
7
1.4142
7
  1.4182
7
1.4128
7
  1.3603
1
1.3486
1
TPSSh   1.3512
3
1.3512
3
1.3463
3
1.3697
5
1.3415
3
1.3589
5
1.3419
3
      1.3549
1
1.3472
3
1.3593
5
  1.3430
3
1.3378
3
  1.3621
1
1.3509
1
Moller Plesset perturbation MP2 1.4024
9
1.4222
12
1.4222
12
1.4193
12
1.3987
12
1.3924
12
1.3868
12
1.4051
12
1.3977
12
1.4283
8
  1.3894
12
1.4058
12
1.4185
9
1.4066
10
1.4146
10
1.3943
12
1.4048
10
1.3382
5
1.3312
5
MP2=FULL 1.4024
9
1.4219
12
1.4453
9
1.4426
9
1.3981
12
1.3916
12
1.3859
12
1.4043
12
1.4172
9
1.4132
9
  1.4198
7
1.4263
9
1.4024
10
1.4006
10
1.3992
12
1.4145
7
1.4055
9
1.3372
5
1.3282
5
ROMP2 1.4565
5
1.4961
5
1.4961
5
1.4893
5
1.4607
5
1.4560
5
1.4563
5
1.4788
5
1.4715
5
1.4638
5
  1.4602
5
1.4760
5
1.4730
5
  1.4769
5
    1.3496
1
1.3392
1
MP3         1.3993
12
  1.4120
9
        1.3401
1
1.3532
1
1.3446
1
        1.3513
1
1.3430
1
MP3=FULL         1.3672
5
  1.3462
5
        1.3391
1
1.3525
1
1.3335
1
        1.3502
1
1.3391
1
MP4   1.4275
12
    1.4135
10
    1.3483
4
1.4191
9
    1.4200
7
1.4340
7
1.3995
12
  1.4352
7
1.4302
7
  1.3533
1
1.3448
1
MP4=FULL   1.4536
7
    1.4222
7
      1.4268
7
      1.4332
7
1.4231
7
  1.4329
7
1.4133
7
  1.3522
1
1.3415
1
B2PLYP 1.3153
1
1.3597
1
1.3597
1
1.3569
1
1.3615
6
1.3444
1
1.3443
1
1.3464
1
1.3410
1
1.3417
1
  1.3426
1
1.3520
1
1.3712
3
  1.3490
1
1.3398
1
  1.3507
1
1.3396
1
B2PLYP=FULL 1.3153
1
1.3596
1
1.3596
1
1.3568
1
1.3478
1
1.3441
1
1.3441
1
1.3462
1
1.3404
1
1.3403
1
  1.3424
1
1.3518
1
1.3381
1
  1.3478
1
1.3327
1
  1.3503
1
1.3386
1
Configuration interaction CID   1.4511
9
1.4511
9
1.4485
9
1.4142
10
    1.4243
10
                    1.3540
1
1.3459
1
CISD   1.4285
12
1.4505
9
1.4481
9
1.4139
10
    1.4330
9
                    1.3560
1
1.3478
1
Quadratic configuration interaction QCISD   1.4289
12
1.4501
9
1.4414
10
1.4012
12
1.3926
12
1.3986
10
1.4260
10
1.3996
12
1.4161
9
  1.4216
7
1.4078
12
1.4013
12
  1.4362
7
1.3925
5
  1.3560
1
1.3478
1
QCISD(T)         1.4013
12
1.3329
6
1.3336
6
1.3482
6
      1.4212
7
1.4286
9
1.4220
9
  1.4241
9
1.4180
9
  1.3567
1
1.3478
1
QCISD(T)=FULL         1.3572
1
  1.3437
1
          1.3579
1
1.3386
1
1.3402
1
1.3562
1
1.3211
1
1.3400
1
1.3556
1
 
QCISD(TQ)=FULL         1.3575
1
  1.3439
1
          1.3582
1
  1.3405
1
1.3565
1
1.3213
1
1.3403
1
   
Coupled Cluster CCD   1.4288
12
1.4513
9
1.4488
9
1.4142
10
1.3919
12
1.3979
10
1.4245
10
1.4196
9
1.4153
9
  1.4209
7
1.4065
12
1.4210
9
  1.4237
9
1.4170
9
  1.3394
5
1.3348
5
CCSD         1.3926
11
1.3324
6
1.3332
6
1.3476
6
      1.4216
7
1.4353
7
1.4332
7
1.3893
5
1.4361
7
1.4320
7
1.4290
7
1.3560
1
1.3478
1
CCSD=FULL         1.4212
7
            1.4206
7
1.4343
7
1.4250
7
1.4226
7
1.4337
7
1.4147
7
1.4220
7
1.3548
1
1.3445
1
CCSD(T)   1.3806
1
    1.4012
12
1.3328
6
1.3336
6
1.3482
6
1.3471
1
  1.3501
2
1.4212
7
1.4078
12
1.4013
12
1.4173
9
1.4046
12
1.3981
12
1.4152
9
1.3408
5
1.3356
5
CCSD(T)=FULL         1.4192
9
            1.4202
7
1.4339
7
1.4245
7
1.4109
9
1.4332
7
1.4143
7
1.3777
7
1.3397
5
1.3326
5

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 1.4312
12
1.4101
12
1.4103
12
1.4089
12
1.4168
12
1.4056
12
density functional B1B95 1.3561
6
1.3418
3
       
B3LYP 1.4237
10
1.4095
10
1.4101
10
1.4084
10
1.4096
10
1.4007
10
Moller Plesset perturbation MP2 1.4376
12
1.4127
12
1.4159
12
1.4078
12
1.4215
12
1.4083
12
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.