return to home page

III.G.1.a.

Comparison of levels of theory for H-S


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 1.3667
12
PM3 1.3221
40
PM6 1.2922
45
composite G2 1.3951
36
G3 1.3827
44
G3B3 1.4091
46
G4 1.4491
46
CBS-Q 1.4036
32
molecular mechanics DREIDING 1.3599
3

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(D+d)Z cc-pV(T+d)Z aug-cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ Sadlej_pVTZ
hartree fock HF 1.3533
44
1.3992
44
1.3751
44
1.4113
44
1.4006
111
1.3775
44
1.4241
44
1.4052
44
1.3846
44
1.3757
44
1.3267
28
1.3247
46
1.3687
44
1.3615
44
1.3799
21
1.3804
44
1.3690
44
1.3910
20
1.3351
6
1.3543
17
1.3747
9
1.3394
4
1.3286
5
1.3431
2
ROHF 1.3648
2
1.6307
7
1.6065
7
1.8355
5
1.6177
8
1.6195
7
1.9310
7
1.7752
7
1.7697
5
1.3419
2
  1.7325
3
1.4999
7
1.5057
7
1.5975
5
1.6667
5
1.6424
5
1.6319
5
  1.3301
1
    1.3315
1
 
density functional LSDA 1.3892
43
1.4057
44
1.3856
43
1.4155
44
1.3850
44
1.3834
44
1.3665
44
1.3843
44
1.3807
44
1.3823
44
  1.5022
8
1.3915
43
1.3774
44
1.3813
3
1.3741
42
1.3720
18
1.3813
3
1.3664
6
1.4119
7
1.4362
5
  1.3730
1
 
SVWN   1.3448
41
    1.4073
38
1.5173
8
1.3070
41
1.5067
8
1.5017
8
1.5224
8
    1.5190
8
1.4963
8
  1.4270
8
1.4150
8
  1.3694
2
1.4364
5
1.4362
5
  1.3730
1
 
BLYP 1.4014
44
1.4174
43
1.3978
35
1.4221
44
1.3933
42
1.3892
44
1.3840
44
1.3959
35
1.3855
44
1.3862
44
  1.5257
8
1.4010
44
1.3821
44
  1.3684
28
    1.3687
6
1.4330
5
1.4327
5
  1.3709
1
 
B1B95 1.3809
43
1.3878
43
1.3715
43
1.3997
43
1.3725
44
1.3728
43
1.3670
42
1.3719
43
1.3692
43
1.3685
43
  1.5027
8
1.3787
43
1.3655
43
1.3578
4
1.3567
42
1.3565
16
1.3576
4
1.3498
6
1.3855
9
1.3990
7
1.3574
2
1.3468
3
 
B3LYP 1.3861
44
1.4015
44
1.3761
44
1.4060
44
1.3971
46
1.3753
44
1.3719
44
1.3764
44
1.4161
16
1.3741
42
1.3429
28
1.3306
46
1.3841
44
1.3707
43
1.3805
20
1.3662
30
1.3540
30
1.3359
20
1.3565
6
1.3692
17
1.4016
7
1.3624
2
1.3507
3
1.3584
2
B3LYPultrafine         1.3775
43
  1.3492
8
        1.4812
3
1.5757
6
1.4509
16
  1.4314
6
1.3509
44
          1.3566
1
 
B3PW91 1.4144
19
1.3993
44
1.3739
44
1.4019
44
1.3734
44
1.3720
44
1.3742
35
1.3747
43
1.4112
16
1.3709
43
  1.5014
8
1.3808
44
1.3684
44
  1.3561
28
    1.3544
6
1.4263
5
1.4262
5
  1.3570
1
 
mPW1PW91 1.4104
19
1.3965
43
1.4040
19
1.3984
44
1.3703
44
1.3695
43
1.3657
44
1.3714
44
1.3701
44
1.3722
44
  1.4978
8
1.3778
44
1.3768
30
  1.3583
40
1.3581
12
  1.3517
6
1.4246
5
1.4245
5
  1.3540
1
 
M06-2X 1.4817
8
1.5335
8
1.5128
8
1.5412
8
1.3154
41
1.5134
8
1.4992
8
1.5032
8
1.5011
8
1.5099
8
  1.4985
8
1.5114
8
1.4935
8
  1.4065
8
1.3945
8
    1.4185
5
1.4184
5
  1.3491
1
 
PBEPBE 1.4286
19
1.4129
44
1.4340
19
1.4499
19
1.3873
43
1.3845
44
1.3654
44
1.3865
44
1.3827
44
1.3830
43
1.3535
28
1.5138
8
1.3932
43
1.3795
44
1.3731
4
1.3802
15
1.3640
26
1.3729
4
1.3665
6
1.3921
11
1.4150
7
1.3732
2
1.3642
3
1.3678
2
PBEPBEultrafine         1.4014
44
  1.3567
2
        1.4953
3
1.5806
6
1.5572
6
  1.4437
6
1.4319
6
          1.3721
1
 
PBE1PBE 1.5343
6
1.5693
6
1.5693
6
1.5954
6
1.3973
44
1.5670
6
1.5357
6
1.5537
6
1.5596
6
1.5603
6
  1.5473
6
1.5608
6
1.5419
6
  1.4304
6
1.4194
6
    1.4269
5
1.4268
5
  1.3557
1
 
HSEh1PBE 1.4921
8
1.5387
8
1.5157
8
1.5429
8
1.3161
40
1.5117
8
1.4912
8
1.5048
8
1.5074
8
1.5087
8
  1.5001
8
1.5121
8
1.4947
8
  1.4131
8
1.4017
8
  1.3555
2
1.4265
5
1.4264
5
  1.3559
1
 
TPSSh   1.6396
5
1.6179
5
1.6434
5
1.3756
48
1.6120
5
1.3700
48
1.6027
5
      1.4811
3
1.6105
5
1.3725
48
  1.4399
5
1.4288
5
    1.4752
3
1.4751
3
     
Moller Plesset perturbation MP2 1.4008
19
1.4058
44
1.3727
44
1.4114
44
1.3705
50
1.3608
44
1.3725
96
1.3832
41
1.3594
44
1.3763
35
  1.3192
46
1.3724
44
1.3588
46
1.4034
12
1.3591
30
1.3475
25
1.3439
11
1.3449
6
1.3605
17
1.3817
9
1.3483
4
1.3367
5
1.3579
2
MP2=FULL 1.4104
16
1.4206
30
1.4309
16
1.4689
16
1.3704
50
1.3685
35
1.4445
35
1.3806
44
1.4000
16
1.4243
16
  1.4881
8
1.3843
28
1.3721
26
1.3794
11
1.3578
21
1.3645
17
1.3120
10
1.3429
6
1.3568
17
1.3768
9
1.3476
4
1.3347
5
 
ROMP2 1.3739
3
1.6175
5
1.6052
5
1.6860
5
1.6010
5
1.5444
5
2.0620
5
1.5870
5
1.4960
5
1.5528
5
  1.5836
3
1.5117
5
1.4873
5
1.3525
2
1.3651
5
1.3551
2
1.3529
2
  1.4716
3
1.4724
3
  1.3441
1
 
MP3         1.3786
44
  1.3901
48
        1.4739
3
1.4835
3
1.4748
3
        1.3452
4
1.4719
3
1.4726
3
  1.3430
1
 
MP3=FULL         1.3776
48
  1.3634
47
        1.4728
3
1.4829
3
1.4711
3
          1.4672
3
1.4678
3
     
MP4   1.4416
22
    1.3994
26
    1.3518
9
1.3994
16
    1.5330
6
1.5498
6
1.3797
25
  1.4279
6
1.3525
3
  1.3489
6
      1.3479
1
 
MP4=FULL   1.6484
6
    1.6082
6
      1.5336
6
      1.5488
6
1.5280
6
  1.4253
6
1.4111
6
          1.3464
1
 
B2PLYP 1.4382
3
1.4869
3
1.4755
3
1.4927
3
1.2854
36
1.4739
3
1.4733
3
1.4745
3
1.4737
3
1.4740
3
  1.4771
3
1.4855
3
1.3480
39
  1.4847
3
1.4751
3
    1.4720
3
1.4721
3
     
B2PLYP=FULL 1.4382
3
1.4870
3
1.4754
3
1.4927
3
1.4774
3
1.4736
3
1.4730
3
1.4745
3
1.4734
3
1.4733
3
  1.4767
3
1.4853
3
1.4739
3
  1.4837
3
1.4740
3
    1.4706
3
1.4706
3
     
B2PLYP=FULLultrafine         1.3532
26
                                     
Configuration interaction CID   1.4607
16
1.4279
16
1.4653
16
1.3843
35
    1.3930
25
          1.3369
6
          1.4651
3
1.4653
3
  1.3375
1
 
CISD   1.4390
22
1.4279
16
1.4652
16
1.3853
35
    1.4202
16
          1.3375
6
          1.4652
3
1.4654
3
  1.3381
1
 
Quadratic configuration interaction QCISD   1.4161
39
1.4201
22
1.4706
16
1.4289
30
1.3906
22
1.3811
24
1.3905
30
1.3824
23
1.4151
16
  1.4892
8
1.3915
26
1.3810
24
  1.3679
12
1.3550
9
  1.3485
6
1.3720
12
1.4210
5
  1.3457
1
 
QCISD(T)         1.4012
26
1.3370
6
1.3376
6
1.3540
9
      1.4909
8
1.4000
22
1.3867
22
  1.3997
12
1.3861
12
  1.3521
2
1.3981
7
1.4232
5
  1.3499
1
 
Coupled Cluster CCD   1.4418
22
1.4308
16
1.4688
16
1.3892
37
1.3890
22
1.3853
22
1.3964
25
1.3984
16
1.4146
16
  1.4855
8
1.3898
26
1.3831
22
  1.3662
18
1.3526
15
  1.3474
6
1.3832
9
1.4202
5
1.3498
2
1.3384
3
 
CCSD         1.4012
25
1.3365
6
1.3363
6
1.3515
9
      1.5378
6
1.4043
18
1.3905
18
1.5834
3
1.4267
6
1.4136
6
1.3466
3
1.3499
2
1.4202
5
1.4208
5
  1.3455
1
 
CCSD=FULL         1.6095
6
            1.5364
6
1.5523
6
1.5313
6
1.5795
3
1.4241
6
1.3451
3
1.3443
3
  1.4693
3
1.4697
3
  1.3433
1
 
CCSD(T)   1.3815
2
    1.4081
22
1.3377
10
1.3376
6
1.3540
9
1.3392
2
  1.3437
2
1.4910
8
1.3963
24
1.3832
24
1.4258
5
1.3686
20
1.3562
18
1.3108
8
1.3504
6
1.3694
15
1.3865
9
1.3539
4
1.3416
5
 
CCSD(T)=FULL         1.4238
19
            1.4900
8
1.4156
15
1.3919
17
1.5223
4
1.3647
17
1.3138
11
1.3472
4
1.3483
6
1.3742
11
1.3370
6
1.3531
4
1.3399
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 1.4313
44
1.4080
44
1.4146
44
1.3679
44
1.4035
44
1.3982
44
density functional B1B95 1.3898
28
1.3612
28
1.3936
3
1.3600
3
1.3812
3
1.3705
3
B3LYP 1.4182
44
1.3899
44
1.4160
44
1.3842
43
1.4052
44
1.4007
44
Moller Plesset perturbation MP2 1.4462
44
1.4127
44
1.4166
44
1.3787
44
1.4073
44
1.4036
44
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.