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Release 17bSeptember 2015
NIST Standard Reference Database 101
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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 1.3293
13
PM3 1.3126
13
PM6 1.2708
43
composite G2 1.3866
34
G3 1.3776
40
G3B3 1.4061
43
G3MP2 1.3276
3
G4 1.4519
41
CBS-Q 1.3969
29
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 cc-pCVQZ Sadlej_pVTZ
hartree fock HF 1.3486
40
1.3935
41
1.3684
41
1.4061
41
1.3772
44
1.3708
41
1.5527
17
1.4006
41
1.3795
40
1.3698
40
1.3267
27
1.3052
44
1.3606
41
1.3535
41
1.3823
20
1.3731
41
1.3623
40
1.3942
19
1.3355
7
1.3285
13
1.3271
7
1.3401
5
1.3277
6
1.3294
1
1.3431
2
ROHF 1.3648
2
1.6307
7
1.6065
7
1.7564
6
1.6177
8
1.6195
7
1.9310
7
1.7752
7
1.6972
6
1.3419
2
  1.6338
4
1.4999
7
1.5057
7
1.5531
6
1.6128
6
1.5908
6
1.5817
6
1.3381
1
1.3264
2
1.3224
1
1.3427
1
1.3272
2
1.3293
1
 
density functional LSDA 1.3848
40
1.3987
41
1.3775
40
1.4089
41
1.3771
41
1.3753
41
1.3572
41
1.3765
41
1.3726
41
1.3742
41
  1.4421
9
1.3830
40
1.3691
41
1.3813
3
1.3642
39
1.3499
19
1.3813
3
1.3664
7
1.3540
7
1.3552
5
1.3706
1
1.3583
4
1.3557
1
 
SVWN   1.3235
39
    1.3865
37
1.4553
9
1.2832
39
1.4481
9
1.4419
9
1.4589
9
  1.2844
39
1.4569
9
1.4358
9
  1.3757
9
1.3635
9
  1.3684
3
1.3552
5
1.3552
5
1.3706
1
1.3583
4
1.3557
1
 
BLYP 1.3979
40
1.4114
40
1.3893
32
1.4162
41
1.3977
47
1.3819
41
1.3765
41
1.3874
32
1.3785
40
1.3794
40
  1.4652
9
1.3939
41
1.3746
41
  1.3683
26
1.3564
4
  1.3687
7
1.3556
5
1.3554
5
1.3730
1
1.3586
4
1.3567
1
 
B1B95 1.3760
41
1.3795
41
1.3631
41
1.3926
41
1.3647
41
1.3644
41
1.3585
39
1.3636
41
1.3607
41
1.3600
41
  1.4406
9
1.3702
41
1.3568
41
1.3578
4
1.3469
40
1.3332
20
1.3576
4
1.3500
7
1.3400
9
1.3406
7
1.3568
3
1.3426
6
1.3409
1
 
B3LYP 1.3822
40
1.3951
41
1.3685
41
1.3996
41
1.3913
43
1.3677
41
1.3641
41
1.3689
41
1.3895
17
1.3742
41
1.3427
26
1.3113
44
1.3764
41
1.3626
40
1.3823
19
1.3529
28
1.3287
40
1.3353
19
1.3567
7
1.3445
12
1.3450
7
1.3623
3
1.3473
6
1.3458
1
1.3584
2
B3LYPultrafine   1.3764
4
    1.3698
40
1.3495
4
1.3496
10
1.3527
4
      1.3516
4
1.4890
7
1.4077
14
  1.3655
7
1.3416
41
  1.3578
1
1.3430
3
1.3429
3
1.3621
1
1.3470
4
1.3456
1
 
B3PW91 1.3990
20
1.3925
41
1.3659
41
1.3951
41
1.3654
41
1.3640
41
1.3642
32
1.3667
40
1.3839
17
1.3626
40
  1.4399
9
1.3726
41
1.3600
41
  1.3561
27
1.3461
6
  1.3545
7
1.3442
5
1.3441
5
1.3595
1
1.3465
4
1.3452
1
 
mPW1PW91 1.3966
19
1.3895
40
1.3825
19
1.3918
40
1.3622
41
1.3612
40
1.3573
41
1.3634
41
1.3623
40
1.3648
40
  1.4361
9
1.3696
41
1.3644
28
  1.3473
36
1.3254
13
  1.3518
7
1.3419
5
1.3419
5
1.3570
1
1.3441
4
1.3431
1
 
M06-2X 1.4388
9
1.4774
9
1.3949
34
1.4840
9
1.2928
39
1.4498
9
1.4374
9
1.4429
9
1.4396
9
1.4201
12
  1.4373
9
1.4494
9
1.4094
12
  1.3561
9
1.3433
12
  1.3509
1
1.3377
5
1.3376
5
1.3549
1
1.3396
4
1.3395
1
 
PBEPBE 1.4151
19
1.4067
40
1.4127
19
1.4314
19
1.3815
39
1.3769
40
1.3559
40
1.3790
40
1.3750
40
1.3752
39
1.3534
26
1.4520
9
1.3853
39
1.3715
40
1.3731
4
1.3530
15
1.3471
23
1.3729
4
1.3665
7
1.3555
9
1.3565
7
1.3722
3
1.3592
6
1.3560
1
1.3678
2
PBEPBEultrafine   1.3877
4
    1.3925
30
1.3585
4
1.3587
4
1.3634
4
      1.3610
4
1.4921
7
1.4700
7
  1.3752
7
1.3627
7
  1.3663
1
1.3532
3
1.3532
3
1.3705
1
1.3586
4
1.3555
1
 
PBE1PBE 1.4719
7
1.4789
7
1.4789
7
1.5129
7
1.3798
42
1.4771
7
1.4501
7
1.4679
7
1.4712
7
1.4704
7
  1.4605
7
1.4726
7
1.4546
7
  1.3612
7
1.3497
7
  1.3538
1
1.3433
5
1.3433
5
1.3581
1
1.3456
4
1.3445
1
 
HSEh1PBE 1.4484
9
1.3108
38
1.4515
9
1.4847
9
1.2926
38
1.4477
9
1.2871
38
1.4437
9
1.4447
9
1.4447
9
  1.4380
9
1.4491
9
1.2879
38
  1.3614
9
1.3497
9
  1.3550
3
1.3433
5
1.3433
5
1.3584
1
1.3454
4
1.3446
1
 
TPSSh   1.5395
6
1.5081
6
1.5424
6
1.3597
44
1.5024
6
1.3536
44
1.4973
6
  1.3842
44
  1.3504
4
1.5035
6
1.3563
44
  1.3616
6
1.3488
6
  1.3559
1
1.3423
3
1.3423
3
1.3601
1
1.3430
3
1.3455
1
 
wB97X-D 1.3531
2
1.3664
2
1.3820
47
1.3700
2
1.3821
47
1.3425
2
1.3426
2
1.3454
2
1.3826
47
1.3404
2
  1.3460
2
1.3526
2
1.3798
47
1.3389
2
1.3524
2
1.3764
47
1.3389
2
1.3525
1
    1.3567
1
1.3390
2
1.3419
1
 
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 cc-pCVQZ Sadlej_pVTZ
Moller Plesset perturbation MP2 1.3851
20
1.3995
41
1.3651
41
1.4051
41
1.3825
46
1.3528
41
1.4162
41
1.3859
44
1.3512
41
1.3647
35
  1.2994
44
1.3642
41
1.3530
37
1.4035
12
1.3454
28
1.3308
24
1.3439
11
1.3451
7
1.3367
14
1.3360
7
1.3488
5
1.3359
6
1.3352
1
1.3579
2
MP2=FULL 1.3925
17
1.4114
28
1.4012
17
1.4422
17
1.3666
41
1.3591
32
1.4422
32
1.3737
41
1.3724
17
1.3862
20
  1.4268
9
1.3714
26
1.3602
22
1.3720
13
1.3378
19
1.3388
22
1.3153
12
1.3431
7
1.3333
14
1.3311
7
1.3481
5
1.3339
6
1.3329
1
1.3587
2
ROMP2 1.3688
4
1.5714
6
1.5612
6
1.6353
6
1.5581
6
1.5094
6
1.9407
6
1.5469
6
1.4695
6
1.5171
6
  1.5230
4
1.4849
6
1.4625
6
1.3525
2
1.3631
6
1.3551
2
1.3529
2
1.3456
1
1.3355
1
1.3363
1
1.3503
1
1.3399
2
1.3348
1
 
MP3         1.3716
40
  1.3763
44
        1.3407
4
1.3509
4
1.3385
4
        1.3460
5
1.3347
3
1.3357
3
1.3537
1
1.3370
4
1.3379
1
 
MP3=FULL   1.3743
2
1.3400
2
1.3799
2
1.3615
44
1.3304
2
1.3469
43
1.3451
2
1.3345
2
1.3351
2
  1.3408
4
1.3494
4
1.3355
4
  1.3501
2
1.3337
2
  1.3473
1
1.3317
3
1.3308
3
1.3530
1
1.3329
3
1.3357
1
 
MP4   1.4300
20
    1.3865
24
    1.3518
9
1.3725
17
    1.4487
7
1.4647
7
1.3662
22
  1.3609
7
1.3474
6
  1.3493
7
1.3381
3
1.3394
3
1.3560
1
1.3407
4
1.3407
1
 
MP4=FULL   1.5599
7
    1.5125
7
      1.4491
7
      1.4632
7
1.4598
6
  1.3591
7
1.3425
6
  1.3494
1
1.3350
3
1.3345
3
1.3553
1
1.3393
4
1.3388
1
 
B2PLYP 1.3547
4
1.3723
4
1.3429
4
1.3774
4
1.2579
34
1.3413
4
1.3416
4
1.3473
4
1.3430
4
1.3419
7
  1.3457
4
1.3538
4
1.3261
37
  1.3540
4
1.3420
7
  1.3517
1
1.3377
3
1.3381
3
1.3562
1
1.3383
3
1.3406
1
 
B2PLYP=FULL 1.3547
4
1.3706
4
1.3430
4
1.3775
4
1.3456
4
1.3410
4
1.3412
4
1.3473
4
1.3429
4
1.3409
4
  1.3457
4
1.3533
4
1.3406
4
  1.3535
4
1.3406
4
  1.3512
1
1.3368
3
1.3367
3
1.3560
1
1.3378
3
1.3399
1
 
B2PLYP=FULLultrafine 1.3517
2
1.3696
2
1.3412
2
1.3748
2
1.3363
25
1.3394
2
1.3396
2
1.3452
2
1.3415
2
1.3394
2
  1.3441
2
1.3514
2
1.3392
2
  1.3519
2
1.3393
2
  1.3511
1
    1.3560
1
1.3372
2
1.3399
1
 
Configuration interaction CID   1.4359
17
1.3996
17
1.4403
17
1.3760
32
    1.3806
23
          1.3369
6
        1.3488
1
1.3327
3
1.3333
3
1.3535
1
1.3340
4
1.3360
1
 
CISD   1.4280
20
1.3997
17
1.4404
17
1.3770
32
    1.3939
17
          1.3375
6
        1.3495
1
1.3333
3
1.3339
3
1.3543
1
1.3347
4
1.3366
1
 
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 cc-pCVQZ Sadlej_pVTZ
Quadratic configuration interaction QCISD   1.4091
36
1.4071
20
1.4448
17
1.3816
28
1.3758
20
1.3668
22
1.3793
28
1.3676
21
1.3803
20
  1.4288
9
1.3782
24
1.3638
24
  1.3366
13
1.3194
13
  1.3489
7
1.3380
10
1.3388
5
1.3565
1
1.3392
4
1.3395
1
 
QCISD(T)         1.3884
24
1.3370
6
1.3376
6
1.3540
9
      1.4305
9
1.3847
20
1.3722
19
  1.3660
13
1.3521
12
  1.3524
3
1.3396
7
1.3416
5
1.3579
1
1.3419
4
1.3412
1
 
QCISD(T)=FULL         1.3502
4
  1.3364
4
          1.3531
4
1.3390
3
1.3388
3
1.3555
4
1.3387
3
1.3387
3
1.3511
1
1.3345
2
1.3345
2
1.3571
1
1.3359
2
1.3397
1
 
QCISD(TQ)         1.3505
3
  1.3376
3
          1.3549
3
1.3423
3
1.3407
3
1.3576
3
1.3433
3
1.3415
3
  1.3425
1
1.3436
1
  1.3428
1
   
QCISD(TQ)=FULL         1.3504
3
  1.3364
3
          1.3533
3
1.3393
3
1.3390
3
1.3558
3
1.3389
3
1.3420
1
  1.3392
1
1.3383
1
  1.3411
1
   
Coupled Cluster CCD   1.4302
20
1.4017
17
1.4429
17
1.3809
34
1.3741
20
1.3701
20
1.3833
23
1.3715
17
1.3867
17
  1.4253
9
1.3764
24
1.3669
20
  1.3437
17
1.3244
14
  1.3479
7
1.3373
8
1.3378
5
1.3517
3
1.3381
4
1.3387
1
 
CCSD         1.3882
23
1.3365
6
1.3363
6
1.3515
9
  1.3408
7
  1.4532
7
1.3859
16
1.3676
18
1.5228
4
1.3626
5
1.3438
10
1.3427
6
1.3505
3
1.3378
5
1.3387
5
1.3564
1
1.3391
4
1.3394
1
 
CCSD=FULL         1.4650
10
        1.3386
7
  1.4525
7
1.4667
7
1.4129
10
1.4579
6
1.3581
7
1.3392
10
1.3404
6
1.3497
1
1.3335
3
1.3325
3
1.3553
1
1.3370
4
1.3369
1
 
CCSD(T)   1.3815
2
    1.3955
19
1.3377
10
1.3376
6
1.3540
9
1.3392
2
  1.3437
1
1.4306
9
1.3821
22
1.3696
21
1.3938
8
1.3486
19
1.3325
16
1.3191
11
1.3508
7
1.3408
11
1.3418
7
1.3547
5
1.3418
6
1.3411
1
 
CCSD(T)=FULL         1.4110
16
            1.4300
9
1.3886
15
1.3741
14
1.4436
7
1.3399
15
1.3138
11
1.3435
7
1.3487
7
1.3378
8
1.3372
7
1.3539
5
1.3401
6
1.3396
1
 
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 cc-pCVQZ Sadlej_pVTZ

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 1.4272
41
1.4027
41
1.4094
41
1.3596
41
1.3990
41
1.3926
41
density functional B1B95 1.3898
27
1.3611
27
1.3936
3
1.3600
3
1.3812
3
1.3705
3
B3LYP 1.4123
41
1.3825
41
1.4098
41
1.3761
40
1.3999
41
1.3946
41
wB97X-D 1.3821
2
1.3563
2
1.3856
2
1.3561
2
1.3732
2
1.3666
2
Moller Plesset perturbation MP2 1.4418
41
1.4069
41
1.4103
41
1.3704
41
1.4019
41
1.3973
41
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.