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Computational Chemistry Comparison and Benchmark DataBase
Release 18October 2016
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 1.3291
22
PM3 1.3122
22
PM6 1.2808
49
composite G2 1.3789
40
G3 1.3761
46
G3B3 1.4008
49
G3MP2 1.3290
8
G4 1.4397
47
CBS-Q 1.3916
35
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 cc-pV(Q+d)Z aug-cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ cc-pCVQZ aug-cc-pCVTZ daug-cc-pVTZ Sadlej_pVTZ
hartree fock HF 1.3483
46
1.3887
47
1.3635
47
1.3999
47
1.3714
50
1.3659
47
1.4761
26
1.3922
47
1.3739
46
1.3651
46
1.3267
27
1.3094
50
1.3587
47
1.3514
47
1.3748
24
1.3698
47
1.3590
46
1.3843
23
1.3354
8
1.3298
17
1.3262
2
1.3289
12
1.3399
6
1.3310
11
1.3294
1
1.3284
2
1.3296
2
1.3431
2
ROHF 1.3648
2
1.5489
10
1.5239
10
1.6241
9
1.5393
11
1.5338
10
1.7512
10
1.6437
10
1.5778
9
1.3419
2
  1.5092
7
1.4544
10
1.4559
10
1.4812
9
1.5252
9
1.5071
9
1.5003
9
1.3381
1
1.3316
3
  1.3316
3
1.3427
1
1.3331
5
1.3293
1
     
density functional LSDA 1.3854
45
1.3946
46
1.3768
45
1.4085
46
1.3765
46
1.3749
46
1.3588
46
1.3763
46
1.3725
46
1.3738
46
  1.4063
18
1.3830
45
1.3692
46
1.3813
3
1.3663
44
1.3549
27
1.3813
3
1.3658
8
1.3583
15
1.3507
2
1.3585
12
1.3682
2
1.3625
11
1.3557
1
1.3598
2
1.3542
2
 
SVWN   1.3340
45
    1.3843
43
1.4117
18
1.2949
45
1.4096
18
1.4050
18
1.4125
18
  1.2844
39
1.4174
18
1.4009
18
  1.3765
18
1.3647
18
  1.3667
4
1.3594
13
1.3507
2
1.3585
12
1.3682
2
1.3625
11
1.3557
1
1.3598
2
1.3542
2
 
BLYP 1.3978
46
1.4097
46
1.3862
38
1.4146
47
1.3957
51
1.3805
47
1.3757
47
1.3851
38
1.3774
46
1.3779
46
  1.4176
18
1.3923
47
1.3736
47
  1.3702
30
1.3620
13
  1.3682
8
1.3588
13
1.3512
2
1.3579
12
1.3709
2
1.3616
11
1.3567
1
1.3590
2
1.3548
2
 
B1B95 1.3760
46
1.3757
46
1.3617
46
1.3911
46
1.3633
46
1.3629
46
1.3579
42
1.3623
46
1.3599
46
1.3590
46
  1.3967
18
1.3693
46
1.3564
46
1.3578
4
1.3488
45
1.3379
28
1.3576
4
1.3496
8
1.3422
15
1.3363
2
1.3421
12
1.3545
4
1.3453
11
1.3409
1
1.3427
2
1.3400
2
 
B3LYP 1.3822
46
1.3938
47
1.3670
47
1.3982
47
1.3871
49
1.3664
47
1.3633
47
1.3678
47
1.3779
26
1.3711
49
1.3427
26
1.3173
50
1.3755
47
1.3618
46
1.3779
23
1.3556
34
1.3323
46
1.3390
23
1.3562
8
1.3468
16
1.3413
2
1.3468
12
1.3611
4
1.3503
11
1.3458
1
1.3476
2
1.3449
2
1.3584
2
B3LYPultrafine   1.3804
13
    1.3682
46
1.3536
13
1.3527
16
1.3563
13
      1.3563
13
1.4201
16
1.3922
20
  1.3655
16
1.3434
47
  1.3554
2
1.3478
9
1.3412
2
1.3466
8
1.3597
2
1.3502
11
1.3456
1
1.3474
2
1.3448
2
 
B3PW91 1.3923
28
1.3913
47
1.3646
47
1.3938
47
1.3640
47
1.3628
47
1.3628
38
1.3656
46
1.3739
26
1.3619
45
  1.3988
18
1.3719
47
1.3596
47
  1.3579
30
1.3510
12
  1.3541
8
1.3476
13
1.3411
2
1.3468
12
1.3574
2
1.3501
11
1.3452
1
1.3476
2
1.3445
2
 
mPW1PW91 1.3882
28
1.3882
46
1.3719
28
1.3905
46
1.3608
47
1.3600
46
1.3567
47
1.3625
47
1.3614
46
1.3631
46
  1.3956
18
1.3689
47
1.3626
34
  1.3498
42
1.3360
22
  1.3514
8
1.3453
13
1.3391
2
1.3446
12
1.3549
2
1.3478
11
1.3431
1
1.3453
2
1.3425
2
 
M06-2X 1.4007
18
1.4255
18
1.3902
38
1.4307
18
1.3003
45
1.3989
18
1.3929
18
1.3964
18
1.3941
18
1.3913
20
  1.3943
18
1.4044
18
1.3849
20
  1.3576
18
1.3453
20
  1.3489
2
1.3413
13
1.3349
2
1.3405
12
1.3529
2
1.3439
11
1.3395
1
1.3410
2
1.3381
2
 
PBEPBE 1.4063
28
1.4054
46
1.3979
28
1.4208
28
1.3798
45
1.3758
46
1.3576
46
1.3780
46
1.3743
46
1.3742
45
1.3533
26
1.4108
18
1.3845
45
1.3710
46
1.3731
4
1.3618
24
1.3515
29
1.3729
4
1.3659
8
1.3582
15
1.3514
2
1.3584
12
1.3707
4
1.3621
11
1.3560
1
1.3598
2
1.3548
2
1.3678
2
PBEPBEultrafine   1.3930
13
    1.3885
36
1.3639
13
1.3641
13
1.3682
13
      1.3669
13
1.4273
16
1.4111
16
  1.3758
16
1.3641
16
  1.3641
2
1.3591
9
1.3513
2
1.3579
8
1.3683
2
1.3621
11
1.3555
1
1.3596
2
1.3547
2
 
PBE1PBE 1.4147
16
1.4075
16
1.4075
16
1.4390
16
1.3765
48
1.4066
16
1.3950
16
1.4049
16
1.4053
16
1.4035
16
  1.4021
16
1.4110
16
1.3973
16
  1.3624
16
1.3514
16
  1.3517
2
1.3469
13
1.3402
2
1.3461
12
1.3560
2
1.3495
11
1.3445
1
1.3469
2
1.3440
2
 
HSEh1PBE 1.4095
18
1.3204
44
1.4019
18
1.4334
18
1.3009
44
1.3999
18
1.2963
44
1.3998
18
1.3994
18
1.3982
18
  1.3974
18
1.4063
18
1.2971
44
  1.3625
18
1.3512
18
  1.3538
4
1.3469
13
1.3402
2
1.3461
12
1.3564
2
1.3494
11
1.3446
1
1.3469
2
1.3440
2
 
TPSSh 1.3765
7
1.4435
15
1.4147
15
1.4459
15
1.3589
50
1.4121
15
1.3537
50
1.4128
15
1.3553
7
1.3818
48
  1.3551
13
1.4200
15
1.3562
50
1.3518
7
1.3633
15
1.3513
15
1.3517
7
1.3537
2
1.3473
9
1.3409
2
1.3464
8
1.3579
2
1.3490
10
1.3455
1
1.3475
2
1.3443
2
 
wB97X-D 1.3667
9
1.3732
9
1.3796
51
1.3757
9
1.3796
51
1.3476
9
1.3785
51
1.3507
9
1.3804
51
1.3469
9
  1.3824
51
1.3798
51
1.3778
51
1.3458
9
1.3594
9
1.3747
51
1.3458
9
1.3503
2
1.3458
6
1.3376
2
1.3447
5
1.3545
2
1.3457
9
1.3419
1
1.3427
2
1.3410
2
 
B97D3 1.3827
5
1.4080
49
1.3585
5
1.3901
5
1.3908
49
1.3575
5
1.3577
5
1.3612
5
1.3896
49
1.3558
5
  1.3605
5
1.3686
5
1.3558
5
1.3542
5
1.3679
5
1.3823
49
1.3541
5
1.3562
1
1.3452
1
  1.3451
1
1.3604
1
1.3461
1
  1.3521
2
   
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 cc-pV(Q+d)Z aug-cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ cc-pCVQZ aug-cc-pCVTZ daug-cc-pVTZ Sadlej_pVTZ
Moller Plesset perturbation MP2 1.3792
28
1.3970
47
1.3626
47
1.4024
47
1.3784
52
1.3511
47
1.4064
47
1.3816
50
1.3504
46
1.3621
41
  1.3052
50
1.3634
47
1.3521
43
1.3812
19
1.3481
34
1.3342
30
1.3438
18
1.3447
8
1.3385
18
1.3323
2
1.3383
12
1.3485
6
1.3396
11
1.3352
1
1.3377
2
1.3363
2
1.3579
2
MP2=FULL 1.3833
26
1.4059
34
1.3813
26
1.4215
26
1.3642
47
1.3558
38
1.4258
38
1.3707
47
1.3612
26
1.3739
28
  1.3860
18
1.3675
34
1.3566
28
1.3626
19
1.3428
25
1.3399
26
1.3249
19
1.3428
8
1.3352
18
1.3297
2
1.3334
12
1.3477
6
1.3377
11
1.3329
1
1.3356
2
1.3319
2
1.3587
2
ROMP2 1.3711
7
1.4969
9
1.4900
9
1.5522
9
1.4884
9
1.4533
9
1.7411
9
1.4819
9
1.4281
9
1.4614
9
  1.4492
7
1.4436
9
1.4251
9
1.3525
2
1.3636
9
1.3551
2
1.3529
2
1.3456
1
1.3430
3
  1.3442
3
1.3503
1
1.3444
5
1.3348
1
     
MP3         1.3687
46
  1.3719
50
        1.3439
13
1.3546
13
1.3425
13
        1.3456
6
1.3390
9
1.3341
2
1.3390
8
1.3511
2
1.3405
11
1.3379
1
1.3381
2
1.3384
2
 
MP3=FULL   1.3794
9
1.3451
9
1.3839
9
1.3601
50
1.3354
9
1.3459
49
1.3503
9
1.3398
9
1.3415
9
  1.3440
13
1.3531
13
1.3394
13
  1.3563
9
1.3400
9
  1.3447
2
1.3358
9
1.3322
2
1.3343
8
1.3504
2
1.3384
10
1.3357
1
1.3361
2
1.3337
2
 
MP4   1.4161
29
    1.3800
30
    1.3518
9
1.3627
26
    1.3924
16
1.4054
16
1.3621
29
  1.3616
16
1.3483
15
  1.3490
8
1.3424
9
1.3370
2
1.3429
8
1.3536
2
1.3441
11
1.3407
1
1.3422
2
1.3410
2
 
MP4=FULL   1.4617
16
    1.4223
16
      1.3899
16
      1.4038
16
1.3908
15
  1.3598
16
1.3437
15
  1.3469
2
1.3393
9
1.3349
2
1.3381
8
1.3528
2
1.3426
11
1.3388
1
1.3405
2
1.3366
2
 
B2PLYP 1.3642
13
1.3762
13
1.3466
13
1.3809
13
1.2719
40
1.3452
13
1.3470
15
1.3507
13
1.3469
13
1.3459
15
  1.3501
13
1.3585
13
1.3296
43
  1.3590
13
1.3462
15
  1.3507
4
1.3428
11
1.3369
2
1.3423
10
1.3540
2
1.3443
10
1.3406
1
1.3424
2
1.3406
2
 
B2PLYP=FULL 1.3642
13
1.3757
15
1.3466
13
1.3810
13
1.3496
15
1.3449
13
1.3466
15
1.3508
13
1.3468
13
1.3457
13
  1.3501
13
1.3580
13
1.3455
13
  1.3585
13
1.3454
13
  1.3490
2
1.3419
9
1.3361
2
1.3408
8
1.3538
2
1.3438
10
1.3399
1
1.3419
2
1.3393
2
 
B2PLYP=FULLultrafine 1.3664
9
1.3767
9
1.3468
9
1.3810
9
1.3385
29
1.3452
9
1.3456
9
1.3510
9
1.3474
9
1.3465
9
  1.3508
9
1.3587
9
1.3463
9
  1.3593
9
1.3463
9
  1.3489
2
1.3443
6
1.3361
2
1.3432
5
1.3537
2
1.3443
9
1.3399
1
1.3418
2
1.3393
2
 
Configuration interaction CID   1.4156
26
1.3798
26
1.4200
26
1.3711
38
    1.3738
29
          1.3369
6
        1.3445
2
1.3349
9
1.3315
2
1.3347
8
1.3491
2
1.3361
11
1.3360
1
1.3324
2
1.3358
2
 
CISD   1.4126
29
1.3800
26
1.4203
26
1.3719
38
1.3325
2
  1.3776
26
          1.3375
6
        1.3451
2
1.3353
9
1.3323
2
1.3351
8
1.3498
2
1.3355
9
1.3366
1
1.3328
2
1.3363
2
 
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 cc-pV(Q+d)Z aug-cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ cc-pCVQZ aug-cc-pCVTZ daug-cc-pVTZ Sadlej_pVTZ
Quadratic configuration interaction QCISD   1.4063
42
1.3893
29
1.4264
26
1.3766
34
1.3648
29
1.3601
30
1.3754
34
1.3628
27
1.3709
28
  1.3885
18
1.3748
30
1.3608
30
  1.3466
22
1.3303
21
  1.3486
8
1.3400
15
1.3359
2
1.3408
12
1.3538
2
1.3425
11
1.3395
1
1.3400
2
1.3399
2
 
QCISD(T)         1.3818
30
1.3370
6
1.3376
6
1.3563
13
      1.3904
18
1.3773
29
1.3647
28
  1.3650
22
1.3511
21
  1.3513
4
1.3424
15
1.3375
2
1.3436
12
1.3552
2
1.3452
11
1.3412
1
1.3429
2
1.3416
2
 
QCISD(T)=FULL         1.3528
13
  1.3400
13
          1.3574
13
1.3440
12
1.3441
10
1.3599
13
1.3436
12
1.3422
8
1.3485
2
1.3403
8
1.3355
2
1.3391
7
1.3544
2
1.3433
9
1.3397
1
1.3412
2
1.3375
2
 
QCISD(TQ)         1.3530
9
  1.3411
9
          1.3591
9
1.3468
9
1.3455
5
1.3620
9
1.3433
3
1.3415
3
  1.3425
1
  1.3436
1
  1.3428
1
       
QCISD(TQ)=FULL         1.3530
9
  1.3399
9
          1.3575
9
1.3432
7
1.3390
3
1.3601
9
1.3389
3
1.3420
1
  1.3392
1
  1.3383
1
  1.3411
1
       
Coupled Cluster CCD   1.4162
29
1.3833
26
1.4244
26
1.3766
40
1.3632
29
1.3606
29
1.3777
29
1.3615
26
1.3724
26
  1.3861
18
1.3731
30
1.3602
29
  1.3493
26
1.3329
23
  1.3476
8
1.3393
15
1.3352
2
1.3398
12
1.3513
4
1.3416
11
1.3387
1
1.3389
2
1.3392
2
 
CCSD         1.3809
29
1.3365
6
1.3363
6
1.3515
9
  1.3442
15
  1.3941
16
1.3761
25
1.3613
26
1.4098
11
1.3616
14
1.3456
18
1.3436
12
1.3494
4
1.3405
13
1.3358
2
1.3407
12
1.3537
2
1.3424
11
1.3394
1
1.3398
2
1.3398
2
 
CCSD=FULL         1.4149
18
        1.3421
15
  1.3938
16
1.4051
16
1.3822
18
1.3962
13
1.3588
16
1.3410
18
1.3413
12
1.3469
2
1.3375
9
1.3332
2
1.3358
8
1.3526
2
1.3404
11
1.3369
1
1.3376
2
1.3354
2
 
CCSD(T)   1.3815
2
    1.3840
27
1.3399
14
1.3393
11
1.3562
13
1.3428
7
1.3473
5
1.3437
1
1.3904
18
1.3772
29
1.3647
28
1.3725
15
1.3530
26
1.3381
23
1.3305
18
1.3504
8
1.3426
16
1.3375
2
1.3435
12
1.3544
6
1.3451
11
1.3411
1
1.3428
2
1.3415
2
 
CCSD(T)=FULL         1.3942
25
            1.3902
18
1.3796
22
1.3650
21
1.3950
14
1.3472
22
1.3265
18
1.3444
13
1.3483
8
1.3399
13
1.3354
2
1.3389
12
1.3535
6
1.3434
11
1.3396
1
1.3411
2
1.3375
2
 
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 cc-pV(Q+d)Z aug-cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ cc-pCVQZ aug-cc-pCVTZ daug-cc-pVTZ 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 1.4195
47
1.3949
47
1.4047
47
1.3574
47
1.3936
47
1.3879
47
density functional B1B95 1.3891
26
1.3610
26
1.3905
2
1.3576
2
1.3774
2
1.3677
2
B3LYP 1.4108
47
1.3808
47
1.4091
47
1.3751
46
1.3985
47
1.3932
47
wB97X-D 1.3880
9
1.3605
9
1.3928
9
1.3606
9
1.3790
9
1.3727
9
Moller Plesset perturbation MP2 1.4356
47
1.4010
47
1.4088
47
1.3690
47
1.3991
47
1.3949
47
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.