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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-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 1.4405
17
PM3 1.6858
11
PM6 1.2901
21
composite G2 1.3594
21
G3 1.3211
21
G3B3 1.3330
24
G3MP2 1.3349
4
G4 1.3338
24
CBS-Q 1.3561
19

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) 6-311+G(3df,2pd) TZVP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ Sadlej_pVTZ
hartree fock HF 1.3769
16
1.3420
22
1.3311
21
1.3358
21
1.3158
24
1.3307
21
1.3434
22
1.3351
21
1.3271
21
1.3327
21
1.1689
8
1.3551
5
1.3172
24
1.3388
21
1.3310
21
1.4598
12
1.3109
21
1.3254
17
1.4457
12
0.7555
1
ROHF   2.7466
2
2.7466
2
2.7497
2
1.9624
4
2.6662
2
2.6723
2
2.6592
2
2.6611
2
      2.6696
2
2.6655
2
2.6619
2
2.6631
2
2.6703
2
2.6651
2
2.6642
2
 
density functional LSDA 1.3645
21
1.3576
22
1.3576
22
1.3589
22
1.3494
22
1.3488
22
1.3548
22
1.3409
22
1.3319
22
1.3504
22
0.7640
3
0.7641
1
1.6485
9
1.3486
22
1.3342
22
0.7634
1
1.3270
22
1.4903
11
0.7634
1
 
SVWN 0.7360
1
1.3380
23
0.7666
1
0.7633
1
1.3353
23
1.6403
9
1.3399
23
1.6389
9
1.6404
9
1.6456
9
0.7640
1
0.7641
1
1.1840
22
1.6421
9
1.6460
9
0.7634
1
1.6556
9
1.6517
9
0.7634
1
 
BLYP 1.4093
16
1.3961
21
1.3961
21
1.3478
20
1.1601
29
1.3698
21
1.3762
21
1.3521
21
1.3426
21
1.3713
21
0.7463
1
0.7462
1
1.6876
9
1.3675
21
1.3458
21
0.7454
1
1.1032
8
0.7463
1
0.7454
1
 
B1B95 1.4998
12
1.4552
18
1.4552
18
1.4537
18
1.4489
18
1.4485
18
1.4540
18
1.4371
18
1.4279
18
1.4500
18
0.7414
1
0.7413
1
1.6738
9
1.4461
18
1.4304
18
0.8457
2
1.4473
17
1.5714
10
0.7455
2
 
B3LYP 1.3944
16
1.3630
22
1.3527
21
1.3530
21
1.3533
20
1.3475
21
1.3617
22
1.3393
21
1.3300
21
1.3342
24
0.7428
3
1.3254
5
1.3220
24
1.3513
21
1.3330
21
1.4622
12
1.3514
20
1.3038
24
1.4486
12
0.7689
1
B3LYPultrafine 0.7284
1
1.3134
5
0.7462
1
0.7427
1
1.3564
22
0.7427
1
1.3112
5
0.7418
1
0.7440
1
0.7427
1
0.7427
1
1.3253
5
1.3673
7
1.6687
9
1.6735
9
0.7419
1
1.6872
9
1.3490
22
0.7419
1
 
B3PW91 1.3964
16
1.3451
21
1.3451
21
1.3467
21
1.3418
21
1.3415
21
1.3464
21
1.3305
21
1.3228
21
1.3438
21
0.7441
1
0.7441
1
1.6750
9
1.3441
21
1.3270
21
0.7434
1
1.0908
8
0.7442
1
0.7434
1
 
mPW1PW91 1.3903
16
1.3399
21
1.3399
21
1.3419
21
1.3367
21
1.3365
21
1.3412
21
1.3259
21
1.3189
21
1.3387
21
0.7431
1
0.7431
1
1.6691
9
1.3395
21
1.3230
21
0.7425
1
1.4416
16
1.6770
9
0.7425
1
 
M06-2X 1.6543
9
1.6513
9
1.2657
26
1.6680
9
1.3215
24
1.6534
9
1.6619
9
1.6508
9
1.6542
9
1.6588
9
0.7384
1
0.7385
1
1.6621
9
1.6578
9
1.6615
9
0.7369
1
1.6693
9
1.6674
9
0.7368
1
 
PBEPBE 1.4013
16
1.3694
22
1.3592
21
1.3863
20
1.3602
22
1.3514
21
1.3657
22
1.3380
21
1.3292
21
1.6195
21
0.7507
3
1.3157
5
1.6763
9
1.3522
21
1.3329
21
0.8519
2
1.4515
16
1.4597
13
0.7562
2
0.7764
1
PBEPBEultrafine 0.7345
1
1.3046
5
0.7535
1
0.7505
1
1.4429
17
0.7497
1
1.3033
5
0.7504
1
0.7519
1
0.7497
1
0.7507
1
1.3177
5
1.3620
7
1.6690
9
1.6746
9
0.7502
1
1.6880
9
1.6706
10
0.7502
1
 
PBE1PBE 1.6579
9
1.6489
9
1.6489
9
1.6671
9
1.3236
24
1.6573
9
1.6675
9
1.6542
9
1.6573
9
1.6624
9
0.7451
1
0.7451
1
1.6957
9
1.6604
9
1.6661
9
0.7446
1
1.6766
9
1.6741
9
0.7446
1
 
HSEh1PBE 1.6564
9
1.3255
24
1.6480
9
1.6655
9
1.3232
24
1.6552
9
1.3270
24
1.6529
9
1.6557
9
1.6606
9
0.7448
1
0.7449
1
1.6652
9
1.6585
9
1.3108
24
0.7442
1
1.7254
9
1.6720
9
0.7442
1
 
TPSSh   1.3192
7
1.3192
7
1.3383
7
1.2873
24
1.3524
7
1.2900
24
1.3511
7
  1.2665
21
    1.4172
7
1.3574
7
1.2852
24
  1.3793
7
1.3796
7
   
wB97X-D     1.2776
26
  1.2692
26
      1.2666
26
          1.2677
26
    1.2652
26
   
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) 6-311+G(3df,2pd) TZVP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ Sadlej_pVTZ
Moller Plesset perturbation MP2 1.3888
16
1.3582
22
1.3477
21
1.3544
21
1.2866
24
1.3329
21
1.3461
22
1.2828
24
1.3195
21
1.3341
21
0.7366
1
1.3165
5
1.3102
24
1.3402
21
1.3167
21
1.4265
13
1.3191
21
1.4360
12
1.4134
13
0.7660
1
MP2=FULL 1.4838
14
1.3476
21
1.4114
19
1.4192
19
1.3377
21
1.3321
21
1.3358
21
1.3985
19
1.3189
21
1.3951
19
0.7366
1
0.7371
1
1.6786
9
1.4013
19
1.3755
19
1.4251
13
1.4250
13
1.5817
10
1.5825
10
0.7660
1
ROMP2 2.7353
2
2.8433
2
2.8433
2
2.8517
2
2.7546
2
2.7398
2
2.7494
2
2.7483
2
2.7343
2
2.7470
2
    2.7423
2
2.7450
2
2.7396
2
  2.7585
2
     
MP3 0.7301
1
0.7453
1
0.7453
1
0.7418
1
1.3622
20
0.7354
1
1.2999
23
0.7415
1
0.7404
1
0.7354
1
0.7391
1
0.7395
1
1.3731
7
1.4113
7
1.3928
7
0.7387
1
0.7584
1
0.7400
1
0.7389
1
 
MP3=FULL         1.3037
23
  1.3017
23
          1.3700
7
1.3701
7
1.3614
7
         
MP4 0.7331
1
1.3177
10
0.7478
1
0.7442
1
1.3271
13
0.7369
1
0.7369
1
0.7443
3
1.3764
8
0.7369
1
0.7408
1
0.7413
1
1.7603
6
2.0901
3
1.3139
13
0.7405
1
2.0980
3
1.8025
6
0.7406
1
 
MP4=FULL 0.7331
1
1.7987
6
0.7478
1
0.7442
1
1.7641
6
0.7369
1
0.7369
1
0.7443
1
1.7907
6
0.7369
1
0.7408
1
0.7413
1
  2.0901
3
2.0799
3
0.7405
1
1.7705
6
1.7544
6
0.7406
1
 
B2PLYP 1.3624
7
1.3240
7
1.3240
7
1.3476
7
1.2042
21
1.3553
7
1.3656
7
1.3521
7
1.3547
7
1.3604
7
0.7400
1
0.7400
1
1.3645
7
1.3597
7
1.1653
21
0.7390
1
1.3776
7
1.3731
7
0.7391
1
 
B2PLYP=FULL 1.3624
7
1.3240
7
1.3240
7
1.3476
7
1.3563
7
1.3551
7
1.3653
7
1.3519
7
1.3545
7
1.3593
7
    1.3643
7
1.3595
7
1.3626
7
  1.3773
7
1.3717
7
   
B2PLYP=FULLultrafine 0.7254
1
0.7432
1
0.7432
1
0.7395
1
1.1977
6
0.7386
1
0.7386
1
0.7391
1
0.7411
1
0.7386
1
    0.7407
1
0.7581
1
0.7400
1
  0.7576
1
0.7400
1
   
Configuration interaction CID 0.7349
1
1.4072
19
1.4029
19
1.4236
19
1.3384
21
0.7378
1
0.7378
1
1.3691
16
1.1894
6
0.7378
1
0.7416
1
0.7421
1
  0.7603
1
0.7421
3
0.7413
1
0.7608
1
0.7424
1
0.7414
1
 
CISD 0.7349
1
1.3397
21
1.4062
19
1.4123
19
1.3385
21
  0.7385
1
1.4014
19
1.1898
6
0.7385
1
0.7421
1
0.7426
1
  0.7609
1
0.7426
3
0.7418
1
0.7613
1
0.7428
1
0.7419
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) 6-311+G(3df,2pd) TZVP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ Sadlej_pVTZ
Quadratic configuration interaction QCISD 0.7349
1
1.3423
21
1.3515
16
1.3697
16
1.3428
21
1.3454
16
1.3486
16
1.3719
16
1.4132
14
1.4366
14
0.7421
1
0.7426
1
1.6767
9
1.4382
17
1.4941
12
0.7418
1
1.6853
9
1.5880
10
0.7419
1
 
QCISD(T) 0.7349
1
0.7498
1
0.7498
1
0.7462
1
1.3707
16
0.9121
4
0.9121
4
0.9486
4
0.7435
1
0.7385
1
0.7422
1
0.7427
1
1.6716
9
1.3774
15
1.3337
12
0.7419
1
1.4876
12
1.4193
13
0.7420
1
 
QCISD(T)=FULL         0.7462
1
  0.7385
1
            0.7610
1
0.7426
1
0.7419
1
0.7618
1
0.7430
1
0.7420
1
 
QCISD(TQ)         1.5026
3
                1.5108
3
           
Coupled Cluster CCD 0.7349
1
1.3454
21
1.4432
14
1.4646
14
1.3444
21
1.3461
16
1.3500
16
1.3654
16
1.4344
14
1.4379
14
0.7416
1
0.7421
1
1.6788
9
1.4368
17
1.4824
12
0.7413
1
1.6921
9
1.5908
10
0.7414
1
 
CCSD   0.7495
1
0.7495
1
0.7459
1
1.3582
16
0.9701
3
1.1954
5
1.0154
3
0.7434
1
0.7385
1
0.7421
1
0.7426
1
1.6764
9
1.5838
10
1.5756
10
1.6702
9
1.6789
9
1.6801
9
2.0592
3
 
CCSD=FULL   0.7495
1
0.7495
1
0.7459
1
1.6778
9
0.7385
1
1.3090
4
0.7465
1
0.7434
1
0.7385
1
0.7421
1
0.7426
1
1.6726
9
1.6745
9
1.6652
9
1.5673
8
1.6877
9
1.3069
9
1.8401
2
 
CCSD(T)   1.3332
5
0.7498
1
0.7462
1
1.3800
17
0.9121
4
0.9121
4
0.9484
4
  0.7385
1
0.7422
3
0.7427
1
1.6766
9
1.5140
6
1.4894
9
1.4358
10
1.4871
12
1.4130
10
0.8234
5
 
CCSD(T)=FULL   0.7498
1
0.7498
1
0.7462
1
1.4749
14
0.7385
1
0.7385
1
0.7465
1
0.7435
1
0.7385
1
0.7422
1
0.7427
1
1.7511
6
1.6746
9
1.7461
6
1.7907
4
1.8090
6
1.6662
9
1.7370
4
 
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) 6-311+G(3df,2pd) TZVP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ 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 1.3451
21
1.3381
21
1.3487
21
1.3503
22
1.3554
22
1.3439
21
density functional LSDA 0.7639
2
0.7639
2
0.7640
2
0.7640
2
0.7639
2
0.7639
2
SVWN 0.7639
1
0.7639
1
0.7640
1
0.7640
1
0.7639
1
0.7639
1
BLYP 0.7482
1
0.7482
1
0.7462
1
0.7462
1
0.7482
1
0.7482
1
B1B95 1.2401
12
1.2057
11
0.7410
3
0.7410
3
0.7424
3
0.7424
3
B3LYP 1.3691
21
1.3609
21
1.3537
21
1.3556
22
1.3773
22
1.3657
21
B3LYPultrafine 0.7434
1
0.7434
1
0.7418
1
0.7418
1
0.7434
1
0.7434
1
B3PW91 0.7440
1
0.7440
1
0.7434
1
0.7434
1
0.7440
1
0.7440
1
mPW1PW91 0.7424
1
0.7424
1
0.7423
1
0.7423
1
0.7424
1
0.7424
1
M06-2X 0.7375
1
0.7375
1
0.7377
1
0.7377
1
0.7375
1
0.7375
1
PBEPBE 0.7514
1
0.7514
1
0.7504
1
0.7504
1
0.7514
1
0.7514
1
PBEPBEultrafine 0.7514
1
0.7514
1
0.7504
1
0.7504
1
0.7514
1
0.7514
1
PBE1PBE 0.7445
1
0.7445
1
0.7441
1
0.7441
1
0.7445
1
0.7445
1
HSEh1PBE 0.7444
1
0.7444
1
0.7439
1
0.7439
1
0.7444
1
0.7444
1
Moller Plesset perturbation MP2 1.3705
21
1.3494
21
1.3618
21
1.3520
22
1.3779
22
1.3660
21
MP2=FULL 0.7384
1
0.7384
1
0.7373
1
0.7373
1
0.7384
1
0.7384
1
MP3 0.7427
1
0.7427
1
0.7415
1
0.7415
1
0.7427
1
0.7427
1
MP4 0.7452
1
0.7452
1
0.7443
1
0.7443
1
0.7452
1
0.7452
1
MP4=FULL 0.7452
1
0.7452
1
0.7443
1
0.7443
1
0.7452
1
0.7452
1
B2PLYP 0.7400
1
0.7400
1
0.7391
1
0.7391
1
0.7400
1
0.7400
1
Configuration interaction CID 0.7465
1
0.7465
1
0.7461
1
0.7461
1
0.7465
1
0.7465
1
CISD 0.7469
1
0.7469
1
0.7465
1
0.7465
1
0.7469
1
0.7469
1
Quadratic configuration interaction QCISD 0.7469
1
0.7469
1
0.7465
1
0.7465
1
0.7469
1
0.7469
1
QCISD(T) 0.7473
1
0.7473
1
0.7465
1
0.7465
1
0.7473
1
0.7473
1
QCISD(TQ) 0.7667
1
0.7667
1
    0.7667
1
0.7667
1
Coupled Cluster CCD 0.7465
1
0.7465
1
0.7461
1
0.7461
1
0.7465
1
0.7465
1
CCSD 0.7469
1
0.7469
1
0.7465
1
0.7465
1
0.7469
1
0.7469
1
CCSD=FULL 0.7469
1
0.7469
1
0.7465
1
0.7465
1
0.7469
1
0.7469
1
CCSD(T) 0.7473
1
0.7473
1
0.7465
1
0.7465
1
0.7473
1
0.7473
1
CCSD(T)=FULL 0.7473
1
0.7473
1
0.7465
1
0.7465
1
0.7473
1
0.7473
1
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.