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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 1.3101
36
PM3 1.4171
63
PM6 1.2991
63
composite G2 1.3001
60
G3 1.2602
54
G3B3 1.3855
63
G4 1.2917
66
CBS-Q 1.3965
51

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 1.4107
47
1.2855
63
1.2634
61
1.2605
61
1.3877
150
1.2622
59
1.6167
63
1.2634
59
1.2606
59
1.3972
60
1.2640
27
1.4130
8
1.3014
73
1.2681
59
1.2533
61
1.4950
12
1.2532
54
1.2973
62
1.5452
19
0.7555
1
ROHF 3.1014
1
2.8417
3
2.8417
3
2.8472
3
2.1754
5
2.7863
3
2.7906
3
2.7807
3
2.7818
3
3.0221
1
    2.6696
2
2.7910
3
2.7804
3
2.7806
3
2.7933
3
2.7823
3
2.7814
3
 
density functional LSDA 1.3305
50
1.3116
57
1.3116
57
1.3108
57
1.3077
56
1.3070
56
1.3037
53
1.3030
56
1.2994
56
1.3071
56
0.7640
3
0.7641
1
1.6326
12
1.3098
56
1.2990
56
1.9233
2
1.3146
51
1.4342
16
1.9232
2
 
SVWN 0.7360
1
1.2901
59
0.7666
1
0.7633
1
1.2821
59
1.5649
13
1.2831
59
1.5631
13
1.5635
13
1.5653
13
0.7640
1
0.7641
1
  1.5712
13
1.5626
13
0.7634
1
1.5714
13
1.5637
13
0.7634
1
 
BLYP 1.5708
47
1.3041
61
1.3041
61
1.2833
60
1.2771
60
1.2929
59
1.2932
54
1.2858
59
1.2821
59
1.5363
55
0.7463
1
0.7462
1
1.6396
12
1.5546
59
1.2781
54
0.7454
1
1.5200
22
0.7463
1
0.7454
1
 
B1B95 1.4165
52
1.4175
62
1.4175
62
1.4185
62
1.4203
61
1.4205
61
1.3288
61
1.4159
61
1.4132
61
1.4845
50
0.7414
1
0.7413
1
1.6238
12
1.4227
61
1.4130
61
1.5799
3
1.4877
49
1.4237
17
1.5130
3
 
B3LYP 1.4420
50
1.2983
68
1.2823
61
1.2790
61
1.2958
68
1.2788
59
1.2965
66
1.2751
59
1.2754
44
1.5022
63
1.9978
18
1.3717
8
1.3048
73
1.2838
59
1.2695
59
1.5018
15
1.2880
57
1.2676
42
1.5286
19
0.7689
1
B3LYPultrafine 0.7284
1
1.3134
5
0.7462
1
0.7427
1
1.2933
63
0.7427
1
1.3983
12
0.7418
1
0.7440
1
0.7427
1
0.7427
1
1.3253
5
1.7649
4
1.5670
13
1.7148
22
0.7419
1
1.5667
13
1.3030
63
0.7419
1
 
B3PW91 1.2847
36
1.2794
61
1.2794
61
1.2819
59
1.2700
61
1.2755
59
1.2764
59
1.2709
59
1.2714
44
1.5183
55
0.7441
1
0.7441
1
1.6273
12
1.2796
59
1.2664
59
0.7434
1
1.4646
27
0.7442
1
0.7434
1
 
mPW1PW91 1.2935
41
1.2814
54
1.2915
53
1.3848
54
1.2652
56
1.2712
54
1.2721
54
1.2666
54
1.2656
59
1.5150
55
0.7431
1
0.7431
1
1.6244
12
1.2755
54
1.2623
54
0.7425
1
1.5462
34
1.5546
13
0.7425
1
 
M06-2X 1.5616
13
1.5689
13
1.5689
13
1.5699
13
1.2896
62
1.5546
13
1.5573
13
1.5526
13
1.5531
13
1.5543
13
0.7384
1
0.7385
1
1.6231
12
1.5599
13
1.5522
13
0.7369
1
1.5601
13
1.5530
13
0.7368
1
 
PBEPBE 1.2949
36
1.3172
58
1.3072
53
1.3121
52
1.3077
64
1.2925
55
1.3213
62
1.2902
55
1.2768
59
1.6018
60
2.0035
18
1.3580
8
1.6375
12
1.2964
55
1.4268
55
1.5952
3
1.3360
31
1.3320
34
1.5314
3
0.7764
1
PBEPBEultrafine 0.7345
1
1.3386
8
0.7535
1
0.7505
1
1.4405
62
0.7497
1
1.3033
5
0.7504
1
0.7519
1
0.7497
1
0.7507
1
1.3605
8
1.7712
4
1.5750
13
1.5663
13
0.7502
1
1.5749
13
1.5255
20
0.7502
1
 
PBE1PBE 1.5633
13
1.5686
13
1.5686
13
1.5698
13
1.2907
62
1.5575
13
1.5593
13
1.5553
13
1.5560
13
1.5877
14
0.7451
1
0.7451
1
1.6254
12
1.5625
13
1.5549
13
0.7446
1
1.5626
13
1.5559
13
0.7446
1
 
HSEh1PBE 1.5635
13
1.5680
13
1.5680
13
1.5695
13
1.2818
63
1.5564
13
1.5591
13
1.5550
13
1.5558
13
1.5564
13
0.7448
1
0.7449
1
1.6251
12
1.5624
13
1.5545
13
0.7442
1
1.5625
13
1.5554
13
0.7442
1
 
TPSSh   1.7603
4
1.7603
4
1.7638
4
1.2891
60
1.7652
4
1.2907
60
1.7649
4
        1.7662
4
1.7719
4
1.2866
60
  1.7730
4
1.7667
4
   
Moller Plesset perturbation MP2 1.2789
40
1.3062
61
1.2864
54
1.2871
54
1.5728
74
1.2679
54
1.6678
105
1.2716
54
1.2675
59
1.6474
54
0.7366
2
1.3626
8
1.3010
73
1.2798
59
1.4688
72
1.3426
11
1.2690
54
1.4863
17
1.3253
11
0.7660
1
MP2=FULL 1.2931
39
1.2863
54
1.3072
52
1.3081
52
1.2681
62
1.2668
54
1.2683
54
1.3023
51
1.2697
44
1.2752
38
0.7366
1
0.7371
1
1.6292
12
1.3080
51
1.2602
70
1.3417
11
1.3844
21
1.8982
9
1.6151
7
 
ROMP2 2.8729
3
2.9224
3
2.9224
3
2.9329
3
2.8579
3
2.8442
3
2.8509
3
2.8521
3
2.8415
3
2.8479
3
    2.7423
2
2.8571
3
2.8408
3
3.0383
1
2.8654
3
  3.0380
1
 
MP3 0.7301
1
0.7453
1
0.7453
1
0.7418
1
1.2809
58
0.7354
1
1.2989
59
0.7415
1
0.7404
1
0.7354
1
0.7391
1
0.7395
1
1.7670
4
1.6274
5
1.5939
5
0.7387
1
0.7584
1
0.7400
1
0.7389
1
 
MP3=FULL         1.2977
59
  1.3183
53
          1.7617
4
1.7733
4
1.7537
4
         
MP4 0.7331
1
1.2835
26
0.7478
1
1.2830
6
1.3516
23
0.7369
1
0.7369
1
0.7443
3
1.3952
13
0.7369
1
0.7408
1
0.7413
1
2.0978
6
2.2654
4
1.3456
13
0.7405
1
2.2721
4
2.2566
4
0.7406
1
 
MP4=FULL   1.7252
9
    2.1019
6
      2.7576
3
        2.7663
3
2.7474
3
  2.1092
6
2.0894
6
   
B2PLYP 1.7696
4
1.7568
4
1.7568
4
1.7652
4
1.2494
48
1.7628
4
1.7666
4
1.7627
4
1.7632
4
1.7627
4
    1.7633
4
1.7709
4
1.2684
54
  1.7727
4
1.7641
4
   
B2PLYP=FULL 1.7696
4
1.7567
4
1.7567
4
1.7652
4
1.7651
4
1.7623
4
1.7662
4
1.7624
4
1.7630
4
1.7616
4
    1.7631
4
1.7706
4
1.7602
4
  1.7723
4
1.7625
4
   
B2PLYP=FULLultrafine         1.9426
30
                             
Configuration interaction CID 0.7349
1
1.3236
47
1.3266
43
1.3321
43
1.2857
49
0.7378
1
0.7378
1
1.3200
34
1.1894
6
0.7378
1
0.7416
1
0.7421
1
  0.7603
1
0.7421
4
0.7413
1
0.7608
1
0.7424
1
0.7414
1
 
CISD 0.7349
1
1.2984
49
1.3284
43
1.3273
43
1.2677
54
  0.7385
1
1.3151
43
1.1898
6
0.7385
1
0.7421
1
0.7426
1
  0.7609
1
0.7426
4
0.7418
1
0.7613
1
0.7428
1
0.7419
1
 
Quadratic configuration interaction QCISD 1.1196
12
1.2866
54
1.2731
50
1.2874
49
1.2751
54
1.2657
49
1.2908
50
1.2779
49
1.4748
40
1.3171
25
0.7421
1
0.7426
1
1.6250
12
1.3476
44
1.4218
17
0.7418
1
1.5678
13
1.6142
7
0.7419
1
 
QCISD(T) 0.7349
1
0.7498
1
0.7498
1
0.7462
1
1.3588
23
0.8773
5
0.8773
5
0.9486
4
0.7435
1
0.7385
1
0.7422
1
0.7427
1
2.0879
6
1.3844
15
1.3376
12
0.7419
1
1.5615
11
1.4790
12
0.7420
1
 
Coupled Cluster CCD 1.1195
12
1.2771
55
1.3072
47
1.3113
47
1.2766
54
1.2546
50
1.2664
49
1.2751
49
1.2886
31
1.3173
25
0.7418
2
0.7421
1
1.6258
12
1.3186
38
1.4130
17
0.7412
2
1.5376
14
1.5504
8
0.7414
2
 
CCSD   0.7497
2
0.7495
1
0.7459
1
1.3046
24
0.9122
4
0.7385
3
1.0154
3
0.7434
1
0.7385
1
0.7421
2
0.7426
1
2.0876
6
1.6493
9
1.6336
9
1.7456
6
1.7669
8
1.7539
8
2.0592
3
 
CCSD=FULL   0.7495
1
0.7495
1
0.7459
1
1.5637
13
0.7385
1
0.7385
1
0.7465
1
0.7434
1
0.7385
1
0.7421
1
0.7426
1
2.0821
6
1.9024
7
1.8846
7
1.5976
5
1.9098
7
1.8882
7
1.8401
2
 
CCSD(T)   1.3750
8
0.7498
1
0.7462
1
1.4829
25
0.9121
4
0.9456
5
0.9484
4
  0.7385
1
0.7422
4
0.7427
1
2.0880
6
1.4187
12
1.3901
12
1.3985
7
1.4156
15
1.3403
13
0.8234
5
 
CCSD(T)=FULL   0.7498
1
0.7498
1
0.7462
1
1.6482
14
0.7385
1
0.7385
1
0.7465
1
0.7435
1
0.7385
1
0.7422
1
0.7427
1
2.0873
6
2.0976
6
1.9353
7
1.7907
4
2.7589
3
2.0798
6
1.7370
4
 

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 1.2689
61
1.2697
59
1.2678
61
1.2722
60
1.2673
57
1.2637
61
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 1.2729
45
1.2430
41
1.0503
14
1.0504
14
1.0492
14
1.0492
14
B3LYP 1.2917
61
1.2907
59
1.2828
61
1.2860
60
1.2900
62
1.2847
61
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 1.3050
59
1.2865
59
1.2965
59
1.2815
55
1.3024
55
1.2963
54
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
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.