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III.G.1.a.

Comparison of levels of theory for B-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 1.1393
22
PM3 1.2044
12
PM6 1.2322
60
composite G2 1.2482
57
G3 1.2482
57
G3B3 1.2530
57
G4 1.2527
56
CBS-Q 1.2532
57

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(T+d)Z cc-pCVDZ cc-pCVTZ
hartree fock HF 1.2243
55
1.2494
57
1.2495
57
1.2500
57
1.2370
102
1.2491
57
1.2452
57
1.2515
57
1.2494
57
1.2491
57
1.2093
21
1.2446
64
1.2594
57
1.2465
57
1.2458
53
1.2541
57
1.2444
57
1.2463
51
1.1705
2
1.1975
6
1.1871
6
ROHF   1.2039
5
1.2039
5
1.2197
3
1.2205
6
1.2041
5
1.1940
5
1.2043
5
1.2123
3
    1.2040
3
1.2122
5
1.1974
5
1.2033
3
1.2079
3
1.1984
3
1.1969
3
     
density functional LSDA 1.2368
56
1.2645
56
1.2646
56
1.2649
56
1.2621
56
1.2608
56
1.2580
56
1.2596
56
1.2574
56
1.2595
56
  1.2211
14
1.2725
56
1.2547
56
1.2170
3
1.2652
56
1.2843
27
1.2120
3
     
SVWN   1.2325
48
    1.2312
48
1.2295
14
1.2268
48
1.2263
14
1.2242
14
1.2272
14
    1.2389
14
1.2201
14
  1.2283
14
1.2158
14
       
BLYP 1.2495
55
1.2627
57
1.2628
57
1.2642
57
1.2617
57
1.2596
57
1.2562
57
1.2575
57
1.2549
57
1.2579
57
  1.2180
14
1.2716
57
1.2515
57
  1.2278
21
         
B1B95 1.2390
53
1.2562
53
1.2564
53
1.2566
53
1.2544
53
1.2540
53
1.2511
49
1.2525
53
1.2503
53
1.2536
49
  1.2123
14
1.2654
49
1.2485
49
1.2207
5
1.2609
39
1.2753
27
1.2134
5
     
B3LYP 1.2372
57
1.2631
57
1.2552
57
1.2562
57
1.2540
57
1.2525
57
1.2473
60
1.2514
57
1.2640
39
1.2511
57
1.2099
21
1.2447
64
1.2641
57
1.2457
57
1.2478
51
1.2561
57
1.2439
57
1.2495
48
1.1745
2
1.2031
6
1.1882
6
B3LYPultrafine         1.2540
57
  1.2312
12
        1.2527
2
1.2304
14
1.2184
26
  1.2190
14
1.2477
53
       
B3PW91 1.2484
39
1.2579
57
1.2580
57
1.2579
57
1.2560
57
1.2547
57
1.2513
57
1.2543
57
1.2672
39
1.2537
57
  1.2152
14
1.2652
57
1.2493
57
  1.2241
21
         
mPW1PW91 1.2417
41
1.2560
57
1.2693
47
1.2560
57
1.2543
57
1.2531
57
1.2498
57
1.2531
57
1.2510
57
1.2522
57
  1.2140
14
1.2636
57
1.2483
57
  1.2683
42
1.2879
24
       
M06-2X 1.2786
24
1.2961
24
1.2961
24
1.2978
24
1.2508
58
1.2921
24
1.2876
24
1.2910
24
1.2888
24
1.2899
24
  1.2064
18
1.3022
24
1.2848
24
  1.2945
24
1.2826
24
       
PBEPBE 1.2568
39
1.2660
57
1.2823
39
1.2834
39
1.2642
57
1.2627
57
1.2593
57
1.2615
57
1.2594
57
1.2613
57
1.2203
21
1.2223
14
1.2736
57
1.2565
57
1.2313
5
1.3085
24
1.2655
42
1.2247
5
     
PBEPBEultrafine         1.2326
47
            1.2672
2
1.2401
14
1.2217
14
  1.2286
14
1.2168
14
       
PBE1PBE 1.2043
14
1.2266
14
1.2266
14
1.2274
14
1.2239
55
1.2246
14
1.2148
14
1.2215
14
1.2197
14
1.2216
14
  1.2157
14
1.2317
14
1.2155
14
  1.2221
14
1.2113
14
       
HSEh1PBE 1.2833
24
1.3034
24
1.3034
24
1.3040
24
1.2578
54
1.2980
24
1.2931
24
1.2980
24
1.2956
24
1.2966
24
  1.2123
18
1.3089
24
1.2917
24
  1.3012
24
1.2892
24
       
TPSSh   1.2375
5
1.2375
5
1.2393
5
1.2370
51
1.2323
5
1.2330
51
1.2270
5
      1.2562
2
1.2379
5
1.2332
51
  1.2214
5
1.2103
5
       
Moller Plesset perturbation MP2 1.2473
39
1.2559
57
1.2560
57
1.2583
57
1.2478
59
1.2432
57
1.2321
87
1.2516
57
1.2485
57
1.2451
57
  1.2416
64
1.2630
57
1.2420
59
1.3037
39
1.2580
57
1.2496
48
1.3113
36
1.1751
2
1.2031
6
1.1867
6
MP2=FULL 1.2472
39
1.2557
57
1.2690
47
1.2717
47
1.2471
59
1.2419
57
1.2393
57
1.2509
57
1.2627
39
1.2572
39
  1.2072
14
1.2619
57
1.2467
49
1.2995
39
1.2604
41
1.2687
27
1.3092
35
1.1697
2
1.2024
6
1.1849
6
ROMP2 1.1830
3
1.2210
3
1.2210
3
1.2263
3
1.2145
3
1.2086
3
1.1981
3
1.2142
3
1.2115
3
1.2081
3
  1.2036
3
1.2264
3
1.2047
3
  1.2169
3
         
MP3         1.2515
57
  1.2268
57
        1.2493
2
1.2847
2
1.2549
2
             
MP3=FULL         1.2341
53
  1.2249
53
        1.2472
2
1.2835
2
1.2459
2
             
MP4   1.2723
50
    1.2544
57
    1.1984
11
1.2738
36
    1.2122
14
1.2336
14
1.2576
47
  1.2259
14
1.2105
14
       
MP4=FULL   1.2307
14
    1.2222
14
      1.2191
14
      1.2323
14
1.2059
14
  1.2240
14
1.2025
14
       
B2PLYP         1.2210
34
                1.1814
29
             
B2PLYP=FULLultrafine         1.2218
15
                               
Configuration interaction CID   1.2733
47
1.2733
47
1.2761
47
1.2518
57
    1.2570
55
          1.1928
9
             
CISD   1.2652
54
1.2741
47
1.2769
47
1.2526
57
1.1630
1
  1.2681
47
          1.1933
9
             
Quadratic configuration interaction QCISD   1.2632
57
1.2695
53
1.2797
47
1.2549
57
1.2500
54
1.2431
57
1.2580
57
1.2586
51
1.2748
33
  1.2124
14
1.2685
53
1.2622
43
  1.3055
24
1.2755
28
       
QCISD(T)         1.2625
43
1.1924
9
1.1920
9
1.1997
11
      1.2135
14
1.2870
35
1.2659
35
  1.2293
19
1.2136
19
       
QCISD(TQ)         1.2040
4
              1.2154
4
1.1981
4
    1.1984
4
       
Coupled Cluster CCD   1.2683
53
1.2755
47
1.2786
47
1.2538
57
1.2504
53
1.2474
53
1.2593
55
1.2786
33
1.2734
33
  1.2115
14
1.2676
53
1.2639
35
  1.2926
29
1.2664
33
    1.2063
6
1.1899
6
CCSD         1.2647
38
1.1917
9
1.1931
7
1.1987
11
      1.2122
14
1.2922
30
1.2715
30
1.2114
14
1.2258
14
1.2103
14
1.1995
10
     
CCSD=FULL         1.2225
14
            1.2105
14
1.2324
14
1.2060
14
1.2078
14
1.2239
14
1.2024
14
1.1957
10
     
CCSD(T)   1.2614
9
1.2616
8
1.2636
8
1.2612
51
1.2097
21
1.2181
17
1.2252
19
1.2401
1
  1.2497
9
1.2134
14
1.2837
43
1.2632
43
1.2733
30
1.2824
40
1.2616
36
1.2832
26
  1.2072
6
1.1911
6
CCSD(T)=FULL         1.2737
35
            1.2116
14
1.3000
27
1.2725
27
1.2756
26
1.3050
24
1.2693
28
1.3386
28
  1.2066
6
1.1893
6

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 1.2631
57
1.2574
57
1.2599
57
1.2511
57
1.2542
57
1.2540
57
density functional B1B95 1.2291
21
1.2304
18
       
B3LYP 1.2685
57
1.2636
57
1.2658
57
1.2574
57
1.2575
57
1.2576
57
Moller Plesset perturbation MP2 1.2758
57
1.2601
57
1.2700
57
1.2540
54
1.2648
57
1.2645
57
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.