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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 1.1901
91
PM3 1.2546
75
PM6 1.2343
102
composite G2 1.2432
100
G3 1.2380
115
G3B3 1.2437
105
G3MP2 1.2211
24
G4 1.2401
118
CBS-Q 1.2433
115

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 aug-cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ cc-pCVQZ aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
hartree fock HF 1.2188
102
1.2390
102
1.2392
102
1.2388
102
1.2804
115
1.2381
102
1.2392
98
1.2419
102
1.2401
102
1.2392
102
1.2339
60
1.2366
110
1.2487
102
1.2378
102
1.2369
102
1.2458
102
1.2333
94
1.2377
100
1.1918
5
1.1655
1
1.2039
6
1.1948
6
1.2021
3
1.2360
14
1.2370
34
1.2269
100
ROHF   1.2356
24
1.2356
24
1.2419
22
1.2383
25
1.2359
24
1.2338
24
1.2400
24
1.2433
22
  1.2541
14
1.2409
22
1.2477
24
1.2361
24
1.2398
22
1.2490
22
1.2398
22
1.2390
22
1.2059
3
  1.2103
3
1.2025
3
1.2021
3
  1.2679
10
1.2597
10
density functional LSDA 1.2295
92
1.2522
87
1.2522
87
1.2528
88
1.2501
88
1.2478
87
1.2469
87
1.2483
88
1.2458
87
1.2470
87
1.2548
30
1.2497
79
1.2595
87
1.2435
87
  1.2538
87
1.2475
79
  1.2112
3
1.1819
1
1.2248
3
1.2126
3
1.2121
3
1.2414
14
1.2482
12
1.2378
12
BLYP 1.2397
106
1.2505
102
1.2507
102
1.2511
102
1.2414
110
1.2475
102
1.2465
102
1.2469
102
1.2445
102
1.2465
102
1.2435
52
1.2473
95
1.2598
102
1.2416
102
  1.2519
74
1.2504
81
  1.2088
3
1.1733
1
1.2264
3
1.2117
3
1.2115
3
1.2408
14
1.2417
34
1.2309
34
B1B95 1.2277
106
1.2428
101
1.2423
102
1.2420
102
1.2413
102
1.2412
102
1.2392
98
1.2402
102
1.2385
102
1.2395
98
1.2384
52
1.2407
95
1.2505
98
1.2362
98
  1.2406
82
1.2378
81
  1.2036
3
1.1699
1
1.2140
3
1.2038
3
1.2033
3
1.2337
14
1.2276
20
1.2152
24
B3LYP 1.2313
106
1.2432
102
1.2433
102
1.2436
102
1.2425
102
1.2409
102
1.2399
102
1.2410
102
1.2399
100
1.2401
102
1.2320
60
1.2364
110
1.2527
102
1.2362
102
1.2375
98
1.2467
102
1.2356
102
1.2374
97
1.1922
5
1.1686
1
1.2107
6
1.1967
6
1.2047
3
1.2347
14
1.2365
34
1.2264
34
B3LYPultrafine   1.2511
81
    1.2425
102
1.2486
81
1.2489
81
1.2493
81
  1.2422
52
1.2384
52
1.2468
83
1.2565
95
1.2375
99
  1.2504
95
1.2347
106
  1.2040
3
1.1686
1
1.2183
3
1.2052
3
1.2047
3
1.2347
14
1.2365
34
1.2264
34
B3PW91 1.2314
104
1.2457
102
1.2459
102
1.2452
102
1.2443
102
1.2430
102
1.2419
102
1.2439
102
1.2431
100
1.2427
102
1.2420
52
1.2446
95
1.2537
102
1.2397
102
  1.2481
74
1.2433
67
  1.2072
3
1.1731
1
1.2181
3
1.2076
3
1.2072
3
1.2378
14
1.2393
34
1.2303
34
mPW1PW91 1.2293
104
1.2441
102
1.2454
100
1.2435
102
1.2427
102
1.2415
102
1.2404
102
1.2427
102
1.2409
102
1.2413
102
1.2411
52
1.2434
95
1.2522
102
1.2388
102
  1.2491
99
1.2418
95
  1.2063
3
1.1722
1
1.2162
3
1.2064
3
1.2060
3
1.2368
14
1.2383
34
1.2295
34
M06-2X 1.2302
95
1.2434
95
1.2387
110
1.2445
95
1.2395
104
1.2419
95
1.2410
95
1.2420
95
1.2404
95
1.2406
95
1.2334
116
1.2393
95
1.2516
95
1.2380
95
  1.2470
95
1.2375
95
  1.2016
3
1.1688
1
1.2116
3
1.2016
3
1.2006
3
1.2307
14
1.2342
34
1.2255
34
PBEPBE 1.2386
104
1.2538
102
1.2561
98
1.2557
98
1.2520
102
1.2504
102
1.2494
102
1.2507
102
1.2488
102
1.2499
102
1.2437
66
1.2513
95
1.2617
102
1.2465
102
  1.2597
95
1.2483
97
  1.2137
3
1.1800
1
1.2269
3
1.2154
3
1.2150
3
1.2449
14
1.2459
34
1.2366
34
PBEPBEultrafine   1.2616
81
    1.2534
99
1.2580
81
1.2583
81
1.2588
81
  1.2517
52
1.2486
52
1.2566
83
1.2653
95
1.2501
95
  1.2597
95
1.2495
95
  1.2137
3
1.1800
1
1.2268
3
1.2154
3
1.2150
3
1.2449
14
1.2459
34
1.2366
34
PBE1PBE 1.2321
99
1.2496
95
1.2496
95
1.2492
95
1.2441
107
1.2480
95
1.2457
95
1.2480
95
1.2463
95
1.2467
95
1.2430
52
1.2451
95
1.2575
95
1.2441
95
  1.2530
95
1.2436
95
  1.2082
3
1.1745
1
1.2179
3
1.2082
3
1.2077
3
1.2384
14
1.2402
34
1.2315
34
HSEh1PBE 1.2326
99
1.2460
104
1.2495
95
1.2493
95
1.2447
104
1.2468
95
1.2421
104
1.2479
95
1.2461
95
1.2466
95
1.2427
52
1.2450
95
1.2576
95
1.2403
104
  1.2530
95
1.2433
95
  1.2080
3
1.1736
1
1.2181
3
1.2080
3
1.2076
3
1.2381
14
1.2400
34
1.2311
34
TPSSh 1.2317
69
1.2510
86
1.2511
86
1.2495
86
1.2420
113
1.2478
86
1.2394
104
1.2496
86
1.2451
65
1.2293
92
1.2409
52
1.2490
83
1.2597
92
1.2391
104
1.2318
53
1.2548
86
1.2457
86
1.2426
65
1.2065
3
1.1717
1
1.2170
3
1.2073
3
1.2064
3
1.2377
14
1.2378
34
1.2295
34
wB97X-D 1.2314
71
1.2481
67
1.2326
96
1.2476
67
1.2319
96
1.2458
67
1.2296
96
1.2475
67
1.2300
96
1.2457
67
1.2422
52
1.2292
96
1.2354
96
1.2278
96
1.2428
67
1.2535
67
1.2272
96
1.2429
67
1.2069
3
1.1726
1
1.2170
3
1.2063
3
1.2068
3
1.2372
14
1.2397
34
1.2303
34
B97D3 1.2483
58
1.2443
88
1.2590
58
1.2585
58
1.2440
88
1.2557
58
1.2414
88
1.2570
58
1.2404
88
1.2553
58
1.2402
113
1.2426
88
1.2677
58
1.2382
88
1.2521
58
1.2631
58
1.2399
88
1.2543
55
1.2128
3
1.1771
1
1.2265
3
1.2145
3
1.2142
3
1.2040
4
1.2444
34
1.2450
116
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 aug-cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ cc-pCVQZ aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Moller Plesset perturbation MP2 1.2330
100
1.2455
102
1.2456
102
1.2474
102
1.2348
110
1.2333
102
1.2326
102
1.2377
110
1.2398
102
1.2363
102
1.2390
52
1.2345
110
1.2530
102
1.2349
103
1.2374
95
1.2492
102
1.2378
97
1.2373
95
1.1917
5
1.1704
1
1.2097
6
1.1943
6
1.2007
3
1.2322
14
1.2404
34
1.2272
34
MP2=FULL 1.2328
100
1.2452
102
1.2476
98
1.2495
98
1.2387
102
1.2320
102
1.2313
102
1.2420
102
1.2403
100
1.2362
98
1.2366
52
1.2379
95
1.2519
102
1.2308
98
1.2333
95
1.2478
103
1.2332
99
1.2331
95
1.1855
5
1.1652
1
1.2089
6
1.1924
6
1.1982
3
1.2299
14
1.2390
34
1.2228
34
ROMP2 1.2401
18
1.2449
18
1.2449
18
1.2478
18
1.2414
18
1.2367
18
1.2353
18
1.2463
18
1.2446
18
1.2400
18
1.2593
10
1.2402
18
1.2576
18
1.2397
18
  1.2540
18
    1.2028
3
  1.2163
3
1.2016
3
1.2007
3
  1.2730
10
1.2600
10
MP3         1.2409
102
  1.2320
110
      1.2313
33
1.2467
82
1.2641
82
1.2465
82
        1.2039
3
1.1701
1
1.2171
3
1.2023
3
1.2014
3
1.2342
14
1.2482
27
1.2197
17
MP3=FULL   1.2519
66
1.2520
66
1.2541
66
1.2397
106
1.2357
66
1.2306
106
1.2484
66
1.2449
66
1.2387
66
1.2440
45
1.2448
82
1.2629
82
1.2393
82
  1.2544
66
1.2172
46
  1.1968
3
1.1644
1
1.2163
3
1.2005
3
  1.2399
11
1.2288
19
1.2116
19
MP4   1.2469
83
    1.2362
89
    1.1985
8
1.2402
81
  1.2330
29
1.2364
78
1.2542
78
1.2341
84
  1.2508
78
1.2365
78
  1.2064
3
1.1731
1
1.2201
3
1.2057
3
1.2049
3
1.2367
14
1.2511
27
1.2380
27
MP4=FULL   1.2486
78
    1.2405
78
      1.2405
78
  1.2308
29
  1.2531
78
1.2294
78
  1.2492
78
1.2318
75
  1.1991
3
1.1680
1
1.2193
3
1.2039
3
1.2026
3
1.2345
14
1.2497
27
1.2330
27
B2PLYP 1.2398
81
1.2499
81
1.2500
81
1.2509
81
1.2410
97
1.2445
81
1.2435
83
1.2486
81
1.2463
81
1.2455
81
1.2375
52
1.2448
81
1.2593
81
1.2384
92
  1.2551
81
1.2429
82
1.2023
3
1.2027
3
1.1681
1
1.2158
3
1.2028
3
1.2022
3
1.2328
14
1.2358
34
1.2255
34
B2PLYP=FULL 1.2398
81
1.2483
83
1.2500
81
1.2508
81
1.2457
83
1.2441
81
1.2431
83
1.2483
81
1.2461
81
1.2448
81
1.2367
52
1.2442
81
1.2590
81
1.2415
81
  1.2546
81
1.2422
81
  1.2006
3
1.1666
1
1.2155
3
1.2023
3
1.2016
3
1.2321
14
1.2353
34
1.2241
34
B2PLYP=FULLultrafine 1.2326
67
1.2445
67
1.2447
67
1.2456
67
1.2362
129
1.2390
67
1.2395
67
1.2431
67
1.2408
67
1.2397
67
1.2368
52
1.2391
67
1.2474
129
1.2298
129
1.2013
3
1.2497
67
1.2296
129
1.2014
3
1.2006
3
1.1666
1
1.2155
3
1.2023
3
1.2016
3
1.2269
17
1.2353
34
1.2240
34
Configuration interaction CID   1.2496
98
1.2497
98
1.2517
98
1.2396
102
    1.2443
100
    1.2390
49
  1.2557
49
1.2340
55
        1.2019
3
1.1678
1
1.2130
3
1.1985
3
1.1974
3
1.2324
14
1.2406
31
1.1912
15
CISD   1.2490
100
1.2501
98
1.2521
98
1.2400
102
1.1630
1
  1.2392
86
    1.2392
49
  1.2559
49
1.2343
55
        1.2023
3
1.1680
1
1.2132
3
1.1987
3
1.1976
3
1.2327
14
1.2408
31
1.2109
23
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 aug-cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ cc-pCVQZ aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Quadratic configuration interaction QCISD   1.2513
102
1.2528
100
1.2560
98
1.2431
102
1.2358
100
1.2339
102
1.2474
102
1.2441
99
1.2419
95
1.2434
49
1.2418
95
1.2493
90
1.2408
97
  1.2512
81
1.2302
75
  1.2062
3
1.1720
1
1.2189
3
1.2045
3
1.2036
3
1.2364
14
1.2443
31
1.1956
15
QCISD(T)         1.2382
86
1.1948
6
1.1941
6
1.2372
56
    1.2289
33
1.2363
79
1.2524
84
1.2342
84
  1.2495
82
1.2349
82
  1.2072
3
1.1733
1
1.2203
3
1.2059
3
1.2050
3
1.2376
14
1.2456
31
1.2319
31
QCISD(T)=FULL         1.2455
62
  1.2363
62
      1.2268
33
  1.2587
62
1.2350
62
1.2207
38
1.2553
62
1.2375
62
1.2191
40
1.1999
3
1.1678
1
1.2195
3
1.2041
3
1.2026
3
1.2353
14
1.2440
31
1.2109
23
QCISD(TQ)         1.2425
43
  1.2248
36
      1.2425
23
  1.2479
35
1.2318
33
1.2070
9
1.2567
40
1.2057
13
1.2335
1
            1.2363
17
1.1762
2
QCISD(TQ)=FULL         1.2431
41
  1.2339
41
      1.2197
15
  1.2588
40
1.2142
23
1.2020
10
1.2476
30
1.2036
9
1.2083
2
            1.2036
6
1.1692
2
Coupled Cluster CCD   1.2521
100
1.2533
98
1.2555
98
1.2427
102
1.2350
100
1.2343
100
1.2480
100
1.2458
95
1.2412
95
1.2445
38
1.2412
95
1.2554
102
1.2402
97
  1.2556
95
1.2297
75
  1.2056
3
1.1717
1
1.2124
6
1.1969
6
1.2029
3
1.2356
14
1.2441
31
1.2142
23
CCSD         1.2441
99
1.2193
29
1.2223
27
1.2295
30
1.2341
23
1.2462
81
1.2281
37
1.2417
95
1.2585
97
1.2373
89
1.2201
58
1.2560
95
1.2207
61
1.2052
27
1.2061
3
1.1718
1
1.2187
3
1.2043
3
1.2033
3
1.2360
15
1.2443
31
1.1954
15
CCSD=FULL         1.2457
95
        1.2439
81
1.2405
49
1.2408
92
1.2595
92
1.2203
69
1.2166
58
1.2543
95
1.2144
61
1.2039
25
1.1988
3
1.1662
1
1.2179
3
1.2024
3
  1.2287
18
1.2265
23
1.2094
23
CCSD(T)   1.2614
9
1.2616
8
1.2636
8
1.2381
86
1.2218
58
1.2191
39
1.2372
56
1.2317
34
1.2284
33
1.2291
34
1.2363
79
1.2523
84
1.2341
84
1.2205
55
1.2495
82
1.2352
82
1.2191
57
1.2071
3
1.1727
1
1.2137
6
1.1984
6
1.2049
3
1.2375
14
1.2455
31
1.2328
31
CCSD(T)=FULL         1.2397
82
          1.2269
33
1.2344
79
1.2530
79
1.2290
79
1.2150
53
1.2487
79
1.2293
82
1.2141
53
1.1998
3
1.1683
1
1.2130
6
1.1967
6
1.2026
3
1.2352
14
1.2439
31
1.2108
23
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 aug-cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ cc-pCVQZ aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ

average calculated bond lengths (Å)
Methods with effective core potentials (select basis sets)
CEP-31G CEP-31G* CEP-121G CEP-121G* LANL2DZ SDD cc-pVTZ-PP aug-cc-pVTZ-PP Def2TZVPP
hartree fock HF 1.2531
102
1.2469
102
1.2510
102
1.2417
102
1.2458
102
1.2458
102
    1.2304
113
ROHF                 1.2545
14
density functional LSDA                 1.2555
30
BLYP                 1.2442
52
B1B95 1.2326
18
1.2304
18
            1.2389
52
B3LYP 1.2575
102
1.2526
102
1.2556
102
1.2470
102
1.2476
102
1.2477
102
    1.2298
113
B3LYPultrafine                 1.2391
52
B3PW91                 1.2426
52
mPW1PW91                 1.2418
52
M06-2X                 1.2374
52
PBEPBE                 1.2383
113
PBEPBEultrafine                 1.2491
52
PBE1PBE                 1.2436
52
HSEh1PBE                 1.2433
52
TPSSh                 1.2417
52
wB97X-D 1.2616
67
1.2557
67
1.2592
67
1.2503
67
1.2541
67
1.2541
67
    1.2430
52
B97D3                 1.2513
48
Moller Plesset perturbation MP2 1.2657
102
1.2494
102
1.2608
102
1.2415
102
1.2562
102
1.2560
102
    1.2284
113
MP2=FULL                 1.2346
52
ROMP2                 1.2588
10
MP3                 1.2458
45
MP3=FULL                 1.2261
33
MP4                 1.2354
26
MP4=FULL                 1.2280
29
B2PLYP                 1.2378
52
B2PLYP=FULL                 1.2366
52
B2PLYP=FULLultrafine                 1.2366
52
Configuration interaction CID                 1.2244
37
CISD                 1.2245
37
Quadratic configuration interaction QCISD                 1.2428
49
QCISD(T)                 1.2276
33
QCISD(T)=FULL                 1.2233
33
QCISD(TQ)                 1.2193
18
QCISD(TQ)=FULL                 1.2260
11
Coupled Cluster CCD                 1.2424
49
CCSD                 1.2427
49
CCSD=FULL                 1.2234
37
CCSD(T)                 1.2275
33
CCSD(T)=FULL                 1.2232
33
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.