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Release 19April 2018
NIST Standard Reference Database 101
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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 1.1676
55
PM3 1.2320
48
PM6 1.2223
87
composite G2 1.2295
75
G3 1.2295
75
G3B3 1.2341
75
G3MP2 1.2093
12
G4 1.2316
82
CBS-Q 1.2344
75

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 Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
hartree fock HF 1.2075
74
1.2303
75
1.2304
75
1.2305
75
1.2297
87
1.2299
75
1.2285
63
1.2332
75
1.2313
75
1.2306
75
1.2124
27
1.2281
83
1.2156
86
1.2403
75
1.2290
75
1.2282
75
1.2370
75
1.2282
75
1.2289
73
1.1705
2
1.1975
3
1.1871
3
1.2521
10
1.2018
4
1.1934
4
ROHF   1.2207
14
1.2207
14
1.2276
12
1.2262
15
1.2210
14
1.2177
14
1.2232
14
1.2278
12
  1.2417
4
1.2249
12
1.2420
4
1.2318
14
1.2192
14
1.2239
12
1.2326
12
1.2233
12
1.2225
12
           
density functional LSDA 1.2203
80
1.2440
75
1.2441
75
1.2450
76
1.2426
76
1.2402
75
1.2391
75
1.2407
76
1.2379
75
1.2393
75
1.2127
10
1.2413
56
1.2135
10
1.2519
75
1.2357
75
  1.2461
75
1.2387
56
        1.2563
10
1.2172
4
1.2072
4
BLYP 1.2302
78
1.2435
75
1.2436
75
1.2443
75
1.2267
83
1.2403
75
1.2389
75
1.2392
75
1.2368
75
1.2390
75
1.2102
10
1.2406
56
1.2110
10
1.2523
75
1.2339
75
  1.2400
44
1.2460
42
        1.2570
10
1.2121
4
1.2015
4
B1B95 1.2175
79
1.2369
73
1.2353
75
1.2351
75
1.2337
75
1.2335
75
1.2310
71
1.2323
75
1.2305
75
1.2315
71
1.2049
10
1.2333
56
1.2054
10
1.2426
71
1.2275
71
  1.2356
61
1.2315
54
        1.2491
10
  1.1959
4
B3LYP 1.2207
79
1.2421
75
1.2361
75
1.2364
75
1.2349
75
1.2333
75
1.2320
75
1.2331
75
1.2307
64
1.2323
75
1.2121
27
1.2287
83
1.2160
86
1.2450
75
1.2281
75
1.2297
71
1.2386
75
1.2273
75
1.2295
70
1.1745
2
1.2031
3
1.1882
3
1.2504
10
1.2056
4
1.1954
4
B3LYPultrafine   1.2476
42
    1.2349
75
1.2438
42
1.2443
42
1.2445
42
  1.2081
10
1.2049
10
1.2422
44
1.2056
10
1.2497
56
1.2316
68
  1.2430
56
1.2266
79
        1.2504
10
1.2056
4
1.1954
4
B3PW91 1.2182
68
1.2385
75
1.2386
75
1.2379
75
1.2366
75
1.2353
75
1.2338
75
1.2358
75
1.2337
64
1.2347
75
1.2080
10
1.2371
56
1.2087
10
1.2459
75
1.2315
75
  1.2354
44
1.2263
29
        1.2534
10
1.2081
4
1.1990
4
mPW1PW91 1.2151
69
1.2367
75
1.2392
72
1.2361
75
1.2350
75
1.2337
75
1.2323
75
1.2345
75
1.2326
75
1.2333
75
1.2069
10
1.2358
56
1.2076
10
1.2442
75
1.2304
75
  1.2419
69
1.2338
56
        1.2523
10
1.2067
4
1.1978
4
M06-2X 1.2195
56
1.2373
56
1.2316
83
1.2383
56
1.2320
77
1.2351
56
1.2335
56
1.2347
56
1.2330
56
1.2323
57
1.2022
10
1.2317
56
1.2033
10
1.2446
56
1.2293
57
  1.2393
56
1.2285
57
        1.2455
10
1.2020
4
1.1927
4
PBEPBE 1.2258
68
1.2466
75
1.2485
62
1.2484
62
1.2447
75
1.2431
75
1.2416
75
1.2429
75
1.2409
75
1.2421
75
1.2224
27
1.2442
56
1.2234
86
1.2540
75
1.2386
75
  1.2524
56
1.2414
67
        1.2606
10
1.2163
4
1.2070
4
PBEPBEultrafine   1.2580
42
    1.2473
69
1.2534
42
1.2538
42
1.2541
42
  1.2175
10
1.2148
10
1.2521
44
1.2154
10
1.2588
56
1.2429
56
  1.2523
56
1.2418
56
        1.2606
10
1.2163
4
1.2070
4
PBE1PBE 1.2218
60
1.2439
56
1.2439
56
1.2435
56
1.2367
80
1.2413
56
1.2381
56
1.2408
56
1.2389
56
1.2394
56
1.2088
10
1.2374
56
1.2094
10
1.2504
56
1.2364
56
  1.2452
56
1.2355
56
        1.2538
10
1.2086
4
1.1998
4
HSEh1PBE 1.2223
60
1.2389
77
1.2438
56
1.2436
56
1.2373
77
1.2400
56
1.2340
77
1.2407
56
1.2388
56
1.2393
56
1.2084
10
1.2373
56
1.2091
10
1.2505
56
1.2321
77
  1.2452
56
1.2352
56
        1.2535
10
1.2084
4
1.1994
4
TPSSh 1.2124
27
1.2475
47
1.2475
47
1.2456
47
1.2290
77
1.2430
47
1.2260
77
1.2443
47
1.2337
23
1.2088
62
1.2074
10
1.2446
44
1.2082
10
1.2542
47
1.2258
77
1.2308
23
1.2489
47
1.2395
47
1.2310
23
      1.2537
10
1.2070
4
1.1987
4
wB97X-D 1.2086
32
1.2354
28
1.2131
69
1.2346
28
1.2123
69
1.2309
28
1.2094
69
1.2325
28
1.2100
69
1.2303
28
1.2080
10
1.2091
69
1.2088
10
1.2115
69
1.2081
69
1.2273
28
1.2386
28
1.2071
69
1.2274
28
      1.2527
10
1.2076
4
1.1978
4
B97D3 1.2338
16
1.2294
58
1.2554
16
1.2552
16
1.2294
58
1.2496
16
1.2270
58
1.2508
16
1.2256
58
1.2482
16
1.2302
86
1.2473
16
1.2219
6
1.2617
16
1.2237
58
1.2447
16
1.2568
16
1.2287
58
1.2450
16
        1.2147
4
1.2054
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) TZVP Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Moller Plesset perturbation MP2 1.2187
64
1.2375
75
1.2376
75
1.2393
75
1.2206
83
1.2249
75
1.2239
75
1.2228
83
1.2309
75
1.2274
75
1.2038
10
1.2258
83
1.2139
86
1.2444
75
1.2264
75
1.2277
59
1.2403
75
1.2290
70
1.2286
56
1.1751
2
1.2031
3
1.1867
3
1.2469
10
1.2069
4
1.1935
4
MP2=FULL 1.2183
64
1.2373
75
1.2410
70
1.2428
70
1.2302
75
1.2235
75
1.2225
75
1.2332
75
1.2301
64
1.2254
63
1.2017
10
1.2295
56
1.1995
10
1.2433
75
1.2223
71
1.2238
59
1.2367
68
1.2222
64
1.2245
56
1.1697
2
1.2024
3
1.1849
3
1.2446
10
1.2057
4
1.1884
4
ROMP2 1.1966
8
1.2268
8
1.2268
8
1.2289
8
1.2185
8
1.2135
8
1.2105
8
1.2219
8
1.2203
8
1.2150
8
  1.2150
8
  1.2342
8
1.2151
8
  1.2293
8
               
MP3         1.2327
75
  1.2193
83
      1.2057
10
1.2401
44
1.2051
10
1.2585
44
1.2401
44
              1.2494
10
1.2091
4
1.1951
4
MP3=FULL   1.2365
28
1.2365
28
1.2385
28
1.2264
79
1.2189
28
1.2172
79
1.2311
28
1.2276
28
1.2211
28
1.2037
10
1.2382
44
1.2011
10
1.2574
44
1.2329
44
  1.2388
28
1.2186
28
        1.2471
10
1.2078
4
1.1896
4
MP4   1.2479
65
    1.2353
71
    1.1985
8
1.2379
55
  1.1880
6
1.2344
52
1.1876
6
1.2531
52
1.2337
66
  1.2488
52
1.2342
52
        1.2519
10
1.2111
4
1.1973
4
MP4=FULL   1.2490
52
    1.2393
52
      1.2388
52
  1.1860
6
  1.1841
6
1.2519
52
1.2275
52
  1.2471
52
1.2279
52
        1.2496
10
1.2098
4
1.1918
4
B2PLYP 1.2303
42
1.2460
42
1.2460
42
1.2468
42
1.2332
70
1.2394
42
1.2374
44
1.2433
42
1.2408
42
1.2383
43
1.2035
10
1.2394
42
1.2039
10
1.2543
42
1.2241
65
  1.2500
42
1.2363
43
        1.2481
10
1.2046
4
1.1936
4
B2PLYP=FULL 1.2302
42
1.2432
44
1.2459
42
1.2467
42
1.2395
44
1.2389
42
1.2370
44
1.2430
42
1.2407
42
1.2393
42
1.2029
10
1.2389
42
1.2027
10
1.2540
42
1.2360
42
  1.2495
42
1.2366
42
        1.2474
10
1.2042
4
1.1921
4
B2PLYP=FULLultrafine 1.2082
28
1.2313
28
1.2313
28
1.2320
28
1.2253
43
1.2242
28
1.2249
28
1.2279
28
1.2255
28
1.2242
28
1.2029
10
1.2239
28
1.2027
10
1.2395
28
1.2210
28
  1.2353
28
1.2216
28
        1.2474
10
1.2042
4
1.1921
4
Configuration interaction CID   1.2437
70
1.2437
70
1.2456
70
1.2321
75
    1.2367
73
    1.2046
10
  1.2041
10
1.2207
10
1.2007
16
              1.2478
10
1.2071
4
1.1933
4
CISD   1.2430
72
1.2442
70
1.2461
70
1.2326
75
1.1630
1
  1.2393
70
    1.2051
10
  1.2045
10
1.2212
10
1.2011
16
              1.2481
10
1.2074
4
1.1937
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) TZVP Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Quadratic configuration interaction QCISD   1.2439
75
1.2464
72
1.2497
70
1.2356
75
1.2291
72
1.2258
75
1.2394
75
1.2371
69
1.2335
57
1.2082
10
1.2343
56
1.2075
10
1.2481
75
1.2340
67
  1.2368
42
1.2329
57
        1.2516
10
1.2110
4
1.1972
4
QCISD(T)         1.2365
57
1.1948
6
1.1941
6
1.2272
30
    1.1889
6
1.2353
52
1.1886
6
1.2522
54
1.2338
54
  1.2497
52
1.2350
52
        1.2528
10
1.2123
4
1.1984
4
QCISD(T)=FULL         1.2464
38
  1.2375
38
      1.1869
6
  1.1851
6
1.2599
38
1.2360
38
1.2206
24
1.2564
38
1.2379
38
1.2206
24
      1.2504
10
1.2110
4
1.1929
4
QCISD(TQ)         1.2338
22
  1.2241
23
      1.1927
5
  1.1924
5
1.2483
22
1.2332
20
1.2163
7
1.2458
22
1.2111
11
1.2335
1
        1.2125
4
 
QCISD(TQ)=FULL         1.2316
23
  1.2228
23
      1.1907
5
  1.1677
1
1.2483
22
1.2026
13
1.2095
8
1.2465
20
1.2133
7
1.2083
2
        1.2112
4
 
Coupled Cluster CCD   1.2456
72
1.2469
70
1.2490
70
1.2348
75
1.2282
72
1.2271
72
1.2398
73
1.2383
56
1.2336
56
1.2075
10
1.2335
56
1.2068
10
1.2475
75
1.2322
58
  1.2479
56
1.2334
56
    1.2063
3
1.1899
3
1.2507
10
1.2102
4
1.1964
4
CCSD         1.2356
61
1.2099
10
1.2168
8
1.2133
12
1.2397
4
1.2389
43
1.2080
10
1.2341
56
1.2074
10
1.2510
58
1.2316
59
1.2205
42
1.2485
56
1.2203
43
1.2108
22
      1.2498
11
1.2109
4
1.1971
4
CCSD=FULL         1.2380
57
        1.2367
43
1.2059
10
1.2323
56
1.2033
10
1.2514
56
1.2137
43
1.2167
42
1.2468
56
1.2135
43
1.2069
22
      1.2475
11
1.2097
4
1.1916
4
CCSD(T)   1.2614
9
1.2616
8
1.2636
8
1.2387
65
1.2187
40
1.2129
20
1.2341
38
1.1983
7
1.1876
6
1.2254
15
1.2352
52
1.1885
6
1.2545
62
1.2360
62
1.2200
38
1.2519
60
1.2349
52
1.2203
35
  1.2072
3
1.1911
3
1.2527
10
1.2123
4
1.1983
4
CCSD(T)=FULL         1.2392
55
          1.1869
6
1.2334
52
1.1850
6
1.2527
52
1.2281
52
1.2148
34
1.2479
52
1.2285
52
1.2135
34
  1.2066
3
1.1893
3
1.2504
10
1.2110
4
1.1928
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) TZVP Def2TZVPP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ

average calculated bond lengths (Å)
Methods with effective core potentials (select basis sets)
daug-cc-pVDZ daug-cc-pVTZ daug-cc-pVQZ Sadlej_pVTZ CEP-31G CEP-31G* CEP-121G CEP-121G* LANL2DZ SDD
hartree fock HF 1.2018
4
1.1934
4
    1.2434
75
1.2380
75
1.2414
75
1.2330
75
1.2359
75
1.2358
75
density functional LSDA 1.2172
4
1.2072
4
               
BLYP 1.2121
4
1.2015
4
               
B1B95   1.1959
4
    1.2329
18
1.2304
18
       
B3LYP 1.2056
4
1.1954
4
    1.2488
75
1.2444
75
1.2470
75
1.2390
75
1.2390
75
1.2390
75
B3LYPultrafine 1.2056
4
1.1954
4
               
B3PW91 1.2081
4
1.1990
4
               
mPW1PW91 1.2067
4
1.1978
4
               
M06-2X 1.2020
4
1.1927
4
               
PBEPBE 1.2163
4
1.2070
4
               
PBEPBEultrafine 1.2163
4
1.2070
4
               
PBE1PBE 1.2086
4
1.1998
4
               
HSEh1PBE 1.2084
4
1.1994
4
               
TPSSh 1.2070
4
1.1987
4
               
wB97X-D 1.2076
4
1.1978
4
    1.2476
28
1.2410
28
1.2446
28
1.2351
28
1.2391
28
1.2391
28
B97D3 1.2147
4
1.2054
4
               
Moller Plesset perturbation MP2 1.2069
4
1.1935
4
    1.2565
75
1.2411
75
1.2517
75
1.2329
75
1.2468
75
1.2465
75
MP2=FULL 1.2057
4
1.1884
4
               
MP3 1.2091
4
1.1951
4
               
MP3=FULL 1.2078
4
1.1896
4
               
MP4 1.2111
4
1.1973
4
               
MP4=FULL 1.2098
4
1.1918
4
               
B2PLYP 1.2046
4
1.1936
4
               
B2PLYP=FULL 1.2042
4
1.1921
4
               
B2PLYP=FULLultrafine 1.2042
4
1.1921
4
               
Configuration interaction CID 1.2071
4
1.1933
4
               
CISD 1.2074
4
1.1937
4
               
Quadratic configuration interaction QCISD 1.2110
4
1.1972
4
               
QCISD(T) 1.2123
4
1.1984
4
               
QCISD(T)=FULL 1.2110
4
1.1929
4
               
QCISD(TQ) 1.2125
4
                 
QCISD(TQ)=FULL 1.2112
4
                 
Coupled Cluster CCD 1.2102
4
1.1964
4
               
CCSD 1.2109
4
1.1971
4
               
CCSD=FULL 1.2097
4
1.1916
4
               
CCSD(T) 1.2123
4
1.1983
4
               
CCSD(T)=FULL 1.2110
4
1.1928
4
               
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.