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Comparison of levels of theory for B-O


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 1.2312
13
PM3 1.2952
5
PM6 1.2590
17
composite G2 1.2512
17
G3 1.2513
17
G3B3 1.2672
17
G3MP2 1.2422
6
G4 1.2612
17
CBS-Q 1.2491
17

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
hartree fock HF 1.2534
15
1.2756
17
1.2756
17
1.2658
17
1.2512
19
1.2510
17
1.2514
17
1.2456
17
1.2457
17
1.2460
17
1.2039
6
1.2484
17
1.2524
19
1.2502
17
1.2477
17
1.2547
15
1.2725
17
1.2480
17
1.2541
13
ROHF 1.1801
1
1.2575
5
1.2575
5
1.2397
3
1.2323
5
1.2323
5
1.2328
5
1.2262
5
1.2202
3
1.1796
1
1.1780
1
1.1821
1
1.1800
1
1.2301
5
1.2296
5
1.2213
3
1.2271
3
1.2242
3
1.2214
3
density functional LSDA 1.2884
16
1.2923
16
1.2923
16
1.2840
16
1.2710
16
1.2708
16
1.2713
16
1.2647
16
1.2649
16
1.2657
16
1.2002
2
1.2330
4
1.2020
2
1.2705
16
1.2667
16
1.2312
1
1.2713
16
1.2506
9
1.2301
1
BLYP 1.3000
15
1.3026
17
1.3026
17
1.2948
17
1.2820
19
1.2799
17
1.2806
17
1.2741
17
1.2742
17
1.2746
17
1.2109
2
1.2453
4
1.2125
2
1.2791
17
1.2758
17
  1.2479
8
1.2439
4
 
B1B95 1.2803
17
1.2868
17
1.2868
17
1.2782
17
1.2641
17
1.2645
17
1.2648
17
1.2586
17
1.2588
17
1.2597
17
1.1958
2
1.2300
4
1.1974
2
1.2637
17
1.2598
17
1.2080
2
1.2688
16
1.2763
12
1.2075
2
B3LYP 1.2844
17
1.2900
17
1.2900
17
1.2814
17
1.2692
19
1.2673
17
1.2680
17
1.2615
17
1.2701
15
1.2621
17
1.2181
6
1.2644
17
1.2678
19
1.3357
17
1.2634
17
1.2708
13
1.2677
17
1.2637
17
1.2710
13
B3LYPultrafine   1.2607
4
    1.2675
17
1.2371
4
1.2377
4
1.2306
4
  1.2018
2
1.1989
2
1.2337
4
1.2005
2
1.2359
4
1.2320
4
  1.2372
4
1.2645
19
 
B3PW91 1.2933
13
1.2901
17
1.2901
17
1.2811
17
1.3362
17
1.2669
17
1.2672
17
1.2611
17
1.2697
15
1.2622
17
1.1988
2
1.2333
4
1.2005
2
1.2662
17
1.2630
17
  1.2357
8
1.2323
4
 
mPW1PW91 1.2890
15
1.2876
17
1.2955
15
1.2785
17
1.2646
17
1.2644
17
1.2646
17
1.2587
17
1.2589
17
1.2597
17
1.1967
2
1.2311
4
1.1983
2
1.2637
17
1.2606
17
  1.2470
12
1.2503
8
 
M06-2X 1.2332
4
1.2545
4
1.2849
19
1.2453
4
1.2601
13
1.2326
4
1.2329
4
1.2264
4
1.2266
4
1.2278
4
1.1942
2
1.2287
4
1.1954
2
1.2315
4
1.2278
4
  1.2330
4
1.2281
4
 
PBEPBE 1.3070
13
1.3024
17
1.3120
13
1.3039
13
1.2791
17
1.2789
17
1.2793
17
1.2731
17
1.2733
17
1.2740
17
1.2301
6
1.2446
4
1.2775
19
1.2785
17
1.2748
17
1.2235
2
1.2690
8
1.2539
10
1.2230
2
PBEPBEultrafine   1.2726
4
    1.2474
8
1.2480
4
1.2485
4
1.2416
4
  1.2141
2
1.2107
2
1.2446
4
1.2124
2
1.2474
4
1.2429
4
  1.2487
4
1.2434
4
 
PBE1PBE 1.2402
4
1.2599
4
1.2599
4
1.2498
4
1.2652
17
1.2355
4
1.2355
4
1.2291
4
1.2293
4
1.2303
4
1.1975
2
1.2319
4
1.1992
2
1.2345
4
1.2305
4
  1.2358
4
1.2308
4
 
HSEh1PBE 1.2405
4
1.2861
13
1.2597
4
1.2497
4
1.2628
13
1.2350
4
1.2625
13
1.2290
4
1.2292
4
1.2301
4
1.1973
2
1.2318
4
1.1990
2
1.2343
4
1.2583
13
  1.2356
4
1.2307
4
 
TPSSh 1.2198
2
1.2663
4
1.2663
4
1.2567
4
1.2751
19
1.2419
4
1.2759
19
1.2358
4
1.2060
2
1.2720
17
1.2041
2
1.2382
4
1.2057
2
1.2411
4
1.2719
19
1.2039
2
1.2423
4
1.2370
4
1.2042
2
wB97X-D 1.2411
4
1.2589
4
1.2880
19
1.2490
4
1.2686
19
1.2351
4
1.2691
19
1.2290
4
1.2638
19
1.2302
4
1.1971
2
1.2659
19
1.1991
2
1.2690
19
1.2656
19
1.2272
4
1.2353
4
1.2659
19
1.2274
4
B97D3 1.2303
2
1.3025
17
1.2476
2
1.2374
2
1.2824
17
1.2198
2
1.2830
17
1.2136
2
1.2775
17
1.2148
2
1.2763
19
1.2160
2
1.2130
2
1.2192
2
1.2792
17
1.2110
2
1.2202
2
1.2777
17
1.2113
2
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
Moller Plesset perturbation MP2 1.2916
13
1.3042
17
1.3042
17
1.2995
17
1.2807
19
1.2773
17
1.2792
17
1.2737
19
1.2698
17
1.2677
15
1.2085
2
1.2738
17
1.2762
19
1.2777
17
1.2756
19
1.2443
8
1.2829
17
1.2545
10
1.2453
8
MP2=FULL 1.2917
15
1.3041
17
1.3109
13
1.3064
13
1.3449
17
1.2757
17
1.2774
17
1.2682
17
1.2763
15
1.2707
13
1.2058
2
1.2421
4
1.2090
2
1.2769
17
1.2755
13
1.2409
8
1.2823
16
1.2586
11
1.2417
8
ROMP2 1.3271
3
1.3429
3
1.3429
3
1.3383
3
1.3024
3
1.3024
3
1.3047
3
1.2933
3
1.2933
3
1.2929
3
1.2118
1
1.2184
1
1.2158
1
1.3028
3
1.2980
3
  1.3098
3
   
MP3         1.2653
17
  1.2697
19
      1.1924
2
1.2301
4
1.1960
2
1.2347
4
1.2288
4
       
MP3=FULL   1.2594
4
1.2594
4
1.2526
4
1.2684
19
1.2340
4
1.2693
19
1.2253
4
1.2257
4
1.2213
4
1.1900
2
1.2287
4
1.1928
2
1.2341
4
1.2239
4
  1.2367
4
1.2238
4
 
MP4 1.2530
1
1.3260
13
    1.3563
17
    1.2160
2
1.2902
13
1.2505
1
1.2135
2
1.2493
4
1.2177
2
1.2530
4
1.2626
14
  1.2576
4
1.2490
4
 
MP4=FULL   1.2828
4
    1.2511
4
      1.2440
4
  1.2107
2
  1.2142
2
1.2523
4
1.2417
4
  1.2554
4
1.2418
4
 
B2PLYP 1.2458
4
1.2673
4
1.2673
4
1.2587
4
1.2696
13
1.2415
4
1.2507
6
1.2346
4
1.2348
4
1.2352
4
1.2041
2
1.2382
4
1.2065
2
1.2408
4
1.2704
17
  1.2431
4
1.2375
4
 
B2PLYP=FULL 1.2458
4
1.2814
8
1.2673
4
1.2587
4
1.2588
8
1.2411
4
1.2593
8
1.2343
4
1.2345
4
1.2336
4
1.2033
2
1.2377
4
1.2055
2
1.2406
4
1.2352
4
  1.2425
4
1.2356
4
 
B2PLYP=FULLultrafine 1.2458
4
1.2673
4
1.2673
4
1.2587
4
1.2414
4
1.2411
4
1.2419
4
1.2343
4
1.2345
4
1.2336
4
1.2033
2
1.2377
4
1.2055
2
1.2406
4
1.2352
4
  1.2425
4
1.2356
4
 
Configuration interaction CID 1.2153
1
1.2971
13
1.2971
13
1.2914
13
1.3320
17
  1.2394
1
1.2632
13
1.2281
1
1.2299
1
1.1915
2
  1.1950
2
1.2141
3
1.2076
3
       
CISD 1.2219
1
1.3014
13
1.3014
13
1.2954
13
1.3518
15
1.2047
1
1.2452
1
1.2657
13
1.2308
1
1.2319
1
1.1941
2
  1.1978
2
1.2175
3
1.2101
3
       
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
Quadratic configuration interaction QCISD 1.2291
1
1.3031
17
1.3123
13
1.3075
13
1.3445
17
1.2848
13
1.2861
13
1.2672
17
1.2422
12
1.2483
10
1.2033
2
1.2405
4
1.2073
2
1.2856
13
1.2510
10
  1.2681
8
1.2484
6
 
QCISD(T) 1.2345
1
      1.2649
12
    1.2404
4
1.2429
1
1.2445
1
1.2085
2
1.2446
4
1.2127
2
1.2632
10
1.2567
10
  1.2510
6
1.2409
6
 
QCISD(T)=FULL         1.2470
4
  1.2475
4
      1.2058
2
  1.2093
2
1.2482
4
1.2372
4
1.2343
4
1.2508
4
1.2369
4
1.2347
4
QCISD(TQ)         1.2452
4
  1.2460
4
      1.2048
2
  1.2088
2
1.2457
4
1.2488
3
1.2046
2
1.2497
4
1.2108
2
1.2070
1
QCISD(TQ)=FULL         1.2439
4
  1.2442
4
      1.2022
2
  1.2054
2
1.2450
4
1.2046
2
1.2015
2
1.2476
4
1.2046
2
1.2036
1
Coupled Cluster CCD 1.2179
1
1.3016
13
1.3016
13
1.2971
13
1.3675
13
1.2767
13
1.2780
13
1.2685
13
1.2396
10
1.2392
10
1.1960
2
1.2337
4
1.1996
2
1.2769
13
1.2419
10
  1.2522
10
1.2363
8
 
CCSD         1.2537
12
    1.2032
2
  1.2329
4
1.2001
2
1.2374
4
1.2039
2
1.2609
8
1.2550
8
1.2302
4
1.2458
4
1.2365
4
1.2001
2
CCSD=FULL         1.2410
4
        1.2273
4
1.1974
2
1.2360
4
1.2006
2
1.2414
4
1.2301
4
1.2270
4
1.2436
4
1.2297
4
1.1969
2
CCSD(T) 1.2321
1
      1.3466
13
1.2558
6
1.2189
2
1.2390
4
1.2203
3
1.2205
3
1.2069
2
1.2431
4
1.2109
2
1.2614
10
1.2552
10
1.2502
10
1.2661
10
1.2568
10
1.2412
8
CCSD(T)=FULL         1.2594
10
          1.2042
2
1.2417
4
1.2075
2
1.2662
8
1.2565
8
1.2372
8
1.2700
8
1.2564
8
1.2293
6
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

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         1.2726
17
1.2585
17
1.2701
17
1.2541
17
1.2713
17
1.2709
17
density functional B1B95         1.2486
6
1.2334
6
       
B3LYP         1.3001
15
1.2777
17
1.2891
17
1.2723
17
1.2878
17
1.2876
17
wB97X-D         1.2583
4
1.2448
4
1.2539
4
1.2385
4
1.2563
4
1.2559
4
Moller Plesset perturbation MP2         1.3111
17
1.2862
17
1.3048
17
1.2803
17
1.3072
17
1.3066
17
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.