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Comparison of levels of theory for H-Na


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 PM3 2.1496
2
PM6 1.3378
3
composite G2 2.2491
3
G3 2.2491
3
G3B3 2.2265
3
G4 2.2288
3
CBS-Q 2.2491
3

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-pCVTZ
hartree fock HF 1.9481
3
2.2640
3
2.2422
3
2.2846
3
2.2507
3
2.2394
3
2.2210
3
2.2265
3
2.2092
3
2.2383
3
1.9151
1
2.3271
3
2.2574
3
2.2125
3
2.2110
3
2.2287
3
2.2082
3
2.2059
3
2.2821
2
ROHF   2.7965
1
2.7395
1
2.8666
1
2.7700
1
2.7430
1
2.7700
1
2.6905
1
2.6413
1
    2.9879
1
2.7836
1
2.6487
1
2.6622
1
2.7281
1
2.6695
1
2.6661
1
2.6494
1
density functional LSDA 1.8451
2
2.2503
2
2.2503
2
2.2500
2
2.2078
2
2.2023
2
2.2014
2
2.1759
2
2.1709
2
2.1970
2
  2.2850
2
2.2455
2
2.1846
2
  2.2159
2
2.1800
2
  2.1745
2
SVWN   2.2065
3
    2.1455
3
2.2023
2
2.1263
3
2.1759
2
2.1709
2
2.1970
2
  2.1994
3
2.2455
2
2.1846
2
  2.2159
2
2.1800
2
  2.1745
2
BLYP 1.9374
3
2.2237
3
2.2020
3
2.2259
3
2.0838
3
2.1902
3
2.1726
3
2.1821
3
2.1725
3
2.1880
3
  2.3520
2
2.2109
3
2.1788
3
  1.8841
1
    2.2379
2
B1B95 1.8224
2
1.9858
2
1.9834
2
1.8984
1
1.9677
2
1.9668
2
1.9933
1
1.9703
2
1.9692
2
2.2250
3
  2.4406
2
2.2389
3
1.8951
1
2.0188
1
1.9474
2
1.9486
2
1.9956
1
2.2982
2
B3LYP 1.9217
3
2.2144
3
2.1919
3
2.2148
3
2.1836
3
2.1768
3
2.1607
3
2.1665
3
2.1574
3
2.1750
3
1.8822
1
2.2436
3
2.1992
3
2.1645
3
2.1535
3
2.1740
3
2.1525
3
2.1387
3
2.2222
2
B3LYPultrafine         2.1819
3
              2.2749
2
2.2297
2
  2.2579
2
2.2220
3
  2.2222
2
B3PW91 1.9313
3
2.2652
3
2.2413
3
2.2607
3
2.2256
3
2.2173
3
2.2020
3
2.2061
3
2.1936
3
2.2163
3
  2.4143
2
2.2400
3
2.2006
3
  1.8920
1
    2.2713
2
mPW1PW91 1.9285
3
2.2475
3
2.2242
3
2.2477
3
2.2144
3
2.2067
3
2.1918
3
2.1966
3
2.1850
3
2.2055
3
  2.3919
2
2.2282
3
2.1925
3
  2.3011
2
2.2701
2
  2.2615
2
M06-2X 1.6583
1
2.3837
2
2.0805
3
2.4469
2
2.2545
3
2.3568
2
2.3564
2
2.4709
2
2.3777
2
2.3541
2
  2.5162
2
2.4247
2
2.3492
2
  2.4236
2
2.3801
2
  2.3439
2
PBEPBE 1.9346
3
2.2411
3
2.2201
3
2.2351
3
2.2070
3
2.2005
3
2.1850
3
2.1930
3
2.1831
3
2.1988
3
1.8962
1
2.3661
2
2.2210
3
2.1909
3
2.3222
2
2.2923
2
2.2607
2
2.3003
2
2.2552
2
PBEPBEultrafine         2.2810
2
              2.3005
2
2.2602
2
  2.2882
2
2.2578
2
  2.2552
2
PBE1PBE 1.9017
2
2.2942
2
2.2942
2
2.3264
2
2.2020
3
2.2835
2
2.2734
2
2.2581
2
2.2434
2
2.2750
2
  2.3726
2
2.3032
2
2.2552
2
  2.2859
2
2.2559
2
  2.2487
2
HSEh1PBE 1.9018
2
2.2361
3
2.2916
2
2.3224
2
2.2001
3
2.2713
2
2.1783
3
2.2567
2
2.2427
2
2.2726
2
  2.3717
2
2.3007
2
2.1829
3
  2.2838
2
2.2551
2
  2.2478
2
TPSSh   1.9264
1
1.9195
1
1.9025
1
2.0835
3
1.8961
1
2.0818
3
1.9011
1
  2.0819
3
    1.9027
1
2.0802
3
  1.8954
1
1.8979
1
  2.2491
2
wB97X-D     2.0969
3
  2.0885
3
  2.0880
3
  2.0890
3
    2.0889
3
2.0880
3
2.0893
3
    2.0890
3
   
B97D3   2.1006
3
    2.0950
3
      2.0989
3
              2.0947
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 cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pCVTZ
Moller Plesset perturbation MP2 1.9438
3
2.2750
3
2.2465
3
2.2928
3
2.0905
3
2.2323
3
2.2153
3
2.0893
3
2.1975
3
2.3914
2
  2.3180
3
2.2521
3
2.2061
3
2.2893
2
2.2288
3
2.2071
3
2.2920
2
2.2796
2
MP2=FULL 1.9372
3
2.2748
3
2.2444
3
2.2908
3
2.2442
3
2.2259
3
2.2090
3
2.2089
3
2.1857
3
2.2085
3
  2.4392
2
2.2474
3
2.1798
3
2.1384
2
2.3209
2
2.2583
2
1.9196
2
2.2456
2
ROMP2 2.2358
1
2.7397
1
2.7397
1
2.8657
1
2.7741
1
2.7432
1
2.7408
1
2.6912
1
2.6415
1
2.7476
1
  2.9880
1
2.7833
1
2.6495
1
  2.7286
1
    2.6496
1
MP3         1.9919
2
  2.0959
2
                      1.9116
1
MP3=FULL         2.0915
3
  2.0878
3
                      2.2463
2
MP4   2.2868
3
    2.2562
3
    1.9197
1
2.1958
3
    2.4486
2
2.3504
2
2.2086
3
  2.3266
2
2.2970
2
  2.2819
2
MP4=FULL   2.3760
2
    2.3419
2
      2.2579
2
      2.3431
2
2.2388
2
  2.3217
2
2.2564
2
  2.2456
2
B2PLYP         2.1958
3
                2.2812
1
        2.2334
2
B2PLYP=FULL                                     2.2218
2
Configuration interaction CID   2.2887
3
2.2578
3
2.3041
3
2.2566
3
    2.2228
3
                    2.2822
2
CISD   2.2949
3
2.2630
3
2.3096
3
2.2611
3
    2.2272
3
                    2.2837
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 cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pCVTZ
Quadratic configuration interaction QCISD   2.2949
3
2.2631
3
2.3097
3
2.2611
3
2.2402
3
2.2234
3
2.2272
3
2.1999
3
2.2324
3
  2.4526
2
2.2574
3
2.2114
3
  2.3287
2
2.2983
2
  2.2837
2
QCISD(T)         2.2630
3
1.9216
1
1.9214
1
1.9287
1
      2.4524
2
2.2574
3
2.2116
3
  2.2356
3
2.2136
3
  2.2838
2
Coupled Cluster CCD   2.2887
3
2.2578
3
2.3041
3
2.2566
3
2.2363
3
2.2196
3
2.2228
3
2.1966
3
2.2294
3
  2.4490
2
2.2539
3
2.2090
3
  2.2335
3
2.2115
3
  2.2822
2
CCSD         2.2613
3
1.9216
1
1.9214
1
1.9287
1
      2.4526
2
2.3537
2
2.2859
2
2.2939
2
2.3287
2
2.2983
2
2.2961
2
2.2837
2
CCSD=FULL         2.3469
2
            2.4461
2
2.3459
2
2.2422
2
2.1319
2
2.3236
2
2.2587
2
1.9101
2
2.2499
2
CCSD(T)   1.9707
1
    2.3561
2
1.9216
1
1.9214
1
1.9287
1
1.9133
1
  1.9214
1
2.4524
2
2.2574
3
2.2115
3
2.2135
3
2.2356
3
2.2136
3
2.2962
2
2.2838
2
CCSD(T)=FULL   1.9715
1
1.9555
1
1.9565
1
2.7564
1
1.9193
1
1.9190
1
1.9229
1
      2.4461
2
2.3466
2
2.2415
2
2.1295
2
2.3236
2
2.2576
2
1.7995
3
2.2483
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 cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pCVTZ

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 2.4721
2
2.4180
2
2.5659
2
2.4180
2
2.4559
2
2.4062
2
density functional B1B95 1.9580
1
1.9416
1
       
B3LYP 2.4553
2
2.4050
2
2.5567
2
2.4309
2
2.4448
2
2.3261
2
Moller Plesset perturbation MP2 2.4800
2
2.4198
2
2.5683
2
2.4140
2
2.4650
2
2.4107
2
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.