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III.G.1.a.

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 2.4625
3
PM6 1.3359
5
composite G2 2.3793
4
G3 2.2863
5
G3B3 2.2386
5
G4 2.2288
3
CBS-Q 2.2863
5

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
hartree fock HF 1.9467
5
2.3030
5
2.2778
5
2.3275
5
2.2507
6
2.2748
5
2.2633
5
2.2577
5
2.2373
5
2.2744
5
1.9151
2
2.3766
5
2.2948
5
2.3215
4
2.2429
5
2.3536
4
2.2427
5
2.2406
5
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
density functional LSDA 1.7838
3
2.1349
3
2.1327
3
2.1262
3
2.0970
3
2.0923
3
2.0917
3
2.0759
3
2.0715
3
2.0873
3
  2.2850
2
2.1224
3
2.0803
3
  2.0966
3
2.1800
2
 
SVWN   2.2366
5
    2.1703
5
2.2023
2
2.1563
5
2.1759
2
2.1709
2
2.1970
2
    2.2455
2
2.1846
2
  2.2159
2
2.1800
2
 
BLYP 1.8748
4
2.2541
5
2.3105
4
2.3501
4
2.2262
5
2.2187
5
2.2872
4
2.2857
4
2.1971
5
2.2167
5
  2.3520
2
2.3298
4
2.2838
4
  1.8841
2
   
B1B95 1.7718
3
1.9628
3
1.9597
3
1.8984
2
1.9430
3
1.9421
3
1.9933
1
1.9462
3
1.9449
3
2.1412
4
  2.4406
2
2.2783
5
1.8951
2
2.0188
1
1.9283
3
1.9486
2
1.9956
1
B3LYP 1.8593
4
2.2462
5
2.2208
5
2.3391
4
2.2128
5
2.2053
5
2.1953
5
2.2674
4
2.2551
4
2.2039
5
1.8822
2
2.2827
5
2.2313
5
2.2668
4
2.1811
5
2.2920
4
2.1829
5
2.1682
5
B3LYPultrafine         2.2108
5
              2.2749
2
2.2297
2
  2.2579
2
2.2220
3
 
B3PW91 1.9313
3
2.3026
5
2.3650
4
2.4024
4
2.2617
5
2.2522
5
2.3298
4
2.3219
4
2.3044
4
2.2520
5
  2.4143
2
2.3725
4
2.3149
4
  1.8920
2
   
mPW1PW91 1.9285
3
2.2830
5
2.3423
4
2.2874
5
2.2492
5
2.2404
5
2.2312
5
2.2271
5
2.2136
5
2.2399
5
  2.3919
2
2.3563
4
2.3042
4
  2.1643
3
2.2701
2
 
M06-2X 1.6583
1
2.3837
2
2.3137
2
2.4469
2
2.3002
5
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
 
PBEPBE 1.9346
3
2.1624
4
2.3323
4
2.3619
4
2.2382
5
2.2311
5
2.2215
5
2.2215
5
2.2101
5
2.2298
5
1.8962
2
2.3661
2
2.2545
5
2.2198
5
2.4212
3
2.2923
2
2.2607
2
2.4001
3
PBEPBEultrafine         2.1539
3
              2.3005
2
2.2602
2
  2.2882
2
2.2578
2
 
PBE1PBE 1.9017
2
2.2942
2
2.2942
2
2.3264
2
2.2346
5
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
 
HSEh1PBE 1.9018
2
2.3215
2
2.2916
2
2.3224
2
2.2321
5
2.2713
2
2.2705
2
2.2567
2
2.2427
2
2.2726
2
  2.3717
2
2.3007
2
2.2542
2
  2.2838
2
2.2551
2
 
TPSSh   1.9264
1
1.9195
1
1.9025
1
2.0835
3
1.8961
1
2.0818
3
1.9011
1
        1.9027
1
2.0802
3
  1.8954
1
1.8979
1
 
Moller Plesset perturbation MP2 2.0168
4
2.3127
5
2.2820
5
2.3348
5
2.2867
5
2.2695
5
2.2588
5
2.2518
5
2.2281
5
2.5100
3
  2.3696
5
2.2909
5
2.3167
4
2.1652
3
2.2669
5
2.2419
5
2.1673
3
MP2=FULL 2.0074
4
2.3120
5
2.3665
4
2.4325
4
2.2817
5
2.2621
5
2.2514
5
2.2416
5
2.2944
4
2.3305
4
  2.4392
2
2.3780
4
2.2785
4
2.0144
3
2.1800
3
2.2583
2
1.9196
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
   
MP3         1.9689
3
  2.0959
2
                     
MP3=FULL         2.0915
3
  2.0878
3
                     
MP4   2.3230
5
    2.3857
4
    1.9197
1
2.3071
4
    2.4486
2
2.3504
2
2.2388
5
  2.3266
2
2.2970
2
 
MP4=FULL   2.3760
2
    2.3419
2
      2.2579
2
      2.3431
2
2.2388
2
  2.3217
2
2.2564
2
 
B2PLYP         2.1958
3
                2.2812
1
       
Configuration interaction CID   2.4157
4
2.3782
4
2.4447
4
2.3849
4
    2.3397
4
                   
CISD   2.3304
5
2.3821
4
2.4489
4
2.3883
4
    2.3430
4
                   
Quadratic configuration interaction QCISD   2.3304
5
2.3822
4
2.4489
4
2.2982
5
2.2769
5
2.3527
4
2.3430
4
2.2307
5
2.3611
4
  2.4526
2
2.2959
5
2.2412
5
  2.3287
2
2.2983
2
 
QCISD(T)         2.3003
5
1.9216
2
1.9214
2
1.9287
2
      2.4524
2
2.3889
4
2.3210
4
  2.3588
4
2.3278
4
 
Coupled Cluster CCD   2.3248
5
2.3782
4
2.4447
4
2.3849
4
2.2734
5
2.3499
4
2.3397
4
2.3078
4
2.3589
4
  2.4490
2
2.2926
5
2.3189
4
  2.3572
4
2.3260
4
 
CCSD         2.2985
5
1.9216
2
1.9214
2
1.9287
2
      2.4526
2
2.3537
2
2.2859
2
2.2939
2
2.3287
2
2.2983
2
2.2961
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
CCSD(T)   1.9707
1
    2.2168
3
1.9216
2
1.9214
2
1.9287
2
1.9133
1
  1.9214
2
2.4524
2
2.2958
5
2.2414
5
2.3257
4
2.2730
5
2.2477
5
2.4196
3
CCSD(T)=FULL   1.9715
1
1.9555
1
1.9565
1
2.5295
3
1.9193
1
1.9190
1
1.9229
1
      2.4461
2
2.3466
2
2.2415
2
2.2528
3
2.3236
2
2.2576
2
1.9115
4

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 2.5953
3
2.5332
3
2.7332
3
2.5386
3
2.5708
3
2.5203
3
density functional B1B95 1.9580
2
1.9416
1
       
B3LYP 2.5739
3
2.5173
3
2.7205
3
2.5568
3
2.5567
3
2.4279
3
Moller Plesset perturbation MP2 2.4800
2
2.4198
2
2.5683
2
2.4140
2
2.4650
2
2.5233
3
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.