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III.G.1.a.

Comparison of levels of theory for N-S


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 1.4648
5
PM3 1.5393
6
PM6 1.5441
8
composite G2 1.5918
8
G3 1.5917
8
G3B3 1.5970
8
G4 1.5541
5
CBS-Q 1.5912
8

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
hartree fock HF 1.6233
7
1.7291
8
1.6166
8
1.7276
8
1.5843
10
1.5916
8
1.5845
8
1.5900
8
1.5900
8
1.5735
8
1.5192
1
1.5846
6
1.6010
8
1.5749
8
1.5655
8
1.5934
8
1.5700
8
1.5626
8
1.5801
2
1.6364
1
ROHF 1.6753
1
1.7540
4
1.6567
4
1.8019
3
1.6291
5
1.6225
4
1.6140
4
1.6225
4
1.6714
3
1.6383
1
  1.6430
1
1.6313
4
1.6032
4
1.6411
2
1.6668
3
1.6408
3
1.6365
2
   
density functional LSDA 1.6425
8
1.6125
8
1.6026
8
1.6823
8
1.5835
8
1.5835
8
1.5717
8
1.5782
8
1.5783
8
1.5665
8
  1.5937
2
1.5925
8
1.5659
8
1.5005
2
1.5789
8
1.5627
6
1.4330
1
1.5569
1
1.5561
1
SVWN   1.6661
6
    1.5639
6
1.5960
2
1.5514
6
1.5929
2
1.5929
2
1.5790
2
    1.6064
2
1.5802
2
  1.5935
2
1.5714
2
  1.5569
1
1.5561
1
BLYP 1.6774
7
1.7217
8
1.6386
8
1.7318
7
1.6167
8
1.6167
8
1.6038
8
1.6257
7
1.6140
8
1.5988
8
  1.6310
2
1.6251
8
1.6093
7
  1.5393
1
    1.5903
1
1.5894
1
B1B95 1.6315
8
1.6103
8
1.6005
8
1.6785
8
1.5796
8
1.5799
8
1.5697
8
1.5771
8
1.5773
8
1.5654
8
  1.6034
2
1.5887
8
1.5652
8
1.5262
3
1.5774
8
1.5671
7
1.5181
3
1.5297
2
1.5725
1
B3LYP 1.6440
8
1.6973
8
1.6141
8
1.6938
8
1.5938
8
1.5938
8
1.5833
8
1.5908
8
1.6027
7
1.5774
8
1.4903
1
1.5714
6
1.6023
8
1.5772
8
1.5676
8
1.5903
8
1.5688
8
1.5618
8
1.5380
2
1.5826
1
B3LYPultrafine         1.5939
8
              1.6274
2
1.6020
2
  1.6165
2
1.5369
5
     
B3PW91 1.6464
7
1.7021
7
1.6068
8
1.6851
8
1.5862
8
1.5861
8
1.5759
8
1.5828
8
1.5941
7
1.5709
8
  1.6076
2
1.5947
8
1.5705
8
  1.5144
1
    1.5740
1
1.5733
1
mPW1PW91 1.6261
8
1.6659
7
1.6140
7
1.6804
8
1.5819
8
1.5818
8
1.5720
8
1.5788
8
1.5789
8
1.5669
8
  1.6053
2
1.5903
8
1.5667
8
  1.5990
5
1.6007
4
  1.5731
1
1.5725
1
M06-2X 1.6567
3
1.7448
3
1.6621
3
1.7416
3
1.5809
7
1.6399
3
1.6310
3
1.6409
3
1.6410
3
1.6242
3
  1.6135
2
1.6493
3
1.6257
3
  1.6398
3
1.6190
3
  1.5893
1
1.5888
1
PBEPBE 1.6654
7
1.7084
8
1.6370
7
1.7167
7
1.6034
8
1.6034
8
1.5912
8
1.6006
8
1.6008
8
1.5875
8
1.5049
1
1.6164
2
1.6119
8
1.5870
8
1.5479
3
1.6380
4
1.5969
5
1.5370
3
1.5776
1
1.5769
1
PBEPBEultrafine         1.5881
3
              1.6275
2
1.6028
2
  1.6146
2
1.5937
2
     
PBE1PBE 1.6313
2
1.6230
2
1.6230
2
1.7041
2
1.5631
6
1.6044
2
1.5950
2
1.6033
2
1.6033
2
1.5892
2
  1.6048
2
1.6143
2
1.5905
2
  1.6042
2
1.5836
2
  1.5728
1
1.5723
1
HSEh1PBE 1.6640
3
1.7444
3
1.6599
3
1.7413
3
1.5840
7
1.6383
3
1.6271
3
1.6380
3
1.6381
3
1.6222
3
  1.6057
2
1.6473
3
1.6228
3
  1.6357
3
1.6143
3
  1.5732
1
1.5726
1
TPSSh         1.5604
6
  1.5550
6
            1.5513
6
           
Moller Plesset perturbation MP2 1.6606
6
1.7146
8
1.6025
8
1.7120
8
1.5667
9
1.5717
8
1.5615
8
1.5668
8
1.5669
8
1.5763
7
  1.5492
6
1.5856
8
1.5522
9
1.5350
6
1.5791
8
1.5503
8
1.5307
6
1.4868
2
1.5578
1
MP2=FULL 1.6604
6
1.7146
8
1.6229
7
1.7236
7
1.5649
9
1.5699
8
1.5780
7
1.5854
7
1.5855
7
1.5712
7
  1.5888
2
1.5952
8
1.5483
9
1.5387
7
1.5887
6
1.5558
6
1.5553
6
1.4828
2
1.5524
1
ROMP2 1.6853
2
1.6755
3
1.6755
3
1.7734
3
1.6207
3
1.6203
3
1.5932
3
1.6183
3
1.6181
3
1.5934
3
  1.5832
1
1.6324
3
1.5857
3
  1.6015
3
       
MP3         1.5752
8
  1.5495
6
                        1.5910
1
MP3=FULL         1.5484
6
  1.5433
6
                         
MP4   1.7956
7
    1.5920
8
    1.4530
1
1.6059
7
    1.6077
2
1.6227
2
1.5733
7
  1.6188
2
1.5880
2
  1.5767
1
1.5766
1
MP4=FULL   1.7222
2
    1.6049
2
      1.6020
2
      1.6206
2
1.5895
2
  1.6156
2
1.5821
2
  1.5724
1
1.5711
1
B2PLYP         1.5370
5
                1.5025
3
           
Configuration interaction CID   1.7171
7
1.6203
7
1.7143
7
1.5768
8
    1.5715
8
                    1.5966
1
1.5967
1
CISD   1.7284
7
1.6263
7
1.7260
7
1.5831
8
    1.5910
7
                    1.5975
1
1.5976
1
Quadratic configuration interaction QCISD   1.7395
8
1.6423
7
1.7565
7
1.6011
8
1.6123
7
1.6024
7
1.5948
8
1.6067
7
1.5950
7
  1.6328
2
1.6265
7
1.5839
8
  1.6531
4
1.6208
4
  1.6013
1
1.6018
1
QCISD(T)         1.6156
7
    1.5274
1
      1.6283
2
1.6302
7
1.5998
7
  1.6045
5
1.5735
5
  1.5928
1
1.5933
1
Coupled Cluster CCD   1.7217
7
1.6248
7
1.7189
7
1.5794
8
1.5952
7
1.5850
7
1.5739
8
1.5905
7
1.5792
7
  1.6192
2
1.6085
7
1.5791
7
  1.6023
7
1.5725
7
  1.5197
2
1.5975
1
CCSD         1.5955
8
    1.5082
1
      1.6286
2
1.6515
4
1.6223
4
1.5972
2
1.6374
2
1.6048
2
1.5942
2
1.6009
1
1.6013
1
CCSD=FULL         1.6208
2
            1.6277
2
1.6381
2
1.6052
2
1.5940
2
1.6337
2
1.5983
2
1.5901
2
1.5960
1
1.5949
1
CCSD(T)         1.6181
5
1.5235
1
  1.5147
1
    1.4966
1
1.6256
2
1.6278
7
1.5865
8
1.6115
5
1.6221
7
1.5912
7
1.6113
4
1.5463
2
1.5923
1
CCSD(T)=FULL         1.5949
7
            1.6250
2
1.6304
5
1.6016
6
1.5940
3
1.6275
5
1.5935
5
1.5885
2
1.5437
2
1.5862
1

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 1.7253
8
1.5991
8
1.7245
8
1.5990
8
1.7090
7
1.7021
8
density functional B1B95 1.6127
1
1.5201
1
       
B3LYP 1.7037
8
1.6050
8
1.6990
8
1.6031
8
1.7039
7
1.6773
8
Moller Plesset perturbation MP2 1.7170
8
1.5856
8
1.7111
8
1.5820
8
1.7143
7
1.6877
8
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.