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Comparison of levels of theory for N-Mg


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 1.9437
2
PM3 1.8068
2
PM6 1.8952
2
composite G2 3.5995
2
G3 3.5995
2
G3B3 2.0105
2
G4 1.9865
2
CBS-Q 3.5993
2

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 daug-cc-pVDZ daug-cc-pVTZ
hartree fock HF 1.9345
2
3.1965
2
3.0245
2
3.6239
2
3.5526
2
3.6073
2
2.0349
2
3.7363
2
3.7363
2
2.0090
2
2.0068
2
4.3037
2
3.4850
2
1.9848
2
1.9813
2
2.0126
2
1.9876
2
2.0073
2
2.0908
1
2.0609
1
ROHF   2.0685
2
2.0169
2
2.0931
2
2.0172
2
2.0172
2
2.0313
2
2.0232
2
2.0232
2
  2.0042
2
2.0581
2
2.0165
2
2.0035
2
2.0088
1
2.0062
2
2.0065
2
2.0035
2
2.0264
1
2.0123
1
density functional BLYP 2.0427
2
2.0453
2
2.0171
2
2.0695
2
2.0273
2
2.0273
2
2.0376
2
2.0331
2
2.0331
2
2.0052
2
2.0127
2
2.1413
2
2.1035
2
2.0143
2
  2.0284
2
2.0167
2
  2.1276
1
2.1142
1
B1B95 1.9203
2
2.0061
2
2.0061
2
2.0641
2
2.0175
2
2.0175
2
2.0235
2
2.0131
2
2.0131
2
1.9858
2
1.9880
2
2.0449
2
2.0106
2
1.9894
2
  2.0074
2
1.9905
2
  2.1037
1
2.0842
1
B3LYP 1.9275
2
2.0378
2
2.0042
2
2.0614
2
2.0105
2
2.0105
2
2.0186
2
2.0146
2
2.0146
2
1.9865
2
1.9912
2
2.0408
2
2.0101
2
1.9935
2
1.9895
2
2.0084
2
1.9951
2
1.9906
2
2.1030
1
2.0874
1
B3LYPultrafine   2.0378
2
    2.0104
2
2.0104
2
2.0186
2
2.0146
2
  1.9864
2
1.9912
2
2.0407
2
2.0100
2
1.9935
2
  2.0083
2
1.9951
2
  2.1030
1
2.0874
1
B3PW91 1.9201
2
2.0320
2
2.0036
2
2.0543
2
2.0048
2
2.0048
2
2.0110
2
2.0074
2
2.0074
2
1.9813
2
1.9831
2
2.0333
2
2.0046
2
1.9853
2
  2.0013
2
1.9864
2
  2.0936
1
2.0757
1
mPW1PW91 1.9161
2
2.0298
2
2.0007
2
2.0520
2
2.0008
2
2.0008
2
2.0069
2
2.0030
2
2.0030
2
1.9766
2
1.9782
2
2.0297
2
2.0004
2
1.9803
2
  1.9968
2
1.9815
2
  2.0864
1
2.0681
1
M06-2X 1.9161
2
2.0221
2
1.9881
2
2.0509
2
1.9982
2
1.9982
2
2.0045
2
2.0027
2
2.0027
2
1.9868
2
1.9798
2
2.0309
2
1.9963
2
1.9919
2
  1.9956
2
1.9826
2
  2.0909
1
2.0755
1
PBEPBE 2.0298
2
2.0433
2
2.0152
2
2.0651
2
2.0219
2
2.0219
2
2.1064
2
2.0248
2
2.0248
2
1.9990
2
2.0036
2
2.1291
2
2.0212
2
2.0046
2
  2.0211
2
2.0065
2
  2.1155
1
2.0988
1
PBEPBEultrafine   2.0433
2
    2.0219
2
2.0219
2
2.1064
2
2.0248
2
  1.9988
2
2.0036
2
2.1290
2
2.0212
2
2.0045
2
  2.0207
2
2.0065
2
  2.1155
1
2.0988
1
PBE1PBE 1.9160
2
2.0020
2
2.0020
2
2.0590
2
2.0031
2
2.0031
2
2.0094
2
2.0050
2
2.0050
2
1.9784
2
1.9803
2
2.0314
2
2.0026
2
1.9822
2
  1.9991
2
1.9834
2
  2.0902
1
2.0715
1
HSEh1PBE 1.9172
2
2.0318
2
2.0027
2
2.0549
2
2.0035
2
2.0035
2
2.0100
2
2.0057
2
2.0057
2
1.9793
2
1.9812
2
2.0320
2
2.0031
2
1.9834
2
  2.0000
2
1.9847
2
  2.0910
1
2.0728
1
TPSSh 1.9170
2
2.0377
2
2.0061
2
2.0504
2
2.0042
2
2.0042
2
2.0200
2
2.0061
2
2.0061
2
1.9828
2
1.9846
2
2.0290
2
2.0030
2
1.9856
2
1.9827
2
2.0023
2
1.9875
2
1.9838
2
2.0907
1
2.0741
1
wB97X-D 1.9232
2
2.0275
2
1.9997
2
2.0569
2
2.0033
2
2.0033
2
2.0088
2
2.0049
2
2.0049
2
1.9774
2
1.9789
2
2.0365
2
2.0025
2
1.9809
2
1.9770
2
1.9983
2
1.9825
2
1.9779
2
2.0944
1
2.0755
1
B97D3 2.0433
2
2.0785
2
2.0485
2
2.0998
2
2.0532
2
2.0532
2
2.0607
2
2.0586
2
2.0586
2
2.0303
2
2.0351
2
2.0859
2
2.0505
2
2.0361
2
2.0321
2
2.0523
2
2.0385
2
2.0332
2
2.1672
1
2.0380
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 daug-cc-pVDZ daug-cc-pVTZ
Moller Plesset perturbation MP2 1.8980
2
1.9891
2
2.0005
2
2.0444
2
2.0058
2
2.0058
2
2.0144
2
1.9548
2
1.9548
2
1.9378
2
1.9393
2
1.9669
2
2.0037
2
1.9804
2
1.9767
2
2.0110
2
1.9856
2
1.9353
2
2.0668
1
2.0400
1
MP2=FULL 1.8999
2
1.9941
2
2.0040
2
2.0466
2
2.0073
2
2.0073
2
2.0136
2
1.9562
2
1.9562
2
1.9328
2
1.9365
2
1.9672
2
2.0055
2
1.9732
2
1.9624
2
2.0084
2
1.9740
2
1.9218
2
2.0633
1
2.0270
1
ROMP2 1.9858
1
2.0834
1
2.0834
1
2.1546
1
2.0774
1
2.0774
1
2.0839
1
2.0712
1
2.0712
1
2.0464
1
2.0487
1
2.1285
1
2.0772
1
2.0462
1
  2.0786
1
    2.0784
1
2.0525
1
MP3         2.0200
2
  2.0264
2
      1.9664
2
2.0027
2
2.0183
2
1.9850
2
        2.0887
1
2.0515
1
MP3=FULL   3.0226
2
2.0286
2
2.1033
2
2.0220
2
2.0220
2
2.0259
2
1.9952
2
1.9952
2
1.9608
2
1.9643
2
2.0037
2
2.0204
2
1.9779
2
  2.0200
2
1.9779
2
  2.0860
1
2.0366
1
MP4   2.9928
2
    2.0302
2
      1.9949
2
  1.9685
2
2.0152
2
2.0292
2
1.9919
2
  2.0308
2
1.9982
2
  2.1007
1
2.0619
1
MP4=FULL   2.9911
2
    2.0323
2
      1.9966
2
  1.9631
2
  2.0314
2
1.9844
2
  2.0283
2
1.9846
2
  2.0978
1
2.0456
1
B2PLYP 1.9172
2
2.0412
2
1.9962
2
2.0475
2
1.9979
2
1.9979
2
2.0062
2
1.9986
2
1.9986
2
1.9736
2
1.9773
2
2.0236
2
1.9971
2
1.9772
2
  1.9980
2
1.9807
2
  2.0925
1
2.0710
1
B2PLYP=FULL 1.9178
2
2.0419
2
1.9972
2
2.0481
2
1.9984
2
1.9984
2
2.0059
2
1.9990
2
1.9990
2
1.9719
2
1.9758
2
2.0238
2
1.9977
2
1.9748
2
  1.9970
2
1.9767
2
  2.0911
1
2.0654
1
B2PLYP=FULLultrafine 1.9179
2
2.0419
2
1.9972
2
2.0481
2
1.9984
2
1.9984
2
2.0059
2
1.9990
2
1.9990
2
1.9718
2
1.9758
2
2.0237
2
1.9976
2
1.9748
2
  1.9969
2
1.9767
2
  2.0911
1
2.0654
1
Configuration interaction CID   3.0183
2
2.0470
2
3.3651
2
2.0247
2
    1.9981
2
    1.9640
2
  2.0234
2
1.9835
2
        2.0936
1
2.0506
1
CISD   4.0586
1
2.0610
2
3.3365
2
2.0387
2
    2.0232
2
    1.9827
2
  2.0382
2
1.9911
2
        2.1152
1
2.0660
1
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 daug-cc-pVDZ daug-cc-pVTZ
Quadratic configuration interaction QCISD   2.9988
2
2.0683
2
3.3275
2
2.0574
2
2.0574
2
2.0558
2
2.0515
2
2.0515
2
2.0022
2
2.0025
2
2.0849
2
2.0587
2
1.9985
2
  2.0455
2
2.0038
2
  2.1397
1
2.0842
1
QCISD(T)         2.1614
1
    2.1459
1
    2.0833
1
2.1895
1
2.1622
1
2.0821
1
  2.1363
1
2.0863
1
  2.1356
1
2.0854
1
QCISD(T)=FULL         2.1633
1
  2.1484
1
      2.0776
1
  2.1648
1
2.0693
1
2.0514
1
2.1368
1
2.0677
1
2.0527
1
2.1310
1
2.0617
1
Coupled Cluster CCD   3.0119
2
2.0560
2
3.3685
2
2.0344
2
2.0344
2
2.0370
2
2.0046
2
2.0046
2
1.9685
2
1.9688
2
2.0161
2
2.0337
2
1.9892
2
  2.0301
2
1.9938
2
  2.1050
1
2.0591
1
CCSD         2.0565
2
2.0565
2
2.0553
2
2.0498
2
2.0498
2
2.0023
2
2.0017
2
2.0777
2
2.0577
2
1.9979
2
1.9911
2
2.0455
2
2.0035
2
1.9962
2
2.1405
1
2.0826
1
CCSD=FULL         2.0574
2
        1.9956
2
1.9937
2
2.0786
2
2.0589
2
1.9874
2
1.9721
2
2.0428
2
1.9864
2
1.9742
2
2.1352
1
2.0581
1
CCSD(T)         2.1589
1
2.1589
1
2.1478
1
2.1434
1
2.1434
1
2.0844
1
2.0809
1
2.1900
1
2.1615
1
2.0798
1
2.0705
1
2.1336
1
2.0837
1
2.0721
1
2.1324
1
2.0829
1
CCSD(T)=FULL         2.0496
2
          1.9941
2
2.0646
2
2.0508
2
1.9888
2
1.9744
2
2.0407
2
1.9885
2
1.9791
2
2.1285
1
2.0599
1
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 daug-cc-pVDZ daug-cc-pVTZ

average calculated bond lengths (Å)
Methods with effective core potentials (select basis sets)
CEP-31G CEP-31G* CEP-121G CEP-121G* LANL2DZ SDD cc-pVTZ-PP aug-cc-pVTZ-PP Def2TZVPP
hartree fock HF 3.9053
2
3.8093
2
4.1471
2
3.9818
2
3.8304
2
3.7496
2
    1.9856
2
ROHF                 1.9840
2
density functional BLYP                 2.0134
2
B1B95                 1.9891
2
B3LYP 2.0893
2
2.0223
2
2.0731
2
2.0194
2
2.0249
2
2.0636
2
    1.9926
2
B3LYPultrafine                 1.9926
2
B3PW91                 1.9853
2
mPW1PW91                 1.9803
2
M06-2X                 1.9899
2
PBEPBE                 2.0046
2
PBEPBEultrafine                 2.0046
2
PBE1PBE                 1.9819
2
HSEh1PBE                 1.9832
2
TPSSh                 1.9859
2
wB97X-D 2.0920
2
2.0151
2
2.0729
2
2.0115
2
2.0268
2
2.0624
2
    1.9804
2
B97D3                 2.0375
2
Moller Plesset perturbation MP2 3.5524
2
2.0171
2
2.0562
2
2.0061
2
2.0230
2
2.0448
2
    1.9800
2
MP2=FULL                 1.9764
2
ROMP2                 2.0471
1
MP3                 1.9855
2
MP3=FULL                 1.9821
2
MP4                 1.9931
2
MP4=FULL                 1.9898
2
B2PLYP                 1.9773
2
B2PLYP=FULL                 1.9763
2
B2PLYP=FULLultrafine                 1.9762
2
Configuration interaction CID                 1.9839
2
CISD                 1.9921
2
Quadratic configuration interaction QCISD                 1.9998
2
QCISD(T)                 2.0841
1
QCISD(T)=FULL                 2.0814
1
Coupled Cluster CCD                 1.9899
2
CCSD                 1.9992
2
CCSD=FULL                 1.9936
2
CCSD(T)                 2.0816
1
CCSD(T)=FULL                 1.9952
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.