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Comparison of levels of theory for N-Al


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 1.5627
3
PM3 1.8729
1
PM6 1.6686
5
composite G2 1.8053
3
G3 1.8053
3
G3B3 1.7864
3
G3MP2 1.8317
1
G4 1.7594
5
CBS-Q 1.8063
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-pV(D+d)Z cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
hartree fock HF 1.7458
3
1.8311
3
1.7983
3
1.8604
3
1.7852
5
1.8052
3
1.8157
3
1.8029
3
1.8029
3
1.7908
3
1.8336
2
1.7897
5
1.8320
3
1.8035
3
1.7976
3
1.8420
3
1.8049
3
1.7985
3
1.8350
1
1.8219
1
1.8574
1
1.8336
2
1.8428
1
1.8854
1
1.8246
5
ROHF 1.7663
1
1.8581
1
    1.7855
3
1.8275
1
1.8390
1
  1.8234
1
1.8151
1
    1.8529
1
1.8258
1
        1.8293
1
1.8179
1
1.8511
1
1.8198
1
     
density functional LSDA 1.6746
2
1.7534
2
1.7334
2
1.7759
2
1.7225
2
1.7225
2
1.7267
2
1.7193
2
1.7193
2
1.7093
2
    1.7371
2
1.7167
2
  1.7412
2
1.6615
1
  1.7722
1
1.7630
1
1.7908
1
1.8093
2
1.8533
1
   
BLYP 1.7637
3
1.8263
3
1.7971
3
1.8432
3
1.8504
5
1.7975
3
1.8055
3
1.7976
3
1.7976
3
1.7809
3
1.8850
1
1.9017
1
1.8147
3
1.7943
3
  1.9232
1
1.8902
1
  1.8044
1
1.7963
1
1.8231
1
1.8405
2
1.8849
1
1.9232
1
1.8902
1
B1B95 1.7440
3
1.8524
1
1.7829
3
1.8295
3
1.7817
3
1.7817
3
1.7881
3
1.7803
3
1.7803
3
1.7669
3
1.8612
1
1.8772
1
1.8019
3
1.7788
3
1.6682
1
1.8077
3
1.7706
2
1.6687
1
1.7966
1
1.7875
1
1.8174
1
1.8249
2
1.8607
1
1.8993
1
1.8658
1
B3LYP 1.7514
3
1.8157
3
1.7862
3
1.8334
3
1.7864
3
1.7864
3
1.7942
3
1.7858
3
1.7858
3
1.7703
3
1.8672
1
1.7732
5
1.8051
3
1.7835
3
1.7705
2
1.8120
3
1.7843
3
1.7783
3
1.7981
1
1.7895
1
1.8182
1
1.8286
2
1.8670
1
1.9056
1
1.8722
1
B3LYPultrafine   1.8746
1
    1.7786
2
1.8742
1
1.8850
1
1.8766
1
  1.8514
1
1.8672
1
1.8834
1
1.8972
1
1.8713
1
  1.9056
1
1.7706
5
        1.8655
1
1.8670
1
1.9056
1
1.8722
1
B3PW91 1.7482
3
1.8154
3
1.7857
3
1.8312
3
1.7837
3
1.7837
3
1.7897
3
1.7823
3
1.7823
3
1.7683
3
1.8633
1
1.8795
1
1.8034
3
1.7797
3
  1.9023
1
1.8679
1
  1.7967
1
1.7868
1
1.8172
1
1.8256
2
1.8625
1
1.9021
1
1.8681
1
mPW1PW91 1.7454
3
1.8134
3
1.7837
3
1.8295
3
1.7816
3
1.7816
3
1.7877
3
1.7802
3
1.7802
3
1.7665
3
1.8593
1
1.8756
1
1.8018
3
1.7778
3
  1.8983
1
1.8639
1
  1.7966
1
1.7864
1
1.8175
1
1.8234
2
1.8584
1
1.8980
1
1.8641
1
M06-2X 1.8669
1
1.8663
1
1.7661
5
1.8888
1
1.7642
5
1.8698
1
1.8780
1
1.8703
1
1.8703
1
1.8490
1
1.7595
5
1.8765
1
1.8936
1
1.8654
1
  1.8998
1
1.8658
1
  1.8003
1
1.7955
1
1.8208
1
1.8296
2
1.8615
1
1.8995
1
1.8658
1
PBEPBE 1.7570
3
1.8238
3
1.7943
3
1.8381
3
1.7921
3
1.7921
3
1.7987
3
1.7908
3
1.7908
3
1.7764
3
1.8775
1
1.8949
1
1.8108
3
1.7880
3
1.6770
1
1.8108
2
1.7832
2
1.6775
1
1.7997
1
1.7900
1
1.8185
1
1.8339
2
1.8770
1
1.9177
1
1.8831
1
PBEPBEultrafine   1.8914
1
    1.8444
2
1.8854
1
1.8960
1
1.8879
1
  1.8636
1
1.8775
1
1.8949
1
1.9104
1
1.8820
1
  1.9178
1
1.8829
1
        1.8758
1
1.8770
1
1.9177
1
1.8831
1
PBE1PBE 1.8706
1
1.8526
1
1.8526
1
1.8923
1
1.7637
5
1.8687
1
1.8774
1
1.8700
1
1.8700
1
1.8475
1
1.8598
1
1.8762
1
1.8941
1
1.8640
1
  1.8994
1
1.8646
1
        1.8582
1
1.8590
1
1.8991
1
1.8647
1
HSEh1PBE 1.8713
1
1.7905
4
1.8529
1
1.8929
1
1.7948
3
1.8694
1
1.7611
4
1.8709
1
1.8709
1
1.8477
1
1.8604
1
1.8771
1
1.8943
1
1.7508
4
  1.8998
1
1.8653
1
  1.7976
1
1.7872
1
1.8185
1
1.8241
2
1.8597
1
1.8996
1
1.8655
1
TPSSh 1.8756
1
1.8759
1
1.8569
1
1.8957
1
1.7794
5
1.8720
1
1.7846
5
1.8735
1
1.8735
1
1.7640
5
1.8634
1
1.8791
1
1.8962
1
1.7765
5
1.8628
1
1.9016
1
1.8678
1
1.8637
1
      1.8619
1
1.8626
1
1.9014
1
1.8682
1
wB97X-D 1.8692
1
1.8682
1
1.7727
5
1.8895
1
1.7701
5
1.8668
1
1.7770
5
1.8689
1
1.7694
5
1.8438
1
1.8582
1
1.7751
5
1.7800
5
1.7684
5
1.8566
1
1.8983
1
1.7697
5
1.8570
1
      1.8566
1
1.8565
1
1.8983
1
1.8633
1
B97D3 1.8895
1
1.8819
5
1.8718
1
1.9133
1
1.8492
5
1.8865
1
1.8545
5
1.8891
1
1.8482
5
1.8660
1
1.8007
5
1.8746
5
1.9101
1
1.8447
5
1.8779
1
1.9178
1
1.8658
5
1.8791
1
      1.8771
1
1.8784
1
1.9177
1
1.8659
5
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(D+d)Z cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Moller Plesset perturbation MP2 1.7392
3
1.8210
3
1.7843
3
1.8462
3
1.7822
5
1.7830
3
1.7915
3
1.7718
5
1.7783
3
1.7685
3
1.8728
1
1.7788
4
1.8063
3
1.7792
3
1.8428
2
1.8188
3
1.7616
2
1.8448
2
1.8303
1
1.8143
1
1.8500
1
1.8431
2
1.8753
1
1.9240
1
1.8809
1
MP2=FULL 1.7396
3
1.8214
3
1.7839
3
1.8465
3
1.7817
3
1.7817
3
1.7898
3
1.7773
3
1.7773
3
1.7605
3
1.8676
1
1.8901
1
1.8051
3
1.7730
3
1.8100
2
1.8162
3
1.7491
2
1.8232
1
1.8282
1
1.8076
1
1.8500
1
1.8392
2
1.8710
1
1.9190
1
1.8660
1
ROMP2                                     1.8299
1
1.8177
1
1.8500
1
1.8196
1
     
MP3         1.7521
2
  1.7444
4
                      1.8320
1
1.8149
1
1.8528
1
1.8364
2
1.8603
1
   
MP3=FULL         1.7438
4
  1.7486
4
                            1.8542
1
1.8576
1
   
MP4 1.7618
1
1.7888
2
    1.7406
2
      1.7322
2
1.8178
1
      1.7541
3
        1.8351
1
1.8169
1
1.8553
1
1.8416
2
1.8694
1
   
MP4=FULL                                           1.8623
1
1.8659
1
   
B2PLYP 1.8736
1
1.8772
1
1.8560
1
1.9032
1
1.7617
5
1.8731
1
1.8480
2
1.8746
1
1.8374
2
1.8514
1
1.8663
1
1.8832
1
1.8988
1
1.7640
5
  1.9092
1
1.8725
1
  1.8028
1
1.7911
1
1.8233
1
1.8343
2
1.8668
1
1.9091
1
1.8725
1
B2PLYP=FULL 1.8737
1
1.8655
2
1.8558
1
1.9033
1
1.8428
2
1.8724
1
1.8515
2
1.8742
1
1.8742
1
1.8482
1
1.8648
1
1.8830
1
1.8981
1
1.8678
1
  1.9080
1
1.8677
1
        1.8633
1
1.8657
1
1.9075
1
1.8683
1
B2PLYP=FULLultrafine 1.8737
1
1.8773
1
1.8558
1
1.9033
1
1.7642
5
1.8724
1
1.8843
1
1.8742
1
1.8742
1
1.8482
1
1.8648
1
1.8830
1
1.7795
5
1.7568
5
  1.9080
1
1.7581
5
        1.8633
1
1.8658
1
1.9075
1
1.8683
1
Configuration interaction CID 1.7574
1
1.8273
3
1.7898
3
1.8550
3
1.7935
3
  1.8374
1
1.7877
3
1.8199
1
1.8143
1
1.8549
1
  1.8743
2
1.8403
2
              1.8539
1
1.8566
1
1.9049
1
1.8622
1
CISD 1.7535
1
1.8756
2
1.8391
2
1.9045
2
1.7914
3
  1.8247
1
1.7858
3
1.8166
1
1.8109
1
1.8552
1
  1.8731
2
1.8389
2
              1.8542
1
1.8568
1
1.9053
1
1.8624
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 cc-pV(D+d)Z cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ aug-cc-pCVTZ daug-cc-pVDZ daug-cc-pVTZ
Quadratic configuration interaction QCISD 1.7541
1
1.8418
3
1.8082
3
1.8642
3
1.8038
3
1.8038
3
1.8099
3
1.7968
3
1.7968
3
1.7845
3
1.8606
1
1.8791
1
1.8273
3
1.7922
3
  1.9130
1
1.8683
1
  1.8235
1
1.8031
1
1.8437
1
1.8318
2
1.8626
1
1.9125
1
1.8684
1
QCISD(T) 1.7563
1
      1.8119
3
    1.8719
1
1.8122
1
1.8061
1
1.8641
1
1.8815
1
1.8366
3
1.8000
3
  1.8376
2
1.7954
2
  1.8265
1
1.8046
1
1.8461
1
1.8340
2
1.8662
1
1.9174
1
1.8721
1
QCISD(T)=FULL         1.8733
1
  1.8836
1
      1.8592
1
  1.9012
1
1.8604
1
1.8272
1
1.9143
1
1.8553
1
1.8153
1
      1.8588
1
1.8622
1
1.9127
1
1.8578
1
Coupled Cluster CCD 1.7575
1
1.8310
3
1.7927
3
1.8586
3
1.7966
3
1.7966
3
1.8043
3
1.7899
3
1.7899
3
1.7805
3
1.8603
1
1.8784
1
1.8219
3
1.7906
3
  1.8176
2
1.7775
2
  1.8323
1
1.8153
1
1.8530
1
1.8379
2
1.8625
1
1.9121
1
1.8682
1
CCSD         1.7945
3
1.8738
1
1.8831
1
1.8700
1
1.8399
2
1.8272
2
1.8609
1
1.8792
1
1.8728
2
1.8378
2
1.8593
1
1.9134
1
1.8685
1
1.8609
1
1.8223
1
1.8033
1
1.8427
1
1.8321
2
1.8629
1
1.9129
1
1.8686
1
CCSD=FULL         1.8711
1
        1.8409
1
1.8561
1
1.8793
1
1.8988
1
1.8577
1
1.8242
1
1.9101
1
1.8522
1
1.8130
1
      1.8564
1
1.8593
1
1.9084
1
1.8547
1
CCSD(T) 1.7541
1
      1.7971
3
1.8753
1
1.8863
1
1.8718
1
1.8412
2
1.8288
2
1.8641
1
1.8815
1
1.8211
3
1.7878
3
1.7693
2
1.8885
2
1.7907
3
1.8640
1
1.8246
1
1.8033
1
1.8442
1
1.8333
2
1.8661
1
1.9176
1
1.8721
1
CCSD(T)=FULL         1.8462
2
          1.8593
1
1.8819
1
1.8735
2
1.8333
2
1.7421
2
1.8860
2
1.8302
2
1.8154
1
1.8243
1
1.7975
1
1.8451
1
1.8300
2
1.8622
1
1.9127
1
1.8578
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 cc-pV(D+d)Z cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ aug-cc-pCVTZ 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 1.8752
3
1.8162
3
1.8670
3
1.8159
3
1.8621
3
1.8486
3
    1.8035
5
density functional BLYP                 1.8827
1
B1B95 1.8743
1
1.8114
1
            1.8601
1
B3LYP 1.8421
3
1.7999
3
1.8363
3
1.7973
3
1.8283
3
1.8156
3
    1.7689
5
B3LYPultrafine                 1.8656
1
B3PW91                 1.8618
1
mPW1PW91                 1.8578
1
M06-2X                 1.8601
1
PBEPBE                 1.8377
5
PBEPBEultrafine                 1.8761
1
PBE1PBE                 1.8584
1
HSEh1PBE                 1.8590
1
TPSSh                 1.8619
1
wB97X-D 1.9166
1
1.8869
1
1.8966
1
1.8797
1
1.8920
1
1.8705
1
    1.8564
1
B97D3                 1.8776
1
Moller Plesset perturbation MP2 1.8603
3
1.7931
3
1.8490
3
1.7894
3
1.8476
3
1.8329
3
    1.7412
5
MP2=FULL                 1.8692
1
B2PLYP                 1.8650
1
B2PLYP=FULL                 1.8642
1
B2PLYP=FULLultrafine                 1.8642
1
Configuration interaction CID                 1.8545
1
CISD                 1.8548
1
Quadratic configuration interaction QCISD                 1.8602
1
QCISD(T)                 1.8631
1
QCISD(T)=FULL                 1.8608
1
Coupled Cluster CCD                 1.8598
1
CCSD                 1.8604
1
CCSD=FULL                 1.8584
1
CCSD(T)                 1.8631
1
CCSD(T)=FULL                 1.8608
1
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.