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Comparison of levels of theory for C-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 1.7538
4
PM3 1.9043
4
PM6 1.9343
4
composite G2 1.9788
4
G3 1.9788
4
G3B3 1.9768
4
G4 1.9677
4
CBS-Q 1.9785
4

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) 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 1.9034
4
2.0049
4
1.9797
4
2.0007
4
1.9778
4
1.9766
4
1.9791
4
1.9743
4
1.9728
4
1.9681
4
1.9800
4
1.9862
4
1.9746
4
1.9696
1
1.9854
4
1.9736
4
1.9697
1
1.9702
1
1.9706
1
ROHF   2.0268
1
1.9776
1
2.0269
1
1.9705
1
1.9705
1
1.9797
1
1.9718
1
1.9718
1
  1.9829
1
1.9973
1
1.9754
1
1.9693
1
2.0012
1
1.9756
1
1.9694
1
1.9701
1
1.9704
1
density functional LSDA 1.8985
1
1.9654
1
1.9654
1
2.0134
1
1.9561
1
1.9561
1
1.9616
1
1.9542
1
1.9542
1
1.9440
1
1.9609
1
1.9742
1
1.9548
1
  1.9768
1
1.9538
1
  1.9484
1
1.9476
1
SVWN   1.9822
4
    1.9525
4
1.9561
1
1.9536
4
1.9542
1
1.9542
1
1.9440
1
1.9503
3
1.9742
1
1.9548
1
  1.9768
1
1.9538
1
  1.9484
1
1.9476
1
BLYP 1.9291
4
2.0153
4
1.9918
4
2.0115
4
1.9878
4
1.9870
4
1.9901
4
1.9866
4
1.9854
4
1.9767
4
1.9955
1
1.9940
4
1.9849
4
  2.0093
1
1.9880
1
  1.9824
1
1.9820
1
B1B95 1.9085
4
1.9839
4
1.9729
4
1.9912
4
1.9674
4
1.9663
4
1.9686
4
1.9647
4
1.9635
4
1.9594
1
1.9772
1
1.9746
4
1.9720
1
  1.9928
1
1.9718
1
  1.9665
1
1.9665
1
B3LYP 1.9161
4
2.0033
4
1.9789
4
1.9985
4
1.9747
4
1.9737
4
1.9765
4
1.9729
4
1.9716
4
1.9643
4
1.9770
4
1.9813
4
1.9717
4
1.9699
1
1.9982
1
1.9704
4
1.9702
1
1.9704
1
1.9703
1
B3LYPultrafine 1.9163
3
2.0331
1
    1.9747
4
1.9746
1
1.9821
1
1.9747
1
    1.9831
1
1.9935
1
1.9764
1
  1.9981
1
1.9709
4
  1.9704
1
1.9703
1
B3PW91 1.9129
4
2.0022
4
1.9783
4
1.9964
4
1.9720
1
1.9715
4
1.9738
4
1.9697
4
1.9684
4
1.9627
4
1.9802
1
1.9795
4
1.9689
4
  1.9957
1
1.9738
1
  1.9683
1
1.9681
1
mPW1PW91 1.9096
4
1.9995
4
1.9755
4
1.9934
4
1.9698
4
1.9686
4
1.9709
4
1.9667
4
1.9653
4
1.9600
4
1.9778
1
1.9767
4
1.9662
4
  1.9936
1
1.9715
1
  1.9659
1
1.9659
1
M06-2X 1.9062
1
2.0206
1
1.9658
4
2.0241
1
1.9637
4
1.9637
1
1.9711
1
1.9663
1
1.9663
1
1.9572
1
1.9740
1
1.9853
1
1.9707
1
  1.9902
1
1.9702
1
  1.9654
1
1.9651
1
PBEPBE 1.9211
4
2.0100
4
1.9870
4
2.0048
4
1.9811
4
1.9800
4
1.9824
4
1.9784
4
1.9772
4
1.9708
4
1.9885
1
1.9879
4
1.9774
4
  2.0028
1
1.9813
1
  1.9760
1
1.9757
1
PBEPBEultrafine   2.0403
1
    1.9816
1
1.9816
1
1.9876
1
1.9805
1
    1.9884
1
2.0000
1
1.9818
1
  2.0027
1
1.9813
1
  1.9760
1
1.9757
1
PBE1PBE 1.9091
1
1.9795
1
1.9795
1
2.0287
1
1.9697
4
1.9693
1
1.9763
1
1.9690
1
1.9690
1
1.9598
1
1.9782
1
1.9896
1
1.9719
1
  1.9938
1
1.9718
1
  1.9662
1
1.9663
1
HSEh1PBE 1.9102
1
1.9998
4
1.9804
1
2.0300
1
1.9699
4
1.9701
1
1.9711
4
1.9701
1
1.9701
1
1.9601
1
1.9792
1
1.9905
1
1.9665
4
  1.9947
1
1.9725
1
  1.9668
1
1.9668
1
TPSSh   2.0346
1
1.9853
1
2.0320
1
1.9783
4
1.9735
1
1.9788
4
1.9733
1
  1.9712
3
1.9812
1
1.9932
1
1.9738
4
  1.9967
1
1.9747
1
  1.9695
1
1.9694
1
wB97X-D     1.9752
4
  1.9704
4
  1.9709
4
  1.9663
4
  1.9711
4
1.9709
4
1.9667
4
    1.9653
4
     
B97D3   2.0117
4
    1.9857
4
      1.9819
4
            1.9804
4
     
STO-3G 3-21G 3-21G* 6-31G 6-31G* 6-31G** 6-31+G** 6-311G* 6-311G** 6-31G(2df,p) 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
Moller Plesset perturbation MP2 1.9138
4
2.0166
4
1.9803
4
2.0137
4
1.9723
4
1.9712
4
1.9741
4
1.9698
4
1.9684
4
1.9640
4
1.9756
4
1.9875
4
1.9823
1
1.9748
1
1.9914
4
1.9850
1
1.9759
1
1.9770
1
1.9797
1
MP2=FULL 1.9134
4
2.0160
4
1.9780
4
2.0130
4
1.9686
4
1.9675
4
1.9703
4
1.9667
4
1.9658
4
1.9537
4
1.9838
1
1.9847
4
1.9744
1
1.9348
1
2.0134
1
1.9702
1
1.9245
1
1.9679
1
1.9636
1
ROMP2 1.9149
1
1.9741
1
1.9741
1
2.0412
1
1.9707
1
1.9707
1
1.9816
1
1.9754
1
1.9754
1
1.9671
1
1.9855
1
2.0062
1
1.9839
1
  2.0201
1
    1.9785
1
1.9814
1
MP3         1.9707
4
  1.9730
4
      1.9836
1
2.0070
1
1.9838
1
        1.9785
1
1.9817
1
MP3=FULL         1.9679
4
  1.9695
4
      1.9840
1
2.0052
1
1.9762
1
        1.9702
1
1.9664
1
MP4   2.0226
4
    1.9747
4
      1.9761
1
  1.9858
1
2.0093
1
1.9856
1
  2.0266
1
1.9889
1
  1.9805
1
1.9838
1
MP4=FULL   2.0438
1
    1.9685
1
      1.9748
1
    2.0067
1
1.9779
1
  2.0214
1
1.9745
1
  1.9719
1
1.9678
1
B2PLYP 1.9131
1
2.0337
1
1.9775
1
2.0348
1
1.9719
4
1.9698
1
1.9780
1
1.9711
1
1.9711
1
1.9610
1
1.9805
1
1.9939
1
1.9701
4
  2.0007
1
1.9761
1
  1.9695
1
1.9705
1
B2PLYP=FULL 1.9131
1
2.0337
1
1.9771
1
2.0348
1
1.9690
1
1.9690
1
1.9772
1
1.9706
1
1.9706
1
1.9584
1
1.9804
1
1.9932
1
1.9727
1
  2.0000
1
1.9715
1
  1.9665
1
1.9655
1
Configuration interaction CID   2.0138
4
1.9778
4
2.0116
4
1.9697
4
    1.9671
4
                  1.9759
1
1.9785
1
CISD   2.0143
4
1.9786
4
2.0118
4
1.9697
4
    1.9668
4
                  1.9727
1
1.9751
1
STO-3G 3-21G 3-21G* 6-31G 6-31G* 6-31G** 6-31+G** 6-311G* 6-311G** 6-31G(2df,p) 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
Quadratic configuration interaction QCISD   2.0214
4
1.9752
1
2.0439
1
1.9727
4
1.9658
1
1.9745
1
1.9696
1
1.9696
1
1.9625
1
1.9791
1
2.0023
1
1.9766
1
  2.0159
1
1.9789
1
  1.9715
1
1.9738
1
QCISD(T)         1.9745
4
    1.9705
1
    1.9810
1
2.0043
1
1.9784
1
  2.0183
1
1.9807
1
  1.9729
1
1.9758
1
QCISD(T)=FULL         1.9655
1
  1.9732
1
        2.0022
1
1.9697
1
1.9291
1
2.0131
1
1.9661
1
1.9190
1
1.9630
1
1.9592
1
QCISD(TQ)         1.9673
1
  1.9756
1
        2.0036
1
1.9778
1
1.9687
1
2.0174
1
1.9799
1
1.9697
1
   
QCISD(TQ)=FULL         1.9651
1
  1.9726
1
        2.0016
1
1.9693
1
1.9288
1
2.0123
1
1.9656
1
1.9187
1
   
Coupled Cluster CCD   2.0198
4
1.9714
1
2.0438
1
1.9723
4
1.9685
1
1.9787
1
1.9741
1
1.9741
1
1.9671
1
1.9835
1
2.0071
1
1.9830
1
  2.0227
1
1.9860
1
  1.9777
1
1.9807
1
CCSD         1.9722
4
        1.9620
1
1.9786
1
2.0016
1
1.9764
1
1.9678
1
2.0150
1
1.9786
1
1.9686
1
1.9713
1
1.9735
1
CCSD=FULL         1.9630
1
        1.9541
1
1.9786
1
2.0000
1
1.9686
1
1.9282
1
2.0104
1
1.9640
1
1.9180
1
1.9619
1
1.9572
1
CCSD(T)         1.9741
4
1.9669
1
  1.9699
1
    1.9802
1
2.0034
1
1.9779
1
1.9689
1
2.0173
1
1.9802
1
1.9699
1
1.9723
1
1.9752
1
CCSD(T)=FULL         1.9647
1
          1.9801
1
2.0014
1
1.9693
1
1.9289
1
2.0122
1
1.9657
1
1.9189
1
1.9626
1
1.9588
1
STO-3G 3-21G 3-21G* 6-31G 6-31G* 6-31G** 6-31+G** 6-311G* 6-311G** 6-31G(2df,p) 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

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 1.9986
4
1.9850
4
1.9995
4
1.9814
4
2.0003
4
1.9889
4
density functional B1B95 1.9829
3
1.9810
3
1.9824
3
1.9761
3
1.9821
3
1.9678
3
B3LYP 2.0006
4
1.9860
4
2.0003
4
1.9828
4
1.9987
4
1.9872
4
Moller Plesset perturbation MP2 2.0195
4
1.9836
4
2.0157
4
1.9763
4
2.0211
4
2.0047
4
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.