I'm using WebMO to construct molecules that have high multireference character, but I cannot seem to find any, or perhaps I'm not building them correctly on WebMO; I know singlet biradicals generally have high MR character, but when I carry out a CI calculation on them, the weight of the Hartree-Fock configuration is extremely high (1/Norm(A) value). I've carried out CI calculations on TMM, TME, p-quinodimethane, but these do not exhibit high MR character using my diagnostic of looking at the weight of the HF configuration in a CI calculation.

Can anyone suggest any medium-sized molecules that exhibit high MR character?

#N CI/6-31G(d) SP 


0 1
C 1 B1
C 2 B2 1 A1
H 3 B3 2 A2 1 D1
H 3 B4 2 A3 1 D2
C 2 B5 1 A4 3 D3
H 6 B6 2 A5 1 D4
H 6 B7 2 A6 1 D5
H 1 B8 2 A7 3 D6
H 1 B9 2 A8 3 D7

B1 1.322324000
B2 1.469933386
B3 1.089341949
B4 1.089341949
B5 1.469933386
B6 1.089341949
B7 1.089341949
B8 1.087824972
B9 1.087824972
A1 148.4186871
A2 118.9917788
A3 118.9917788
A4 148.4186871
A5 118.9917788
A6 118.9917788
A7 121.5429429
A8 121.5429429
D1 73.31395214
D2 -73.31395214
D3 -180.0000000
D4 -73.31395214
D5 73.31395214
D6 180.0000000
D7 -0.000000000
  • $\begingroup$ Welcome to the site! While someone could probably offer suggestions of molecules, its tough to know if your initial molecules are built correctly without seeing the input files. This paper looked at stretched carbon monoxide and found high multireference character. This may be a good starting point to test if you are doing things right. Once that works, you can try larger molecules and stretch them along some reaction coordinate to possibly induce multireference character. $\endgroup$
    – Tyberius
    Commented Dec 9, 2021 at 15:22
  • $\begingroup$ Thanks! But I also heard that are molecules in their equilibrium geometry that exhibit high MR character, like molecules with (singlet) biradicaloid character- any examples of those? TMM, TME, are, but they don't seem to exhibit MR character. Transition states may also exhibit MR character, but I cannot find such examples. $\endgroup$ Commented Dec 9, 2021 at 15:36
  • $\begingroup$ You can add in the input files you are using as a code block in your question (or at least one of them). This way, other users could spot issues with the calculation setup. $\endgroup$
    – Tyberius
    Commented Dec 9, 2021 at 15:37
  • $\begingroup$ I edited my question with TMM as an example-I'd like to see if the coefficient/weight of the HF config is low. Perhaps this is not a good diagnostic, or I did not build the molecule correctly, or this molecule is not MR. $\endgroup$ Commented Dec 9, 2021 at 15:51
  • 1
    $\begingroup$ Welcome to the site! $\endgroup$ Commented Dec 10, 2021 at 5:27

1 Answer 1


The following small- to medium-sized molecular have multi-reference character, meaning that your CISD calculation will likely show the reference wavefunction to have a weight that is quite a fair bit smaller than 1 (this is not a complete list, but it contains molecules that I've either worked on recently or ones that others in the multi-reference community have studied a lot recently):

  • $\ce{FeMoco}$ (I've published a couple papers on it [1], [2]).
  • $\ce{O3}$ (away from equilibrium, as in this paper of mine).
  • $\ce{Cr2}$ (recent calculations have compared to my empirical potential here).
  • $\ce{N2}$
  • $\ce{C2}$
  • $\ce{CH2}$
  • $\ce{C2H4}$ (ethylene)
  • $\ce{C4H6}$ (butadiene)
  • $\ce{C6H8}$ (hexatriene}

I notice that one of the molecules in my list (butadiene), happens to have the same chemical formula as the molecule you studied in your input file. Butadiene is a very popular benchmark molecule for multi-reference calculations and you could cite my GitHub database of energies on the molecule. If you want the geometry of butadiene used by myself and many others, you can look in this paper and follow the references forwards and backwards if necessary.


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