2
$\begingroup$

I understand that the radical character is quantified by the occupation number of the lowest unoccupied natural orbital obtained from UHF calculations or from CASSCF calculations. My issue is that I already have an organic diradical whose ground state is high-spin state. In this case how can I quantify the radical character ? Is there a way to know about the mixing percentage from higher spin states which in turn could give us information about the radical character of the molecule ?

$\endgroup$
  • 1
    $\begingroup$ I don't understand what you mean by quantifying the radical character. In a triplet state, arguably a diradical, that 'character' obviously does not only depend on the LUMO, because more than that orbital will be partially filled. Are you looking to find the 'position' of the unpaired electrons? If so, you are probably interested in the spin density. $\endgroup$ – Martin - マーチン Aug 1 '18 at 9:19
  • $\begingroup$ I have a plannar molecule with two radical centers, one at each extreme. That electrons are reflected in SOMO's. Now I have increased the distance in these radical centers by increasing the spacer length. The problem now arises in the S_2 value for the complete system which is more that 2 (i.e. S(S+1)). There seems to be mixing from higher spin-states. But I am not able to quantify it. $\endgroup$ – juno Aug 1 '18 at 9:26
  • 1
    $\begingroup$ What level of theory is that on? That sound like spin contamination and appears that the wavefunction you have is not a sensible one. In CAS, you have a pure spin state, so for a triplet S² is 2. If you have a biradicaloid singlet, then the spin is 0, as is S². You can then quantify the character of the wave function by looking at the coefficients of the biradicaloid determinants. $\endgroup$ – Martin - マーチン Aug 1 '18 at 9:36
  • 2
    $\begingroup$ You have not answered what level of theory you are doing that on. Anyway, a broken-symmetry ansatz is the poor-mans way to decribe a multireference system. Except from some qualitative interpretation, there is no way you could quantify anything. If your S² is different from the expected value (How much anyway?) then that is an error in your methodology. It means that your level of theory does not describe your system. Apart from that you cannot learn anything from it, especially not the mixing of higher spin states. Please edit in additional information. $\endgroup$ – Martin - マーチン Aug 1 '18 at 11:32
  • 1
    $\begingroup$ Please edit your question to include any and all information we have gathered in the comments section. $\endgroup$ – Martin - マーチン Aug 2 '18 at 12:30
1
$\begingroup$

Take a look at this is the article, which provides quantitative characterization of radical character: M. Head-Gordon. Characterizing unpaired electrons from the one-particle density matrix. Chem. Phys. Lett., Vol. 372, Issues 3–4, 2003, p. 508-511

Based on natural orbitals, the analysis in this paper is applicable to any correlated method - it needs only one-particle state density matrix.

$\endgroup$
  • $\begingroup$ thank you so much for the reply. I will read the paper and get back if I have any doubts regarding it. $\endgroup$ – juno Dec 4 '18 at 10:30

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.