Some time ago I recall hearing a professor say that looking at a DFT result (I don't remember exactly what, a TD-DFT, spin contamination etc...), he could tell that the system was multireferenced.

My question is: do we have anything in a DFT calculation that is indicative of a multireference system?

  • $\begingroup$ I don't have the time to post an answer right now, but there is a paper by Peter Taylor that introduces the idea that if the norm of the $\hat{T}_1$ operator from a coupled cluster calculation (or roughly $a_1$ from CI) is > o.o2 (I think), the system may have multiconfigurational character. $\endgroup$ – pentavalentcarbon Jan 25 '18 at 13:44
  • $\begingroup$ I note that while the T1 measurement has been used before, many dispute its usefulness and have introduced other such measurements, such as T2 etc. $\endgroup$ – TAR86 Jan 25 '18 at 13:48
  • $\begingroup$ @TAR86 Do you have a reference handy? There's at least one Don Truhlar paper where he evaluates a handful of diagnostics, it could be in there too. $\endgroup$ – pentavalentcarbon Jan 25 '18 at 19:58
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    $\begingroup$ However, $\hat{T}_1, \hat{T}_2, \dots$ cannot come from an SCF-type calculation, they must come from CCSD or CISD, so they aren't useful. I wouldn't be surprised if there is a TD-DFT quantity related to something like number of $(\mathbf{X}+\mathbf{Y})^2$ elements above some threshold that's useful. $\endgroup$ – pentavalentcarbon Jan 25 '18 at 20:08
  • $\begingroup$ @pentavalentcarbon Unfortunately, I no longer have access to publications. My old group did some work on strong correlation recently, I assume that at least some references are in there. It may also be of interest to OP: dx.doi.org/10.1002/chem.201604682 . $\endgroup$ – TAR86 Jan 25 '18 at 20:18

You should have a look at the so called FOD (Fermi Occupied Density) analysis by Grimme et al. That is accessible by ORCA 4 very easy and straight forward by specifying "FOD" as a keyword. [1-3]

FOD Plot from ORCA Input Library
From ORCA Input Library [1]:

The FOD plot above (plotted with Chemcraft) indicates a significant and delocalized FOD. Multiconfigurational methods should be used to study this molecule and any single-reference result (HF, DFT, MP2, CC should be regarded with suspicion)

Via Multiwfn you can access the "local total/dynamic/nondynamic electron correlation function" and "total/dynamic/nondynamic electron correlation index" [4,5].

Local Descriptors of Dynamic and Nondynamic Correlation from [5]
Visual abstract from [5]. You can see the dynamic and non-dynamic correlation from which you also can see if single reference methods are acceptable or not.

[1] ORCA Input Library, FOD analysis
[2] S. Grimme, A. Hansen, Angew. Chem. Int. Ed. 2015, 54 (42), 12308-12313
[3] C. A. Bauer, A. Hansen, S. Grimme, Chem. Eur. J. 2017, 23 (25), 6150-6164
[4] E. Ramos-Cordoba, P. Salvadorc, E. Matito, Phys. Chem. Chem. Phys. 2016, 18, 24015-24023
[5] E. Ramos-Cordoba, E. Matito, J. Chem. Theory Comput. 2017, 13 (6), 2705–2711

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    $\begingroup$ FOD = fractional occupied density acc. [2] $\endgroup$ – Martin - マーチン Oct 29 '18 at 21:24

There are DFT-based multireference diagnostics, for example, one proposed by J. M. L. Martin, (A simple DFT-based diagnostic for nondynamical correlation), that uses the atomization energy calculated with a pure-DFT exchange-correlation functional and the corresponding hybrid with 100% Hartree–Fock-type exchange.

It is more common to use correlated wave functions to estimate multireference character. For example, the T1 diagnostic obtained from a CCSD calculation.

For a complete discussion of multireference character diagnostics and their usefulness, I recommend this paper.


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