# Is there a reliable way to determine if a chemical system is more suited to be calculated using a multireference method instead of DFT?

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?

• 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. – pentavalentcarbon Jan 25 '18 at 13:44
• 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. – TAR86 Jan 25 '18 at 13:48
• @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. – pentavalentcarbon Jan 25 '18 at 19:58
• 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. – pentavalentcarbon Jan 25 '18 at 20:08
• @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 . – 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]

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].

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.

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