Addressing Mixed Valency

[AntObi]

The mixed valency/charge ordering problem of SMACT

SMACT as a package has been used in works to both:

• Generate, hypothetical charge-neutral compositions
• Check if a set of known compositions are charge neutral.

If we have a composition, A_wB_xC_yD_z, where A,B,C and D are unique elements, and w, x, y and z are integers indicating the stoichiometry, then we define the charge neutrality as:

$$wq^{A} + xq^{B} + yq^{C} + zq^{D} = 0$$

Problem I: Conventional SMACT-based screenings for hypothetical compositions will miss compounds where mixed valency is observed.

This problem will typically arise from using smact_filter based approaches using unique combinations of elements to generate the compositions. Considering a chemical system A-B-C-D, our conventional approach cannot determine mixed valency simply as each enumeration of possible oxidation states only considers one oxidation state per element.

Solution

To incorporate mixed-valency, users can include elements more than once in their combinations i.e. to get all the possible mixed binaries in a chemical system A-B, you must also consider the chemical systems A-A-B, A-B-B etc. This logic can be extended to any n-ary system, as well as any number of mixed-valenced elements in a composition

Fe₃O₄ example

For example, for Fe₃O₄, we cannot conventionally solve the charge neutrality by assuming a unique iron atom and unique oxygen atom, instead we need to consider an additional iron atom so that we can have both Fe²⁺ and Fe³⁺ as solutions to the charge neutrality equation.

For the "binary" case of the Fe-O system:
$$wq^{Fe} + xq^{O} = 0 $$

Has no integer solutions for $q^{Fe}$ when $q^{O}=-2$, $w=3$ and $q=4$. If we extend this system to Fe-Fe-O:
$$wq^{Fe'} +xq^{Fe''} + yq^{O} = 0$$
Then it is possible to get a solution that can make the composition Fe₃O₄. Our conditions here are: $w + x = 3$, $y=4$, $q^{O}=-2$, which yields solutions $q^{Fe'}=2, q^{Fe''}=3$ when $w=1$ and $x=2$.

See this colab notebook as a reference for this example.

Problem 2: Using SMACT to check for charge-neutrality of known compositions

Related to issue #55

The neutral_ratios and pauling_test functions in SMACT have seen use in checking if compositions are "SMACT" valid (i.e. charge-neutral and that the most electronegative element carries the most negative charge in a compound) in the following works:

• CDVAE code usage
• Colton C. Seegmiller, Sterling G. Baird, Hasan M. Sayeed, Taylor D. Sparks. Computational Materials Science, 2023 code usage

The smact_validity function in these works attempt to determine if a compound is charge neutral by solving the charge neutrality equation. The stoichiometries are known, so the function iteratively tries all the possible combinations of oxidation states and will return true if at least one combination of oxidation states leads to a solution.

As only one oxidation state is considered per element in each iteration, compounds which contain elements with mixed valency will often fail this check.

Below is an attempt to use the smact_validity script on the GNoME database where about 70% of the compositions can either be (i) charge-balanced or (ii) likely intermetallics where all the constituent elements are metals

Potential solutions

We have yet to determine an ideal solution for this problem.

Using pymatgen (the oxi_state_guesses method of the pymatgen.core.composition.Composition class)

Where smact_validity fails, pymatgen can be used to attempt to assign oxidation states to compositions. If oxidation states can be assigned then the composition would be charge-neutral.

Issues
The smact_validity script can screen through a large set of compositions within a reasonable time using very little resources. My attempts to use an oxi_state_guesses solution have been slow and unsuitable for a large number of compositions. (This can be mitigated with a workstation/HPC with a lot of cores and using parallelising the task though).

My own personal testing would suggest that a SMACT-based approach is about 15 times faster.

[kavanase]

@AntObi just to flag in case it's useful, I was also playing around with the pymatgen oxi_state_guesses / Structure.add_oxidation_state_by_guess() functions recently, in the context of using with doped, and noticed they could be very slow for certain systems.
There is the max_sites parameter which can speed this up massively in certain systems, but I found this needed to be handled a bit differently just to check it was giving reasonable results, as used here:
https://github.com/SMTG-Bham/doped/blob/main/doped/core.py#L907

Also added to pymatgen-analysis-defects:
https://github.com/materialsproject/pymatgen-analysis-defects/pull/104/files

And with a timeout function here, to avoid hanging forever on tricky cases:
https://github.com/SMTG-Bham/doped/blob/main/doped/generation.py#L1341