# K-conductivity in solids: combined topological and density functional theory analysis

The solid state electrolytes based on K^{+} conductivity are considered as main parts of the possible electrochemical devices. The topological analysis of the known K-containing structures can be used to select substances with respect to presence of migration pathways in a structure. One of the possible ways to predict K^{+}-conducting substances with the appropriate conducting properties is an application of the combined geometrical/topological approach. The latest allows to obtain net of voids in the structure causes cations diffusion, its size and dimensionality properties and connectivity. Recently, the Voronoi–Dirichlet partition-based approach was applied for prediction of the possible sodium conducting materials [1]. *ToposPro* [2] program package is able to perform such analysis for thousands of the known structures (e.g. collected in ICSD) are corresponding to the compositions and stoichiometry requirements. However, a final set of compounds available after that step is often enormously vast to have some experimental checking possibility.

On the other hand, quantum mechanical *ab initio* calculations are applied widely for the studying of the crystal structure and properties in the equilibrium states as well as in transitional ones. Permanent computer performance increase and a vast range of the possible implementations of the *ab initio* codes themselves have resulted in possibilities to investigate of the structures conduction properties by microscopic modelling. For this reason, it is possible to apply density functional theory-based calculations at the next stage of the selection in order to obtain ionic conducting properties (activation energies barriers) [3].

In the scope of the current research a number of potential solid electrolytes predicted by the mentioned above approach using *ToposPro* code were studied by the *ab initio* modelling in order to elucidate their ionic conducting properties which are not studied yet. Previously considered potassium and lithium conducting materials were studied additionally to validate the proposed approach by a comparison of the method predictions with the previous results.We use climbing image nudged elastic band method (CI-NEB) as implemented into the free-license *CP2K* code [4] and pay special attention not only to diffusion activation energies but also to relations between the vacancy formation energies to take into account not only geometrical but also energy favorability of some pathways.

Thanks to use of *QUICKSTEP* electronic structure calculation method [5] implemented in *CP2K* code based on the combined Gaussian and plane waves basis set it has become possible to study more than 65 different pathways for more than 10 structures. Additionally, the developed script-based system allowed to get result within the reasonable period of time using the SCTMS ‘Zeolite’ and ‘Sergey Korolev’ supercomputers at Samara University. It should be noted, that the applied method results a lower computer time consumption (in comparison with well-known pure plane-waves package, e.g. *VASP* [6]). This observation points possibilities to evaluate more complex doped as well as disordered electrolyte systems at the first principles level of description. That is extremely important for predictions of the particular doped electrolytes properties.

In result of the work, more than 30 activation energy values were calculated for five possible solid electrolytes chosen from the topological point of view with not known conducting properties. The obtained values were used to conclude about the energetic/dimensionality properties of K^{+} diffusion in the substances are under consideration.

**References.**

- Meutzner, Falk, et al. "On the Way to New Possible Na‐Ion Conductors: The Voronoi–Dirichlet Approach, Data Mining and Symmetry Considerations in Ternary Na Oxides." Chemistry–A European Journal 21.46 (2015): 16601-16608.
- Blatov, Vladislav A., Alexander P. Shevchenko, and Davide M. Proserpio. "Applied topological analysis of crystal structures with the program package ToposPro." Crystal Growth & Design 14.7 (2014): 3576-3586.
- Peskov, Maxim V., and Udo Schwingenschlögl. "First-Principles Determination of the K-Conductivity Pathways in KAlO2." The Journal of Physical Chemistry C 119.17 (2015): 9092-9098. 44.
- Hutter, Jürg, et al. "cp2k: atomistic simulations of condensed matter systems." Wiley Interdisciplinary Reviews: Computational Molecular Science 4.1 (2014): 15-25.
- VandeVondele, Joost, et al. "Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach." Computer Physics Communications 167.2 (2005): 103-128.
- Kresse, Georg, and Jürgen Furthmüller. "Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set." Physical Review B 54.16 (1996): 11169.