Rotational Behavior Analysis of Cluster Anions in Solid-State Electrolytes via MD Simulation
Authors: Mair Sunil , Smith Jeffrey , Siegel Donald J. , Carter W. Craig , Chiang Yet-Ming 
Published: December 2024

Solid-state batteries (SSBs) have the potential to bring about dramatic increases in safety and performance compared to current liquid electrolyte systems, allowing for electrification of crucial sectors such as transportation as well as development of novel device architectures for consumer electronics. Finding a suitable solid-state electrolyte remains a key challenge in the path to realization of SSBs, and finding candidate materials that exhibit sufficient ionic conductivity alongside the many other materials properties required of a solid-state electrolyte is the crux of this challenge. Within the past two decades, historic improvements in the conductivities of solid-state electrolytes have been made by understanding and exploiting the effects of lattice volume, vacancy concentration, and concerted migration mechanisms (amongst others), to the point at which the conductivities of some solid-state electrolytes have surpassed those of commercially used liquid electrolytes.[1] Recently, the influence of the dynamics of the anions, specifically the rotation of “cluster anions” (also known as molecular anions or polyanions such as PS4
3- or BH4
-), on cation migration mechanisms has garnered attention as a potential avenue for designing high conductivity materials.[2]

Typical experimental signatures of cluster anion rotation include rotor atom spatial probability density calculated from diffraction techniques showing a different, more spherically symmetric geometry, such as a tetrahedral anion showing an octahedral signal, or a disorder-increasing phase transformation accompanied by a sharp jump in ionic conductivity. Because the cluster anion rotations occur at picosecond and Angstrom time and length scales, understanding the rotational behavior of the cluster anions and determining whether this behavior has an impact on the migration mechanism anion is difficult to do experimentally. Molecular dynamics simulations have been used to probe the rotational behavior of cluster anions, with typical characterizations including vibration/libration spectra, rotational autocorrelation functions, spatial probability densities of rotor atoms, and 2D histograms of θ-ϕ spherical coordinates of rotor bond vectors. However, most of these techniques average the signals from the rotor atoms across clusters and across simulation times in a way that obfuscates important time dependent behavior (see Figure 1A). For example, they are unable to determine the specific set of orientations accessed by a cluster anion species that creates the time and space averaged signal seen by diffraction techniques.
In this work, we present a novel framework for MD trajectory analysis which uses a 3D parameterization of the orientation of each cluster in each frame to (1) determine the stable orientations (an orientation-based analog of the position-based concept of a lattice site) of a rotationally active cluster anion, (2) characterize the rotations between stable orientations, and (3) probe the interaction between cluster anion rotations and cation migrations. We apply this framework to the dual cluster anion containing electrolyte sodium amide borohydride (Na2NH2BH4), for which both the tetrahedral borohydride (BH4
-) anion and the bent amide (NH2
-) anion show octahedral signals by X-ray and neutron diffraction. We determine that the borohydride anions achieve this averaged spatial density by pointing one hydrogen atom along the +/- a, b, or c axis and rotating about that axis, while the amide anions achieve this by pointing both hydrogen atoms roughly along two adjacent +/- a, b, or c axes (see Figure 1B). We also corroborate previous results showing that the migration of the sodium cations happens in close concert with the rotation of the amide anions, while the borohydride anions spin more freely.
This work was supported as part of the Joint Center for Energy Storage Research (JCESR), an Energy Innovation Hub funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences.
References
[1] N. Kamaya, K. Homma, Y. Yamakawa, M. Hirayama, R. Kanno, M. Yonemura, T. Kamiyama, Y. Kato, S. Hama, K. Kawamoto, A. Mitsui, A lithium superionic conductor. Nature Materials 10, 682–686 (2011).
[2] Z. Zhang, L. F. Nazar, Exploiting the paddle-wheel mechanism for the design of fast ion conductors. Nat Rev Mater 7, 389–405 (2022).
Figure 1. (A) Traditional MD cluster anion rotation analyses applied to the amide anion in Na2NH2BH4. (B) 100 sampled amide anion positions from each stable orientation within the trajectory. Na: Purple (frontmost Na omitted for clarity), B: pink (hydrogens on BH4
- anions omitted for clarity) N: blue, H: white.

Figure 1