B4-engine as the rotational driver of the B13+ Cluster: Study based on BOMD and AdNDP analysis

Abstract Context Boron clusters are of significant interest due to their inherent fluxionality and aromaticity. Among them, the B₄ unit exhibits a unique dynamic behavior, interconverting between a square-shaped transition state (TS, D4h) and a diamond-shaped ground state (GS, D2h). This dynamic motif also plays a pivotal role within the cationic B₁₃⁺ molecular rotor, where the B₄ subunit acts as a driving element in the rotational motion of the outer B₁₀ ring around the inner B₃ core which are analogous to the rim and axel of a wheel. The present study aims to establish a dynamic correlation between the isolated B₄ cluster and that of the B₁₃⁺cluster containing embedded B₄ units within it, using Born–Oppenheimer Molecular Dynamics (BOMD) simulations. The key observation is a recurring diamond-square–diamond (DSD) to diamond-diamond (DD) transformation involving multiple B₄ units, which governs the stepwise rotation of the B₁₃⁺ cluster. By comparing the timescales and change in bonding pattern studied through AdNDP analysis a direct correspondence between dynamics of isolated B₄ cluster and that of B₁₃⁺ cluster has been revealed. This study highlights the fundamental role of the intrinsic dynamics of the B₄ unit in orchestrating the collective rotational behavior of the B₁₃⁺ molecular rotor containing multiple B₄subunits. Methods All quantum chemical calculations were carried out using Density Functional Theory (DFT) as implemented in Gaussian 09 (Revision D.01). Geometry optimizations and frequency analyses were performed using the PBE1PBE hybrid functional in conjunction with the 6-311 + G(d) basis set. To ensure accurate determination of stationary points, a superfine integration grid and very tight convergence criteria were applied throughout. Minimum energy structures (NImag = 0) and transition states (NImag = 1) for both the B₄ and B₁₃⁺ clusters were identified based on vibrational frequency analysis. Born–Oppenheimer Molecular Dynamics (BOMD) simulations were also performed within Gaussian 09 to investigate the real-time structural dynamics of the clusters. Simulations were conducted under an NVT ensemble by coupling the system to a thermal reservoir at 300 K. Each cluster was propagated over a 5000-femtosecond (fs) time scale to capture thermally driven transformations. To explore the bonding evolution during structural transitions, Adaptive Natural Density Partitioning (AdNDP) analysis was conducted using the Multiwfn3.8 program. Electron density distribution plots were also generated via Multiwfn to visualize bonding changes and electronic flux during dynamic processes.