Context <p>Boron clusters are of significant interest due to their inherent fluxionality and aromaticity. Among them, the B<sub>4</sub> unit exhibits a unique dynamic behavior, interconverting between a square-shaped transition state (TS, D<sub>4h</sub>) and a diamond-shaped ground state (GS, D<sub>2h</sub>). This dynamic motif also plays a pivotal role within the cationic B<sub>13</sub><sup>+</sup> molecular rotor, where the B<sub>4</sub> subunit acts as a driving element in the rotational motion of the outer B<sub>10</sub> ring around the inner B<sub>3</sub> core which are analogous to the rim and axle of a wheel. The present study aims to establish a dynamic correlation between the isolated B<sub>4</sub> cluster and that of the B<sub>13</sub><sup>+</sup> cluster containing embedded B<sub>4</sub> 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 B<sub>4</sub> units, which governs the stepwise rotation of the B<sub>13</sub><sup>+</sup> cluster. By comparing the timescales and change in bonding pattern studied through AdNDP analysis, a direct correspondence between dynamics of isolated B<sub>4</sub> cluster and that of B<sub>13</sub><sup>+</sup> cluster has been revealed. This study highlights the fundamental role of the intrinsic dynamics of the B<sub>4</sub> unit in orchestrating the collective rotational behavior of the B<sub>13</sub><sup>+</sup> molecular rotor containing multiple B<sub>4</sub> subunits.</p> Methods <p>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 (N<sub>Imag</sub> = 0) and transition states (N<sub>Imag</sub> = 1) for both the B<sub>4</sub> and B<sub>13</sub><sup>+</sup> 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 NVE ensemble by coupling the system to a thermal reservoir at 150&#xa0;K. Each cluster was propagated over a 5000-fs timescale 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.</p>

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B4-engine as the rotational driver of the B13+ cluster: study based on BOMD analysis

  • Sourav Ranjan Ghosh,
  • Sasthi Charan Halder,
  • Atish Dipankar Jana

摘要

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 axle 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 B4 subunits.

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 NVE ensemble by coupling the system to a thermal reservoir at 150 K. Each cluster was propagated over a 5000-fs timescale 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.