Optimized Geometry and Electronic Structure of the Al₄O₆ Nanocluster from DFT Calculations

Methods<br>We optimized a neutral singlet <b>Al₄O₆</b> cluster at <b>RB3LYP/6-311++G(d,p)</b> with an analytic frequency calculation (<code>opt freq</code>) on Gaussian 16 Rev. C.01 (120 GB RAM; Linda with up to 64 procs).Electronic energy and thermochemistry<br>The self-consistent field converged cleanly; the final <b>SCF energy is −1421.79753269 Eh</b>.Thermochemistry (298.15 K, 1 atm): <b>ZPE = 0.029187 Eh</b>, with thermal corrections and totals reported (e.g., <b>E_elec+ZPE = −1421.768346 Eh</b>, <b>E_elec+H_therm = −1421.758469 Eh</b>, <b>G = −1421.802185 Eh</b>).<br>Geometry and bondingThe optimized structure is a compact oxide cluster (C₁). Representative interatomic separations from the final distance matrix show <b>Al–O ≈ 1.745 Å</b> to each O neighbor; e.g., Al(1)–O(2) = 1.7447 Å, Al(1)–O(3) = 1.7447 Å, Al(1)–O(4) = 1.7447 Å.Standard-orientation coordinates and rotational constants for the optimized structure are provided in the log.Vibrational analysis<br>The frequency job confirms a <b>true minimum</b>: the reported fundamental modes are <b>all positive</b> (e.g., 321.68, 321.98, 409.06, 409.11, 409.17, 511.45 cm⁻¹ for the first six listed bands).Thermochemical summaries (ZPE, S, C_V, etc.) are tabulated at 298 K.Charge analysis and moments<br>Population analysis shows the expected oxide polarity: <b>Mulliken charges</b> of roughly <b>+1.01 e</b> on Al and <b>−0.672 e</b> on O (summing to zero), and <b>APT charges</b> ~<b>+1.51 e</b> (Al) and <b>−1.006 e</b> (O).The log also lists very small dipole/quadrupole moments (near-symmetric charge distribution in this frame).<b>One-sentence summary:</b> <i>DFT (RB3LYP/6-311++G(d,p)) optimization and frequency analysis of Al₄O₆ yields a C₁ minimum with Al–O ≈ 1.745 Å, robust positive frequencies, SCF energy −1421.7975 Eh, and strongly ionic charge partitioning (Al δ⁺, O δ⁻).</i><br><br>We optimized a neutral singlet <b>Al₄O₆</b> cluster (<b>Q = 0, M = 1</b>) using <b>DFT/B3LYP</b> with the <b>6-311++G(d,p)</b> basis set as implemented in <b>Gaussian 16 (ES64L-G16RevC.01)</b>. The job specification was <code>#p B3LYP/6-311++G(d,p) opt freq</code>, and the calculation employed <b>252 basis functions</b>. Geometry optimization converged, and an analytic <b>frequency</b> calculation verified that the stationary point is a <b>true minimum</b> (no imaginary frequencies). The final self-consistent field energy is <b>E(SCF) = −1421.79753269 Eh</b>; the <b>zero-point correction</b> reported by Gaussian is <b>0.029187 Eh</b>. For figures and supplemental data, Cartesian coordinates were taken from the optimized structure, converted to Å, and visualized with a covalent-radii bonding criterion; ball-and-stick images and labeled Al–O distances were generated from the resulting bonded graph.