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

MethodsWe optimized a neutral singlet Al₄O₆ cluster at RB3LYP/6-311++G(d,p) with an analytic frequency calculation (opt freq) on Gaussian 16 Rev. C.01 (120 GB RAM; Linda with up to 64 procs).Electronic energy and thermochemistryThe self-consistent field converged cleanly; the final SCF energy is −1421.79753269 Eh.Thermochemistry (298.15 K, 1 atm): ZPE = 0.029187 Eh, with thermal corrections and totals reported (e.g., E_elec+ZPE = −1421.768346 Eh, E_elec+H_therm = −1421.758469 Eh, G = −1421.802185 Eh).Geometry and bondingThe optimized structure is a compact oxide cluster (C₁). Representative interatomic separations from the final distance matrix show Al–O ≈ 1.745 Å 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 analysisThe frequency job confirms a true minimum: the reported fundamental modes are all positive (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 momentsPopulation analysis shows the expected oxide polarity: Mulliken charges of roughly +1.01 e on Al and −0.672 e on O (summing to zero), and APT charges ~+1.51 e (Al) and −1.006 e (O).The log also lists very small dipole/quadrupole moments (near-symmetric charge distribution in this frame).One-sentence summary: 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⁻).We optimized a neutral singlet Al₄O₆ cluster (Q = 0, M = 1) using DFT/B3LYP with the 6-311++G(d,p) basis set as implemented in Gaussian 16 (ES64L-G16RevC.01). The job specification was #p B3LYP/6-311++G(d,p) opt freq, and the calculation employed 252 basis functions. Geometry optimization converged, and an analytic frequency calculation verified that the stationary point is a true minimum (no imaginary frequencies). The final self-consistent field energy is E(SCF) = −1421.79753269 Eh; the zero-point correction reported by Gaussian is 0.029187 Eh. 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.