A DFT study on molecular modeling of aluminum-germanium Cu-doped/undoped cluster for NLO responses by structural...

The design of metallic clusters offers a promising nonlinear optical (NLO) responses pathway with tunable properties. Using density functional theory (DFT), a systematic investigation of the structural, electronic, and optical characteristics of aluminum-germanium (Al-Ge) clusters have been made to identify stable configurations with enhanced NLO activity.

For the designed clusters, the structural analysis reveals bond lengths in 2.38-2.65 Å and bond angles of 57-135°, with dopants to inducing notable elongation and angular distortion. The energy decomposition analysis (EDA) shows its stabilizing electrostatic contributions of -121.16 to -943.86 kcal/mol and large repulsive interactions of 343.96-6235.59 kcal/mol, balanced by polarization energies (-160.69 to -1609.79 kcal/mol) and correlation energies (-28.95-2658.16 kcal/mol). Frontier orbital analysis (FMOs) highlights its charge delocalization in undoped clusters and strong HOMO-LUMO localization in Cu-doped systems. The optical property evaluation reveals polarizability (<α₀>) values of 44.56-65.16 a.u. and hyperpolarizability (β₀) to range 0-84,884.73 a.u., with Cu-containing clusters to exhibit the strongest NLO responses. The global chemical reactivity descriptors further confirm tunability, with ionization potentials of 4.05-5.94 eV, electron affinity (EA) of 2.08-3.78 eV, and electrophilicity indices (ω) reaching 20.04 eV. The charge density difference (CDD) analysis demonstrates strong Al-Ge covalent bonding in smaller clusters and significant electron redistribution in Cu-doped systems. Collectively, the results establish that structural tuning and targeted doping can yield clusters with tailored stability, electronic properties, and exceptionally high NLO activity, positioning Al-Ge clusters as strong candidates for next-generation nonlinear optical materials.