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Context <p>The design of metallic clusters offers a promising nonlinear optical (<i>NLO</i>) responses pathway with tunable properties. Using density functional theory (<i>DFT</i>), a systematic investigation of the structural, electronic, and optical characteristics of aluminum–germanium (<i>Al–Ge</i>) clusters have been made to identify stable configurations with enhanced <i>NLO</i> activity.</p> Methods <p>For the designed clusters, the structural analysis reveals bond lengths in 2.38–2.65&#xa0;Å and bond angles of 57–135°, with dopants to inducing notable elongation and angular distortion. The energy decomposition analysis (<i>EDA</i>) shows its stabilizing electrostatic contributions of −121.16 to −943.86&#xa0;kcal<i>/mol</i> and large repulsive interactions of 343.96–6235.59&#xa0;kcal<i>/mol</i>, balanced by polarization energies (−160.69 to −1609.79&#xa0;kcal<i>/mol</i>) and correlation energies (−28.95–2658.16&#xa0;kcal<i>/mol</i>). Frontier orbital analysis (<i>FMOs</i>) highlights its charge delocalization in undoped clusters and strong <i>HOMO–LUMO</i> localization in <i>Cu</i>-doped systems. The optical property evaluation reveals polarizability (&lt;<i>α</i><sub><i>0</i></sub>&gt;) values of 44.56–65.16 <i>a.u</i>. and hyperpolarizability (<i>β</i><sub><i>0</i></sub>) to range 0–84,884.73 <i>a.u</i>., with <i>Cu</i>-containing clusters to exhibit the strongest <i>NLO</i> responses. The global chemical reactivity descriptors further confirm tunability, with ionization potentials of 4.05–5.94&#xa0;eV, electron affinity (<i>EA)</i> of 2.08–3.78&#xa0;eV, and electrophilicity indices (<i>ω</i>) reaching 20.04&#xa0;eV. The charge density difference (<i>CDD</i>) analysis demonstrates strong <i>Al–Ge</i> covalent bonding in smaller clusters and significant electron redistribution in <i>Cu</i>-doped systems. Collectively, the results establish that structural tuning and targeted doping can yield clusters with tailored stability, electronic properties, and exceptionally high <i>NLO</i> activity, positioning <i>Al–Ge</i> clusters as strong candidates for next-generation nonlinear optical materials.</p> Graphical abstract <p></p>

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

  • 期刊论文

  • 发表日期：

    2026年7月3日

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  • Javed Akram,
  • Kanwal Ranian,
  • Saeed A. Asiri,
  • Islam H. El Azab

摘要

Context

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.

Methods

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.

Graphical abstract