Context The engineering of supramolecular π–cation interaction systems can offer a route to enhance nonlinear optical (NLO) properties. In this work, molecular C10 systems, externally doped with alkali (Li, Na, K) and alkaline earth metals (Be, Mg, Ca) are investigated computationally to quantify quadrupole moments and hyperpolarizabilities (β0). The C10 exhibits a large HOMO–LUMO gap (Egap) (4.05 eV), high hardness (η, 2.03 eV), and negligible β0, consistent with stability and low reactivity. The doping alters C10 dramatically as Na@C10 shows highest β0 (17,105 a.u.) and strongest quadrupole distortion (–8.97 × 1017 Å), while Mg@C10 yields the lowest Egap (0.19 eV), reflecting extreme reactivity but moderate optical response. In contrast, K@C10 exhibits the weakest enhancement (β0 = 254 a.u.), and Ca@C10 positive quadrupole (+ 1.49 × 1017 Å) highlights a distinct charge redistribution mechanism. Global reactivity parameters confirm enhanced softness (σ) (up to 1.68 for Na@C10) and reduced ionization potentials (0.29 eV for Mg@C10). Methods Density functional theory (DFT) calculations are performed with PBE-D3/def2-TZVP level, with electronic spectra evaluated via TD-DFT. Quadrupole moments (Qzz), polarizabilities (α), and hyperpolarizabilities (β) are computed, alongside, transition density matrix (TDM), hole–electron overlap, and charge density difference (CDD) studies. Quadrupole moments were computed as the Qzz component of the traceless Cartesian quadrupole tensor, as implemented in Gaussian 09 (using the keyword “pop = full”). The Qzz values are reported in Debye•Å (D•Å), which is the SI-compatible unit for molecular quadrupole moments (1 D•Å = 3.336 × 10–30 C•m2). To facilitate comparison with literature, the values are scaled by a factor of 101⁷ and tabulated in Table 1 as Qzz /101⁷ D•Å. The Qzz component was selected because the molecular principal axis of C10 and all doped systems lies along the z-axis, making Qzz the most physically meaningful descriptor of axial charge redistribution upon metal doping. This definition, unit system, and conversion factor are now explicitly stated in Table 1 caption. The global reactivity parameters (IP, EA, χ, μ, η, σ, ω) are derived using Koopmans theorem, and density of states (DOS) spectra are generated. Graphical Abstract

Building molecular C₁₀-π-cationic interaction systems for reporting quadrupole moments basis

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发表日期：

2026年4月27日

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Abrar U. Hassan,
Sajjad H. Sumrra,
Mamduh J. Aljaafreh

摘要

Context

The engineering of supramolecular π–cation interaction systems can offer a route to enhance nonlinear optical (NLO) properties. In this work, molecular C₁₀ systems, externally doped with alkali (Li, Na, K) and alkaline earth metals (Be, Mg, Ca) are investigated computationally to quantify quadrupole moments and hyperpolarizabilities (β₀). The C₁₀ exhibits a large HOMO–LUMO gap (E_gap) (4.05 eV), high hardness (η, 2.03 eV), and negligible β₀, consistent with stability and low reactivity. The doping alters C₁₀ dramatically as Na@C₁₀ shows highest β₀ (17,105 a.u.) and strongest quadrupole distortion (–8.97 × 10¹⁷ Å), while Mg@C₁₀ yields the lowest E_gap (0.19 eV), reflecting extreme reactivity but moderate optical response. In contrast, K@C₁₀ exhibits the weakest enhancement (β₀ = 254 a.u.), and Ca@C₁₀ positive quadrupole (+ 1.49 × 10¹⁷ Å) highlights a distinct charge redistribution mechanism. Global reactivity parameters confirm enhanced softness (σ) (up to 1.68 for Na@C₁₀) and reduced ionization potentials (0.29 eV for Mg@C₁₀).

Methods

Density functional theory (DFT) calculations are performed with PBE-D3/def2-TZVP level, with electronic spectra evaluated via TD-DFT. Quadrupole moments (Q_zz), polarizabilities (α), and hyperpolarizabilities (β) are computed, alongside, transition density matrix (TDM), hole–electron overlap, and charge density difference (CDD) studies. Quadrupole moments were computed as the Q_zz component of the traceless Cartesian quadrupole tensor, as implemented in Gaussian 09 (using the keyword “pop = full”). The Q_zz values are reported in Debye•Å (D•Å), which is the SI-compatible unit for molecular quadrupole moments (1 D•Å = 3.336 × 10–30 C•m²). To facilitate comparison with literature, the values are scaled by a factor of 10¹⁷ and tabulated in Table 1 as Q_zz /10¹⁷ D•Å. The Q_zz component was selected because the molecular principal axis of C10 and all doped systems lies along the z-axis, making Q_zz the most physically meaningful descriptor of axial charge redistribution upon metal doping. This definition, unit system, and conversion factor are now explicitly stated in Table 1 caption. The global reactivity parameters (IP, EA, χ, μ, η, σ, ω) are derived using Koopmans theorem, and density of states (DOS) spectra are generated.

Graphical Abstract

Building molecular C10-π-cationic interaction systems for reporting quadrupole moments basis

摘要

Building molecular C₁₀-π-cationic interaction systems for reporting quadrupole moments basis