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

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).

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.