Electric polarizabilities of the C x Si 4-x (0 ⩽ x ⩽ 4) clusters. A conventional and time-dependent density functional theory study

The dipole polarizabilities of the pure tetramers (C₄, Si₄) and mixed carbon silicon hetero-clusters (C_x Si 4 − x , 0 ⩽ x ⩽ 4 ) have been calculated within the framework of time independent and Time-Dependent (TD) Density Functional Theory (DFT) methods. The convergence of the two approaches is remarkably good revealing the absence of any systematic error. The Si- substitution leads to clusters with enhanced properties. The effect is more pronounced in the case of second hyperpolarizability (x 10³ e 4 a 0 4 E h − 3 ): 8.51(C₄) → 18.04(SiC₃) → 32.45(Si₂C₂) → 60.45(Si₃C) → 100.79(Si₄). To further extend our study, we have performed a spectral decomposition of dipole polarizabilities by employing the TD excitation energies and their corresponding oscillator strengths. Such a decomposition allows for a pictorial insight into some of the factors controlling the evolution of the property for these clusters.