Optical excitation energies, Stokes shift, and spin-splitting of $C24H72Si14$

As an initial step toward the synthesis and characterization of sila-diamondoids, such as sila-adamantane $(Si10H16,Td)$⁠, the synthesis of a fourfold silylated sila-adamantane molecule $(C24H72Si14,Td)$ has been reported in literature [Fischer et al, Science 310, 825 (2005)]. We present the electronic structure, ionization energies, quasiparticle gap, and the excitation energies for the $Si14(CH3)24$ and the exact silicon analog of adamantane $Si10H16$ obtained at the all-electron level using the delta-self-consistent-field and transitional state methods within two different density functional models: (i) Perdew–Burke–Ernzerhof generalized gradient approximation and (ii) fully analytic density functional (ADFT) implementation with atom dependent potential. The ADFT is designed so that molecules separate into atoms having exact atomic energies. The calculations within the two models agree well, to within 0.25 eV for optical excitations. The effect of structural relaxation in the presence of electron-hole-pair excitations is examined to obtain its contribution to the luminescence Stokes shift. The spin-influence on exciton energies is also determined. Our calculations indicate overall decrease in the absorption, emission, quasiparticle, and highest occupied molecular orbital-lowest unoccupied molecular orbital gaps, ionization energies, Stokes shift, and exciton binding energy when passivating hydrogens in the $Si10H16$ are replaced with electron donating groups such as methyl (Me) and trimehylsilyl $(–Si(Me)3)$⁠.