Effect of geometry on the energetic properties of stoichiometric CdSe clusters

II-VI semiconductor materials (CdSe belongs to this class of materials) exhibit unique electronic and optical properties arising from quantum confinement effects. The optical characteristics of these materials can be tuned by modulating the size of the constituent nanoparticles. CdSe is known for its narrow bulk band gap (~ 1.6 eV) and relatively large exciton Bohr radius (~ 5.4 nm). The clusters of CdSe hold significant potential for applications in novel light emitters, next-generation solar cells, sensor technologies, and biomedical diagnostics. Thus, the determination of energetic and quantum-chemical parameters for CdSe clusters with different geometries (linear, ring, and 3D) is highly valuable. Given the limited information regarding the impact of geometries change from linear (1D) to three-dimensional (3D) geometries on the energetic parameters and stability of Cd_mSe_m clusters, the present study is of relevance. The stoichiometric Cd_mSe_m (m = 1-6) clusters with linear, ring and spatial (3D) forms are studied. Structural properties, average bond length, and electronic properties like the highest-occupied-lowest-unoccupied molecular orbital (HOMO-LUMO gap (ΔE), binding energy (E_b), electronegativity (χ), chemical potential (π), chemical hardness (η), global softness (S), global electrophilicity (ω), and stability factor (SF) have been analysed. These parameters are calculated for the CdSe clusters in the solvent (ethanol). Based on the binding energy and relative stability values, the most favourable Cd_mSe_m (m < 6) cluster geometry was determined for the studied samples. Data regarding the most stable geometric configurations of CdSe clusters are constrained by the sample set presented in this study, the specific cluster sizes, and the structural limitations in their construction.

All calculations including geometry optimization and energy spectra of the CdSe were made using density functional theory (DFT). The GGA + PBE approximation was used to describe the exchange-correlation energy of the electronic subsystem with Hubbard corrections (GGA + U). Initially, structural optimization and electronic band structure calculations were performed for bulk CdSe to estimate the appropriate Hubbard corrections (U). A plane-wave cut-off energy E_cut-off = 660 eV was employed. The valence electron states were defined by the 4d¹⁰5s² and 4s²4p⁴ configurations for Cd and Se atoms, respectively. The self-consistent field convergence threshold for total energy was set to 5.0 10^-6 eV/atom. Geometry optimization, including lattice parameters and internal atomic coordinates, was conducted using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. The convergence criteria were defined by a maximum Hellmann-Feynman force of 0.01 eV/Å, a maximum ionic displacement of 5.0 10^-4 Å, and a maximum stress of 0.02 GPa. To ensure an accurate description of the electronic spectrum, Hubbard corrections were applied to the Cd d-orbitals (U_4d = 5.80 eV) and Se p-orbitals (U_4p = 4.00 eV). Based on the optimized bulk CdSe structure, stoichiometric Cd_mSe_m (m = 1-6) clusters were constructed with various geometries, including linear, ring, and spatial (3D) configurations. For all cluster calculations, the energy and force convergence criteria were established at approximately ~ 3 10^-4 eV and ~ 5 10^-2 eV/Å, respectively.