OPTIMISATION OF A SEMI-EMPIRICAL MODEL FOR ACCURATE DETERMINATION OF EXCITATION ENERGIES AND ABSORPTION SPECTRA OF QUANTUM DOTS

Abstract

Quantum dots are nanomaterials that have several potential applications including the production of efficient solar cells. Accurate theoretical studies of excitation energies and absorption spectra of quantum dots are essential for harnessing such potentials. The existing high-level ab-initio methods for obtaining excitation energies and absorption spectra are computationally expensive for quantum dots. However, the semi-empirical methods, including the Intermediate Neglect of Differential Overlap for spectroscopy (INDO/s) model, are computationally cheap but are generally less accurate. Unlike some ground-state semi-empirical methods, INDO/s has not attracted significant attention to improving its level of accuracy because of some difficulties associated with optimising its parameters. Therefore, this research was aimed at developing an improved INDO/s model that will be computationally cheap and capable of producing accurate excitation energies and absorption spectra for quantum dots. A semi-empirical Hamiltonian based on INDO/s was parameterised with benchmark excitation energies from Equation-Of-Motion Coupled-Cluster Singles Doubles (EOM CCSD) for Si, S, Cd and Zn diatomics at different interatomic separations. The Mean Absolute Errors (MAE) were calculated for different sets of parameters and the opti mised set of parameters were those with the least MAEs. The optimised model was called optimised for excitation Intermediate Neglect of Differential Overlap (oeINDO). The oeINDO was validated by computing the MAEs of the oeINDO and INDO/s excita tion energies and absorption spectra maxima for Sin, Sn, Znn ,Cdn, (ZnS)n and (CdS)n (n is the number of atoms) clusters. The validation was carried out relative to EOM-CCSD for small clusters (n<6) and Time-Dependent Density Functional Theory (TDDFT) for large clusters (n ≥ 6). All computation times were recorded. The oeINDO was then employed to predict the absorption spectra of Si, S, Zn, Cd, ZnS, and CdS quantum dots, and the optimal size of CdS and ZnS quantum dots for solar cell applications. The optimised parameters obtained for Si, S, Zn and Cd diatomics had MAEs 0.21, 0.19, 0.23,and 0.29 eV, respectively. The oeINDO produced excitation energies with MAEs 0.18, 0.56, 0.25, 0.22 eV for small Si, S, Zn, and Cd clusters, respectively, and MAEs 0.22, 0.36, 0.15, 0.24, 0.36 and 0.23 eV, for large Si, S, Zn, Cd, ZnS, and CdS clus i ters, respectively. The unoptimised INDO/s however, produced excitation energies with MAEs 1.23, 1.29, 0.70, and 1.23eV for small Si, S, Zn, Cd clusters, respectively, and MAEs 1.05, 2.51, 2.49, 0.63, 0.76 and 1.04eV for large Si, S, Zn, Cd, ZnS, and CdS clusters, respectively. Also, the MAEs of oeINDO and INDO/s absorption spectra max ima relative to those from TDDFT were 0.41eV and 1.49eV, respectively. The results showed that oeINDO agreed reasonably well with the benchmarks and it was more ac curate than INDO/s. The time of computing with oeINDO (0.08 minutes) was found to be less than a hundredth of the time utilised for EOM-CCSD (2946.51 minutes). The oeINDO predicted a red-shift in the quantum dots absorption spectra with an increase in dot size. It also predicted Si, Zn and Cd dots to be metallic. The 1.2 nm and 1.4 nm spherical-like CdS and ZnS quantum dots, respectively, were found to be theoretically optimal for solar cell applications. The improved INDO/s was computationally cheap and capable of producing more accu rate excitation energies and absorption spectra for quantum dots.