Efficient determination of excitation energies and absorption spectra for quantum dots and large systems from ab initio data

Highlights: • Computing excited states of big systems is costly; a new method is proposed for this. • This method parameterizes a Hamiltonian using ab inito excitation energies of diatomics. • The new method is applied to Si₂ with EOM-CCSD energies and the INDO Hamiltonian. • The parameterized Hamiltonian is transferable with mean error of 0.3 eV. • Excitation energies and UV–VIS spectra are predicted for large clusters up to Si₇₇₉. -- Abstract: A semi-empirical Hamiltonian with the INDO approximation and CIS was parameterized to reproduce EOM-CCSD excitation energies for diatomic silicon Si₂ with different inter-atomic separations. The model Hamiltonian is transferable, producing excitation energies for clusters, Si_n $(n=3,4,5)$ with mean absolute errors (MAEs) of 0.26, 0.18, and 0.09 eV, respectively, from the EOM-CCSD energies. The absorption spectra are also in qualitative agreement with the EOM-CCSD spectra. For clusters Si₁₉ and Si₄₀, comparison with TDDFT gave MAEs of 0.32 and 0.12 eV, respectively. Predictions of excitation energies and absorption spectra are also given for Si_n ($n=124,147,172,779$) using the model Hamiltonian.