  We present optimized tight-binding models with atomic orbitals to improve
\textit{ab initio} tight-binding models constructed by truncating full density
functional theory (DFT) Hamiltonian based on localized orbitals. Retaining
qualitative features of the original Hamiltonian, the optimization reduces
quantitative deviations in overall band structures between the \textit{ab
initio} tight-binding model and the full DFT Hamiltonian. The optimization
procedure and related details are demonstrated by using semiconducting and
metallic Janus transition metal dichalcogenides monolayers in the $2H$
configuration. Varying the truncation range from partial second neighbors to
third ones, we show differences in electronic structures between the truncated
tight-binding model and the original full Hamiltonian, and how much the
optimization can remedy the quantitative loss induced by truncation. We further
elaborate the optimization process so that local electronic properties such as
valence and conduction band edges and Fermi surfaces are precisely reproduced
by the optimized tight-binding model. We also extend our discussions to
tight-binding models including spin-orbit interactions, so we provide the
optimized tight-binding model replicating spin-related properties of the
original Hamiltonian such as spin textures. The optimization process described
here can be readily applied to construct the fine-tuned tight-binding model
based on various DFT calculations.
