  Tetragonal CuO (T-CuO) has attracted attention because of its structure
similar to that of the cuprates. It has been recently proposed as a compound
whose study can give an end to the long debate about the proper microscopic
modeling for cuprates. In this work, we rigorously derive an effective one-band
generalized $t\!-\!J$ model for T-CuO, based on orthogonalized Zhang-Rice
singlets, and make an estimative calculation of its parameters, based on
previous \textit{ab initio} calculations. By means of the self-consistent Born
approximation, we then evaluate the spectral function and the quasiparticle
dispersion for a single hole doped in antiferromagnetically ordered half-filled
T-CuO. Our predictions show very good agreement with angle-resolved
photoemission spectra and with theoretical multiband results. We conclude that
a generalized $t\!-\!J$ model remains the minimal Hamiltonian for a correct
description of single-hole dynamics in cuprates.
