  Optical spectra of two-dimensional transition-metal dichalcogenides (TMDC)
are influenced by complex multi-particle excitonic states. Their theoretical
analysis requires solving the many-body problem, which in most cases, is
prohibitively complicated. In this work, we calculate the optical spectra by
exact diagonalization of the three-particle Hamiltonian within the Tamm-Dancoff
approximation where the doping effects are accounted for via the Pauli blocking
mechanism, modelled by a discretized mesh in the momentum space. The
single-particle basis is extracted from the {\it ab initio} calculations.
Obtained three-particle eigenstates and the corresponding transition dipole
matrix elements are used to calculate the linear absorption spectra as a
function of the doping level. Results for negatively doped MoS$_2$ monolayer
(ML) are in an excellent quantitative agreement with the available experimental
data, validating our approach. The results predict additional spectral features
due to the intervalley exciton that is optically dark in an undoped ML but is
brightened by the doping. Our approach can be applied to a plethora of other
atomically thin semiconductors, where the doping induced brightening of the
many-particle states is also anticipated.
