  Experimental observations of large exciton binding energies and
non-hydrogenic Rydberg series in 2D semiconducting TMDs, along with deviations
in plasmon dispersion in 2D metallic TMDs, suggest the presence of a
nonconventional screening of the Coulomb interaction. The experimentally
observed Mott insulating state in the charge density wave (CDW) reconstructed
lattice of TMDs containing 4d and 5d elements further confirms the presence of
strong Coulomb interactions in these systems. In this study, we use
first-principles electronic structure calculations and constrained random-phase
approximation to calculate the Coulomb interaction parameters (partially
screened U and fully screened W) between localized $d$ electrons in 2D TMDs. We
specifically explore materials represented by the formula MX2 (M=Nb, Ta, Mo, W,
and X=S, Se, Te) and consider three different phases (1H, 1T, and 1T'). Our
results show that the short-range interactions are strongly screened in all
three phases, whereas the long-range interactions remain significant even in
metallic systems. This nonconventional screening provides a compelling
explanation for the deviations observed in the usual hydrogenic Rydberg series
and conventional plasmon dispersion in 2D semiconducting and metallic TMDs,
respectively. Our calculations yield on-site Coulomb interaction parameters U
within the ranges of 0.8-2.5 eV, 0.8-1.9 eV, and 0.9-2.4 eV for the 1H, 1T, and
1T' structures, respectively. Furthermore, our findings indicate a
substantially high ratio of on-site effective Coulomb interaction to bandwidth
(U_eff/W_b >> 1) in CDW TMDs, providing robust evidence for the experimentally
observed strongly correlated Mott phase.
