  The van der Waals bonded transition metal phosphorous trichalcogenides
FePS$_3$, NiPS$_3$ and MnPS$_3$ have recently attracted renewed attention due
to the possibility of exfoliating them into their monolayers. Although the
three compounds have similar electronic structure, the magnetic structure
differs due to subtle differences in exchange and magnetic anisotropy and the
materials thus comprise a unique playground for studying different aspects of
magnetism in 2D. Here we calculate the exchange and anisotropy parameters of
the three materials from first principles paying special attention to the
choice of Hubbard parameter U. We find a strong dependence of the choice of U
and show that the calculated N\'eel temperature of FePS$_3$ varies by an order
of magnitude over commonly applied values of U for the Fe $d$-orbitals. The
results are compared with parameters fitted to experimental spin-wave spectra
of the bulk materials and we find excellent agreement between the exchange
constants when a proper value of U is chosen. However, the anisotropy
parameters are severely underestimated by DFT and we discuss possible origins
of this discrepancy.
