The Feshbach resonance provides precise control over the scattering length and effective range of interactions between ultracold atoms. We propose the ultratransferable pseudopotential to model effective interaction ranges -1.5≤kF2Reff2≤0, where Reff is the effective range and kF is the Fermi wave vector, describing narrow to broad Feshbach resonances. We develop a mean-field treatment and exploit the pseudopotential to perform a variational and diffusion Monte Carlo study of the ground state of the two-dimensional Fermi gas, reporting on the ground-state energy, contact, condensate fraction, momentum distribution, and pair-correlation functions as a function of the effective interaction range across the BEC-BCS crossover. The limit kF2Reff2→- is a gas of bosons with zero binding energy, whereas ln(kFa)→- corresponds to noninteracting bosons with infinite binding energy.The authors acknowledge the financial support of the EPSRC Grant no. [EP/J017639/1], L.M.S. acknowledges financial support from the Cambridge European Trust, Cambridge Philosophical Society, VSB Fonds, and the Prins Bernhard Cultuurfonds, and G.J.C. acknowledges the financial support of the Royal Society and Gonville & Caius College. Computational facilities were provided by the University of Cambridge High Performance Computing Service
