The exponentially repulsive EXP pair potential defines a system of particles in terms of which simple liquids quasiuniversality may be explained [A. K. Bacher et al., Nat. Commun. 5, 5424 (2014); J. C. Dyre, J. Phys. Condens. Matter 28, 323001 (2016)]. This paper and its companion present a detailed simulation study of the EXP system. Here we study how structure monitored via the radial distribution function and dynamics monitored via the mean-square displacement as a function of time evolve along the systems isotherms and isochores. The focus is on the gas and liquid phases, which are distinguished pragmatically by the absence or presence of a minimum in the radial distribution function above its first maximum. An NVU-based proof of quasiuniversality is presented, and quasiuniversality is illustrated by showing that the structure of the Lennard-Jones system at four selected state points is well approximated by those of EXP pair-potential systems with the same reduced diffusion constant. The companion paper studies the EXP systems isomorphs, focusing also on the gas and liquid phases.
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