  We consider several spin-unrestricted random-phase approximation (RPA)
variants for calculating correlation energies, with and without range
separation, and test them on datasets of atomization energies and reaction
barrier heights. We show that range separation greatly improves the accuracy of
all RPA variants for these properties. Moreover, we show that a RPA variant
with exchange, hereafter referred to as RPAx-SO2, first proposed by Sz-abo and
Ostlund [A. Szabo and N. S. Ostlund, J. Chem. Phys. 67, 4351 (1977)] in a
spin-restricted closed-shell formalism, and extended here to a
spin-unrestricted formalism , provides on average the most accurate
range-separated RPA variant for atomization energies and reaction barrier
heights. Since this range-separated RPAx-SO2 method had already been shown to
be among the most accurate range-separated RPA variants for weak intermolecular
interactions [J. Toulouse, W. Zhu, A. Savin, G. Jansen, and J. G.
{\'A}ngy{\'a}n, J. Chem. Phys. 135, 084119 (2011)], this works confirms
range-separated RPAx-SO2 as a promising method for general chemical
applications.
