  Hydrogen molecules (H2) come in two forms in the interstellar medium, ortho-
and para-hydrogen, corresponding to the two different spin configurations of
the two hydrogen atoms. The relative abundances of the two flavours in the
interstellar medium are still very uncertain, and this abundance ratio has a
significant impact on the thermal properties of the gas. In the context of star
formation, theoretical studies have recently adopted two different strategies
when considering the ortho:para ratio (OPR) of H2 molecules; the first
considers the OPR to be frozen at 3:1 while the second assumes that the species
are in thermal equilibrium. As the OPR potentially affects the protostellar
cores which form as a result of the gravitational collapse of a dense molecular
cloud, the aim of this paper is to quantify precisely what role the choice of
OPR plays in the properties and evolution of the cores. We used two different
ideal gas equations of state for a hydrogen and helium mix in a radiation
hydrodynamics code to simulate the collapse of a dense cloud and the formation
of the first and second Larson cores; the first equation of state uses a fixed
OPR of 3:1 while the second assumes thermal equilibrium. Simulations using an
equilibrium ratio collapse faster at early times and show noticeable
oscillations around hydrostatic equilibrium, to the point where the core
expands for a short time right after its formation before resuming its
contraction. In the case of a fixed 3:1 OPR, the core's evolution is a lot
smoother. The OPR was however found to have little impact on the size, mass and
radius of the two Larson cores. We conclude that if one is solely interested in
the final properties of the cores when they are formed, it does not matter
which OPR is used. On the other hand, if one's focus lies primarily in the
evolution of the first core, the choice of OPR becomes important.
