We report for the
first time an accurate ab initio potential energy
surface for the HeH
+
–H
2
system in four
dimensions (4D) treating both diatomic species as rigid rotors. The
computed ab initio potential energy point values are fitted using
an artificial neural network method and used in quantum close coupling
calculations for different initial states of both rotors, in their
ground electronic states, over a range of collision energies. The
state-to-state cross section results are used to compute the rate
coefficients over a range of temperatures relevant to interstellar
conditions. By comparing the four dimensional quantum results with
those obtained by a reduced-dimensions approach that treats the H
2
molecule as an averaged, nonrotating target, it is shown
that the reduced dimensionality results are in good accord with the
four dimensional results as long as the HeH
+
molecule is
not initially rotationally excited. By further comparing the present
rate coefficients with those for HeH
+
–H and for
HeH
+
–He, we demonstrate that H
2
molecules
are the most effective collision partners in inducing rotational excitation
in HeH
+
cation at interstellar temperatures. The rotationally
inelastic rates involving
o
-H
2
and
p
-H
2
excitations are also obtained and they turn
out to be, as in previous systems, orders of magnitude smaller than
those involving the cation. The results for the H
2
molecular
partner clearly indicate its large energy-transfer efficiency to the
HeH
+
system, thereby confirming its expected importance
within the kinetics networks involving HeH
+
in interstellar
environments.