  Modeling environments that are not in local thermal equilibrium, such as
protoplanetary disks or planetary atmospheres, with molecular spectroscopic
data from space telescopes requires knowledge of the rate coefficients of
rovibrationally inelastic molecular collisions. Here, we present such rate
coefficients in a temperature range from 10 to 500 K for collisions of CO$_2$
with He atoms in which CO$_2$ is (de)excited in the bend mode. They are
obtained from numerically exact coupled-channel (CC) calculations as well as
from calculations with the less demanding coupled-states approximation (CSA)
and the vibrational close-coupling rotational infinite-order sudden (VCC-IOS)
method. All of the calculations are based on a newly calculated accurate ab
initio four-dimensional CO$_2$-He potential surface including the CO$_2$ bend
($\nu_2$) mode. We find that the rovibrationally inelastic collision cross
sections and rate coefficients from the CSA and VCC-IOS calculations agree to
within 50% with the CC results at the rotational state-to-state level, except
for the smaller ones and in the low energy resonance region, and to within 20%
for the overall vibrational quenching rates except for temperatures below 50 K
where resonances provide a substantial contribution. Our CC quenching rates
agree with the most recent experimental data within the error bars. We also
compared our results with data from Clary et al. calculated in the 1980's with
the CSA and VCC-IOS methods and a simple atom-atom model potential based on ab
initio Hartree-Fock calculations and found that their cross sections agree
fairly well with ours for collision energies above 500 cm$^{-1}$, but that the
inclusion of long range attractive dispersion interactions is crucial to obtain
reliable cross sections at lower energies and rate coefficients at lower
temperatures.
