  The use of solid-state electrolytes to provide safer, next-generation
rechargeable batteries is becoming more feasible as new materials with greater
stability and higher ionic diffusion coefficients are designed. However,
accurate determination of diffusion coefficients in solids is problematic and
reliable calculations are highly sought-after. In this paper we compare
diffusion coefficients calculated using nonequilibrium and equilibrium ab
initio molecular dynamics simulations for highly diffusive solid-state
electrolytes for the first time, to demonstrate the accuracy that can be
obtained. Moreover, we show that ab initio nonequilibrium molecular dynamics
can be used to determine diffusion coefficients when the diffusion is too slow
for it to be feasible to obtain them using ab initio equilibrium simulations.
Thereby, using ab initio nonequilibrium molecular dynamics simulations we are
able to obtain accurate estimates of the diffusion coefficients of Li ions in
Li$_6$PS$_5$Cl and Li$_5$PS$_4$Cl$_2$, two promising electrolytes for
all-solid-state batteries. Furthermore, these calculations show that the
diffusion coefficient of lithium ions in Li$_5$PS$_4$Cl$_2$ is higher than many
other potential all-solid-state electrolytes, making it promising for future
technologies. The reasons for variation in conductivities determined using
computational and experimental methods are also discussed. It is demonstrated
that small degrees of disorder and vacancies can result in orders of magnitude
differences in diffusivities of Li ions in Li$_6$PS$_5$Cl, and these factors
are likely to contribute to inconsistencies observed in experimentally reported
values. Notably, the introduction of Li-vacancies and disorder can enhance the
ionic conductivity of Li$_6$PS$_5$Cl.
