NWChem implements an error function based partitioning described in J. Chem. Phys. 152, 184102 (2020) on page 8
$$ w_A({\bf r}) = \prod_{B \neq A} \frac 1 2 [ 1 - \text{erf } \mu_{AB}'] $$
where
$$ \mu_{AB}' = \frac 1 \alpha \frac {\mu_{AB}} { [1 - \mu_{AB}^2]^{n}} $$
and
$$ \mu_{AB} = \frac {\mathbf{r}_A - \mathbf{r}_B} {|\mathbf{r}_A - \mathbf{r}_B|} $$
NWChem implements an error function based partitioning described in J. Chem. Phys. 152, 184102 (2020) on page 8
where
and