Remark on the Hopping Transition Probability of Polaron Holes in NiO

For the hopping motion of polaron holes the frequency factor $W_0$ of the transition probability is determined by the observation that hole localization occurs in a molecular orbital of the irreducible set $t_{2g}$ of a cation site group (with transfer integral $b_{\pi }$), whereas the superexchange mechanism is caused by virtual charge transfers between molecular orbitals of the irreducible set $e_g$ (with transfer integral $b_{\sigma }$). The effect of short-range magnetic ordering on $W_0$ is determined by the time-dependent spin-pair correlation function ${\gamma }_{\mathrm{ij}}\mathrm{}\left(t\right)\mathrm{}$ for neighbor cations $i$ and $j$ and for times $t\gg t_0=\mathrm{relaxation}\mathrm{time}\mathrm{for}\mathrm{the}\mathrm{correlation}$.