  Using the perturbation method based on a variational phonon basis obtained by
the modified Lang-Firsov (MLF) transformation, the two-site single polaron
Holstein model is studied in presence of a difference in bare site energies
($\epsilon_d$=$\epsilon_2$-$\epsilon_1$). The polaronic ground-state wave
function is calculated up to the fifth order of perturbation. The effect of
$\epsilon_d$ (acts as a site-energy disorder) on the polaron crossover,
polaronic kinetic energy, oscillator wavefuncion and polaron localization are
studied. Considering a double-exchange Holstein model with finite $\epsilon_d$,
role of disorder on the properties of the double-exchange system is also
discussed.
