A variational approach is developed to study the groundstate (GS) of the
two-site Holstein model. By the extended coherent state, where the more
phonon correlations are easily incorporated, we can get the very accurate
ground state energy for all electron-phonon coupling range in typical values
of hopping integral t = 0.5,1.1, and 2.1 (in units of phonon frequency
ω0), which covers the crossover region from
antiadiabatic limit to the adiabatic limit. Within a very wide t
range [0,2.7], the exact results for the GS energy are obtained
with the twelfth (fourteenth) order corrections to the zeroth order wave
function. Moreover, the present approach is more concise than any
other analytical ones in this field, and hopefully can be easily
generalized to many other Holstein models.