  The two-site two-electron Holstein model is studied within a perturbation
method based on a variational phonon basis obtained through the modified
Lang-Firsov (MLF) transformation. The ground-state wave function and the energy
are found out considering up to the seventh and eighth order of perturbation,
respectively. The convergence of the perturbation corrections of different
orders to the ground state energy as well as to different correlation functions
are investigated. The kinetic energy and the correlation functions involving
charge and lattice deformations are studied as a function of electron-phonon
($e$-ph) coupling for different values of adiabaticity parameter and Coulomb
repulsion. The simultaneous effect of the $e$-ph coupling and Coulomb repulsion
on the kinetic energy shows interesting features.
