  The effects of spin and charge fluctuations and electron-phonon couplings on
charge ordering in \alpha-(BEDT-TTF)_2I_3
(BEDT-TTF=bis(ethylenedithio)-tetrathiafulvalence) are investigated
theoretically for an anisotropic triangular lattice at 3/4 filling. By the
exact-diagonalization method, we have calculated the hole density distributions
and the modulations of transfer integrals from high-temperature values as a
function of electron-phonon coupling strength. The results clearly show that
the lattice effect on \alpha-(BEDT-TTF)_2I_3 is weak compared with that on
\theta-(BEDT-TTF)_2RbZn(SCN)_4, as previously found by experiments. This
finding, which is also consistent with recent mean-field results, is
systematically explained by strong-coupling perturbation theory; the effects of
spin fluctuations are partially canceled by charge fluctuations in
\alpha-(BEDT-TTF)_2I_3.
