  For electronic states and photoinduced charge dynamics near the neutral-ionic
transition in the mixed-stack charge-transfer complex
tetrathiafulvalene-$p$-chloranil (TTF-CA), we review the effects of Peierls
coupling to lattice phonons modulating transfer integrals and Holstein
couplings to molecular vibrations modulating site energies. The former
stabilizes the ionic phase and reduces discontinuities in the phase transition,
while the latter stabilizes the neutral phase and enhances the discontinuities.
To reproduce the experimentally observed ionicity, optical conductivity and
photoinduced charge dynamics, both couplings are quantitatively important. In
particular, strong Holstein couplings to form the highly-stabilized neutral
phase are necessary for the ionic phase to be a Mott insulator with large
ionicity. A comparison with the observed photoinduced charge dynamics indicates
the presence of strings of lattice dimerization in the neutral phase above the
transition temperature.
