At the effective single-particle level, the Hamiltonian of the coupled system of electrons and vibrations is given by
where the first term Ĥe describes the electronic system and the second term Ĥv the vibrational degree of freedom respectively. The last term in the Hamiltonian
describes the first-order EV interaction. The EV coupling constants are given as
where χ = (k,u) and χα = χα∕ are the mass-normalized normal modes, obtained from the eigenvectors χα of the dynamical matrix as calculated from the aoforce module.