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 degrees of freedom. The last term in the Hamiltonian
describes the first order electron-vibration (EV) interaction. The EV coupling constants are given as
where χ = (k,u) is a shorthand notation that refers both to the displacement of atom k from the equilibrium value of the position k along the Cartesian component Rk,u with u = x,y,z as well as the index pair itself. Furthermore, χα = χα∕ are the mass-normalized normal modes, obtained from the eigenvectors χα of the dynamical matrix as calculated from the aoforce module .