14.1 Theoretical background.

At the effective single-particle level, the Hamiltonian of the coupled system of electrons and vibrations is given by

ˆH =  ˆHe + ˆHv + Hˆev,

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

       ∑  ∑
Hˆev  =       dˆ†μλαμν ˆdν(ˆb†α + ˆbα)
       μν  α

describes the first-order EV interaction. The EV coupling constants are given as

      (  h  )1∕2∑  ⟨  |d ˆHe |⟩
λ αμν =  ----        μ |--1 |ν A αχ,
        2ωα      χ     dχ

where χ = (k,u) and Aχα = Cχα√ ----
  Mk are the mass-normalized normal modes, obtained from the eigenvectors Cχα of the dynamical matrix as calculated from the aoforce module.