Frozen-phonon method for state anticrossing situations and its application to zero-point motion effects in diamondoids

The frozen-phonon method, used to calculate electron-phonon coupling effects, requires calculations of the investigated structure using atomic coordinates displaced according to a certain phonon eigenmode. The process of "freezing-in" the specific phonon can bring electronic eigenstates that are energetically close in energy into an anticrossing. This electronic anticrossing effect is, however, unrelated to the wanted electron-phonon coupling, and needs to be removed. We present a procedure how to deal with these problematic anticrossing situations and apply it to the band gap zero-point motion renormalization of sixteen diamondoids and urotropine using different exchange correlation functionals. We find gap renormalizations of diamondoids in the range of 150 - 400 meV and only 62 meV for urotropine due to the lone-pair character of the highest occupied molecular orbital of the latter.