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 certain phonon eigenmodes. 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 electron-phonon coupling and needs to be removed if the eigenvalues are used to obtain electron-phonon coupling. We present a procedure for how to deal with these problematic anticrossing situations and apply it to the band gap zero-point motion renormalization of 16 diamondoids and urotropine using different exchange correlation functionals. From the 17 structures, 5 require the correction presented here, leading to a modification of the zero-point renormalization between 4% and 185%. We find gap renormalizations in the range of $\ensuremath{-}150$ to $\ensuremath{-}370\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$ for diamondoids but only around $\ensuremath{-}40\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$ for urotropine.