The Infrared spectrum of very large (periodic) systems: global versus fragment strategies—the case of three defects in diamond

Abstract

The calculation of the full vibrational spectrum (Infrared or Raman) of very large systems (say larger than one thousand atoms) is not only very expensive, but also of relatively low interest, as in many (most of the) cases only a subset of modes, well separated from the large, diffuse bands resulting from the superposition of thousands of peaks, is used for the spectroscopic characterization of the specific system under study. Here, a fragment strategy, consisting in computing and diagonalizing a reduced (in size) Hessian matrix centered around the zone of interest, is illustrated, and its accuracy and efficiency documented, by comparison with the full Hessian diagonalization (FHD) scheme. Three test cases are considered, showing different vibrational features. They are defects in diamond: the $${\hbox {VN}}_3$$ H defect (V stands for the vacancy), where the interesting point is the characterization of the bending and stretching modes of H, well separated from the large band resulting from the perturbation of the diamond manifold; the $${\hbox {VH}}_4$$ defect (four H atoms in the vacancy, with vibrational modes related to H appearing both at high and low wave numbers); and the $${\hbox {I}}_{2{\mathrm{N}}}$$ interstitial defect, with modes in which the N atoms are involved, appearing at wave numbers not far from the manifold of the perfect diamond modes. So the three cases, apparently similar, explore three different situations of interest for the fragment strategy: (1) localized modes very well separated from the large diamond continuous band ( $${\hbox {VN}}_3$$ H); (2) modes at upper border of the large diamond continuous band ( $${\hbox {I}}_{2{\mathrm{N}}}$$ ): a case in which the modes of interest appear both as separated from and merged with the large continuous band ( $${\hbox {VH}}_4$$ ). It turns out that in all cases relatively small fragments, containing from 2 to 40 atoms, permit to reproduce with high accuracy (the difference with respect to the FHD being always smaller than 5 cm $$^{-1}$$ for the wave numbers, and a few percent for the IR intensity) the spectral feature(s) of interest, at a computational cost that is only a small fraction of the one required by the FHD.