Calculation of the Infrared Intensity of Crystalline Systems. A Comparison of Three Strategies Based on Berry Phase, Wannier Function, and Coupled-Perturbed Kohn–Sham Methods

Three alternative strategies for the calculation of the IR intensity of crystalline systems, as determined by Born charges, have been implemented in the Crystal code, using a Gaussian type basis set. One uses the Berry phase (BP) algorithm to compute the dipole moment; another does so, instead, through well localized crystalline orbitals (Wannier functions, WF); and the third is based on a coupled perturbed Hartree–Fock or Kohn–Sham procedure (CP). In WF and BP, the derivative of the dipole moment with respect to the atomic coordinates is evaluated numerically, whereas in CP it is analytical. In the three cases, very different numerical schemes are utilized, so that the equivalence of the obtained IR intensities is not ensured a priori but instead is the result of the high numerical accuracy of the many computational steps involved. The main aspects of the three schemes are briefly recalled, and the dependence of the results on the computational parameters (number of k points in reciprocal space, tolerances for the truncation of the Coulomb and exchange series, and so on) is documented. It is shown that in standard computational conditions the three schemes produce IR intensities that differ by less than 1%; this difference can be reduced by an order of magnitude by acting on the parameters that control the accuracy of the calculation. A large unit cell system (80 atoms per cell) is used to document the relative cost of the three schemes. Within the current implementation the BP strategy, despite its seminumerical nature, is the most efficient choice. That is because it is the oldest implementation, and it is based on the simplest of the three algorithms. Thus, parallelism and other schemes for improving efficiency have, so far, been implemented to a lesser degree in the other two cases.