### Abstract

The development of a method for calculating the frequency-dependent second harmonic generation coefficient of insulators and semiconductors based on the self-consistent linearized muffin-tin orbitals band structure method is reported. The calculations are at the independent particle level and are based on the formulation introduced by Aversa and Sipe [Phys. Rev. B 52, 14 636 (1995)]. The terms are rearranged in such a way as to exhibit explicitly all required symmetries including the Kleinman symmetry in the static limit. Computational details and convergence tests are presented. The calculated frequency-dependent (Formula presented) for the zinc-blende materials GaAs, GaP and wurtzite GaN and AlN are found to be in excellent agreement with that obtained by other first-principles calculations when corrections to the local density approximation are implemented in the same manner, namely, using the “scissors” approach. Similar agreement is found for the static values of (Formula presented) for zinc-blende GaN, AlN, BN, and SiC. The strict validity of the usual “scissors” operator implementation is, however, questioned. We show that better agreement with experiment is obtained when the corrections to the low-lying conduction bands are applied at the level of the Hamiltonian, which guarantees that eigenvectors are consistent with the eigenvalues. Results are presented for the frequency-dependent (Formula presented) for (Formula presented). The approach is found to be very efficient and flexible, which indicates that it will be useful for a wide variety of material systems including those with many atoms in the unit cell.

Original language | English |
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Pages (from-to) | 3905-3919 |

Number of pages | 15 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 57 |

Issue number | 7 |

DOIs | |

Publication status | Published - 1 Jan 1998 |

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### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*57*(7), 3905-3919. https://doi.org/10.1103/PhysRevB.57.3905