Abstract

A combined approach of first-principles density-functional calculations and the systematic cluster-expansion scheme is presented. The dipole, quadrupole, and Coulomb matrix elements obtained from ab initio calculations are used as an input to the microscopic many-body theory of the excitonic optical response. To demonstrate the hybrid approach for a nontrivial semiconductor system, the near-bandgap excitonic optical absorption of rutile ${\mathrm{TiO}}_2$ is computed. Comparison with experiments yields strong evidence that the observed near-bandgap features are due to a dipole-forbidden but quadrupole-allowed $1s$ exciton state.

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