The calculation of the optical gaps of a series of nonmagnetic direct and indirect semiconductors and simple oxides is addressed using an all-electron perturbative method based on density-functional theory.

Absorption of electromagnetic radiation in a quantum system of nuclei and electrons results in an instantaneous rearrangement of the electronic charge distribution. In quantum-mechanical terms this corresponds to a transition from the ground state to an electronically excited state. This process can be followed by a slower relaxation of the nuclei leading to a new geometrical arrangement of the atoms corresponding to the excited state structure.

In the simplest approximation (independent electrons), absorption of a photon by a system of N electrons promotes an electron from a level below the Fermi energy ("hole"), to an initially empty state, ("particle"). The particle and hole formally carry a negative and a positive charge, and their wave-functions may either be well separated in space or partially overlapping, depending on the nature of the system. The independent electron approximation completely neglects the resulting particle-hole Coulomb attraction. Besides, it does not account for the response of the remaining N-1 electrons to the particle-hole pair creation (many-body screening). For these reasons, common electronic structure methods for the ground state of many-electron systems based on the independent electron approximation, like Hartree-Fock or density functional theory, do not typically predict reliably excited state properties, particularly in condensed matter systems where many-body screening effects are important.

In a recent paper, published in Physical Review B, a team of researchers from the London Centre for Nanotechnology, the Thomas Young Centre at Imperial College, Science and Technology Facilities Council, and the University of Turin have proposed a new method for the calculation of electronic excitations in molecular and condensed phase systems that achieves predictive accuracy for electronically excited states in wide classes of materials, including complex crystalline systems of potential relevance in solar light conversion. The method is based on a reformulation of the basic equations of time-dependent density-functional theory (TD-DFT) in order to determine the response of the self consistent density matrix to an external time-dependent perturbation. It is particularly well suited for periodic systems (polymers, surfaces or bulk crystals), as it explicitly and efficiently couples excitations at different points in the Brillouin zone. The method is implemented in the CRYSTAL09 package, and uses an all-electron basis set of Gaussian functions, in the LCAO approximation.

One of the central results of the paper of Bernasconi et al. is that for systems whose optical absorption edge is dominated by exciton transitions (e.g. crystalline silicon), the response equations of TD-DFT have to be formulated so as to include explicitly spatial non-locality in the response kernel. Physically, the non-local terms account for the residual Coulomb attraction between many-body screened particles and holes, and are responsible for the formation of bound quasi-particle/quasi-hole pairs (excitons). In CRYSTAL09 the calculation of non-local exchange-like integrals of TD-DFT is carried out analytically and exploits sophisticated integral screening techniques, which are particularly efficient for highly symmetric systems like crystals. The ability to account quantitatively for the formation of excitons fully from first principles is very important, as it paves the way for a more complete theoretical description of the complex phenomena occurring in the transduction of solar light into chemical or electric energy in natural and artificial photosynthesis, electron/spin transport in low dimensional systems, and exciton formation, transport and recombination in new photo-voltaic devices.

L. Bernasconi, S. Tomić, M. Ferrero, M. Rérat, R. Orlando, R. Dovesi, and N. M. Harrison, Phys. Rev. B 83, 195325 (2011)

Journal link: http://prb.aps.org/abstract/PRB/v83/i19/e195325

Figure:  Calculated independent electron absorption spectra of crystalline Si (left) and InN and GaAs (right). The vertical continuous line represents the experimental optical gap, the dashed line is the value calculated from TD-DFT. The difference between the energy of the optical gap and the onset of absorption in the independent electron spectrum is the result of the many-body particle/hole screening and (if present) of the quasi-particle/quasi-hole interaction. In the left panels, HF includes exactly the particle-hole attraction but not the many-body screening, LDA includes (approximately) only the many body screening, and B3LYP contains both contributions. In this case, the experimental absorption energy of the exciton is predicted to within an accuracy of less than 0.1 eV. In the case of InN the two continuous vertical lines represent the range of available experimental estimates of the optical gap.