Experimentally materials are often studied by observing their reaction to an external perturbation. For example, when exposed to electromagnetic radiation, the material may emit an electron. Conversely, when exposed to an electron beam, the material may absorb an electron and emit a photon. Such processes, being the subject of photoemission and inverse photoemission spectroscopy (PES and iPES), allow to investigate the electronic, optical and magnetic properties of materials. The ability to predict these properties theoretically is therefore of great importance in chemistry. Particularly, the synergy between experimental and computational approaches can lead to a higher level of understanding, and to a more precise interpretation of the observed data [1]. 

Density functional theory (DFT) is a widely used theoretical framework to describe ground-state properties of materials. But is DFT in principle suitable to predict such quantities as the fundamental and the optical gaps or the absorption spectrum, which are definitely related to excitations? The principal answer to this question is yes. Although the main physical quantity in DFT is the ground-state many-electron density, \(n(\vec r)\), there exists a one-to-one correspondence between \(n(\vec r)\) and the external potential of the system, \(v_{\mathrm{ext}}(\vec r)\). Since the external potential defines the system entirely, i.e., both the ground state and all the excited states, so does the density \(n(\vec r)\). In practice, however, retrieving excited-state information from the ground state density is a very challenging task. Directly using the Kohn-Sham eigenvalues to determine possible transition energies and from them the absorption spectrum is not justified theoretically, except of the highest occupied eigenvalue, which, for the exact exchange-correlation (xc) potential, equals minus the ionization potential (IP). However, when common approximations for the xc potential are used, deviations by as much as 50\% can occur! Same is true for the fundamental gap of the system and other properites.

In this respect our intention is to develop, implement and apply methods and approximations that can accurately predict the excitation spectrum of a material from a DFT calculation of moderate numerical cost. The relevance and applicability of such a method is vast due to the fundamental importance of the excitaion spectrum in chemistry and materials science.

References

1. C. DiValentin, S. Botti and M. Cococcioni (eds.), First Principle Approaches to Spectroscopic Properties of Complex Materials, Topics in Current Chemistry Vol. 347 (Springer, 2014)

2. J. P. Perdew and M. Levy, Physical content of the exact Kohn-Sham orbital energies: Band gaps and derivative discontinuities, Phys. Rev. Lett. 51, 1884 (1983)

3. L. J. Sham and M. Schlueter, Density-functional theory of the energy gap, Phys. Rev. Lett. 51, 1888 (1983)

4. L. Kronik, T. Stein, S. Refaely-Abramson, R. Baer, Excitation Gaps of Finite-Sized Systems from Optimally Tuned Range-Separated Hybrid Functionals, J. Chem. Theory Comp. 8, 1515 (2012) 

5. L. Kronik and J. B. Neaton, Excited-State Properties of Molecular Solids from First Principles, Annu. Rev. Phys. Chem. 67, 587–616 (2016)

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