# Electronic Excitations

Many properties of functional materials, interfaces, and nano-structures derive from electronic excitations. For example, the ionization potential, the electron affinity, the fundamental gap, dielectric screening, charge transition levels of defects or dopants, and the energy level alignment at interfaces are associated with charged excitations. Conversely, the optical gap, absorption spectra, and exciton binding energies correspond to neutral excitations. These properties are critical parameters for the performance of devices, such as transistors, light emitting diodes, and solar cells. A proper description of electronic excitations requires theoretical approaches that go beyond ground state density functional theory (DFT). Within the framework of Green’s function based many-body perturbation theory, the GW approximation, where G is the one-particle Green’s function and W is the screened Coulomb interaction, provides an accurate description of charged excitations and the Bethe-Salpeter equation (BSE) of neutral excitations. We assess the performance of these methods and work on improving them.

We conducted a benchmark study to assess the performance of GW methods with varying degrees of self-consistency, from the non-self-consistent G_{0}W_{0} method, which is a first order perturbative correction of the eigenvalues from a mean-field calculation (such as DFT or Hartree-Fock) to a fully self-consistent solution of the Dyson equation. The accuracy was evaluated for the ionization potentials (IPs) and electron affinities (EAs) of a set of 24 electron acceptors, representing chemical families commonly used for organic electronics and photovoltaics. Errors were evaluated with respect to high-level reference data calculated with coupled cluster singles, doubles, and perturbative triples [CCSD(T)] extrapolated to the complete basis set limit. The best performance was obtained from the second order screened exchange (SOSEX) correction to G_{0}W_{0} and from G_{0}W_{0} based on an IP-tuned long-range corrected (LC) hybrid DFT functional. The performance of GW methods was additionally compared to tuned LC-hybrid functionals and electron propagator (EP) methods. JCTC 12, 615 (2016)

We developed a “beyond GW” second order screened exchange (SOSEX) correction. The SOSEX diagram is obtained by antisymmetrizing the GW correlation diagram and accounts for a subset of exchange type interactions. G_{0}W_{0}+SOSEX provides improved ionization potentials, electron affinities, and valence spectra for organic semiconductors. PRB 92, 081104(R) (2015)

Spectra of the organic semiconductor NDCA, computed with G_{0}W_{0} based on different DFT starting points compared to a gas phase photoemission experiment. The consistent starting point (CSP) yields the lowest mean absolute error. Phys. Rev. B 86, 041110(R) (2012)

**The exchange-correlation functional:**

Mysterious beast

exists in an unknown form

in the land of Kohn

**Hedin's equations:**

Pentagonal wheel

spins a yarn of diagrams

to screen a shy hole