Double and Charge-Transfer Excitations in Time-Dependent Density Functional Theory

Abstract

Time-dependent density functional theory has emerged as a method of choice for calculations of spectra and response properties in physics, chemistry, and biology, with its system-size scaling enabling computations on systems much larger than possible otherwise. While increasingly complex and interesting systems have been successfully tackled with relatively simple functional approximations, there has also been increasing awareness that these functionals tend to fail for certain classes of approximations. I review the fundamental challenges the approximate functionals have in describing double-excitations and charge-transfer excitations, which are two of the most common impediments for the theory to be applied in a black box way. At the same time, I describe the progress made in recent decades in developing functional approximations that give useful predictions for these excitations.

Accurate Total Energies from the Adiabatic-Connection Fluctuation-Dissipation Theorem

“…Whilst the frequency-dependence in the exact f xc [n] along the real ω-axis is critical for recovering the optical spectrum [7,87,88], this is not the case for ACFDT total energies, where it is demonstrated that chemical accuracy can be consistently attained using the AE kernel f xc [n](ω = 0), i.e. neglecting the frequency dependence in the exact xc kernel, but otherwise retaining its nonlocal spatial structure when solving the Dyson equation of linear response time-dependent DFT.…”