This work investigates the effects of molecular size on the accuracy of density-functional ionization potentials for a set of 28 hydrocarbons, including series of alkanes, alkenes, and oligoacenes. As the system size increases, delocalization error introduces a systematic underestimation of the ionization potential, which is rationalized by considering the fractional-charge behavior of the electronic energies. The computation of the ionization potential with many density-functional approximations is not size-extensive due to excessive delocalization of the incipient positive charge. While inclusion of exact exchange reduces the observed errors, system-specific tuning of long-range corrected functionals does not generally improve accuracy. These results emphasize that good performance of a functional for small molecules is not necessarily transferable to larger systems.
Optimizing the optical properties of large chromophore aggregates and molecular solids for applications in photovoltaics and nonlinear optics is an outstanding challenge. It requires efficient and reliable computational models that must be validated against accurate theoretical methods. We show that linear absorption spectra calculated using the molecular exciton model agree well with spectra calculated using time-dependent density functional theory and configuration interaction singles for aggregates of strongly polar chromophores. Similar agreement is obtained for a hybrid functional (B3LYP), a long-range corrected hybrid functional (ωB97X), and configuration interaction singles. Accounting for the electrostatic environment of individual chromophores in the parametrization of the exciton model with the inclusion of atomic point charges significantly improves the agreement of the resulting spectra with those calculated using all-electron methods; different charge definitions (Mulliken and ChelpG) yield similar results. We find that there is a size-dependent error in the exciton model compared with all-electron methods, but for aggregates with more than six chromophores, the errors change slowly with the number of chromophores in the aggregate. Our results validate the use of the molecular exciton model for predicting the absorption spectra of bulk molecular solids; its formalism also allows straightforward extension to calculations of nonlinear optical response.
Density functional theory is often the method of choice for modeling the energetics of large molecules and including explicit solvation effects. It is preferable to use a method that treats systems of different sizes and with different amounts of explicit solvent on equal footing. However, recent work suggests that approximate density functional theory has a size-dependent error in the computation of the ionization potential. We here investigate the lack of size-intensivity of the ionization potential computed with approximate density functionals in vacuum and solution. We show that local and semi-local approximations to exchange do not yield a constant ionization potential for an increasing number of identical isolated molecules in vacuum. Instead, as the number of molecules increases, the total energy required to ionize the system decreases. Rather surprisingly, we find that this is still the case in solution, whether using a polarizable continuum model or with explicit solvent that breaks the degeneracy of each solute, and we find that explicit solvent in the calculation can exacerbate the size-dependent delocalization error. We demonstrate that increasing the amount of exact exchange changes the character of the polarization of the solvent molecules; for small amounts of exact exchange the solvent molecules contribute a fraction of their electron density to the ionized electron, but for larger amounts of exact exchange they properly polarize in response to the cationic solute. In vacuum and explicit solvent, the ionization potential can be made size-intensive by optimally tuning a long-range corrected hybrid functional.
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