While density-functional theory is an effective and popular method in quantum chemistry, approximations within the exchange-correlation functional can produce substantial inaccuracies. For example, generalized-gradient approximation (GGA) functionals produce convex energy versus charge curves that violate the correct piecewise-linearity constraint of E(N) for fractional charges, referred to as delocalization error. This leads to a false description of molecular properties, such as the HOMO and LUMO energy levels. This work investigates the delocalization error in a series of gas-phase organic molecules, including alkanes, alkenes, oligoacenes, and ensembles of methane molecules. In addition, the effect of continuum solvation on the delocalization error is explored. The GGA deviation from linearity of the E(N) curves is evaluated and ?-tuning of a long-range corrected functional is performed for each molecule/system. It is found that the deviation from linearity, and thus the optimal ?, decrease with increasing molecular size and/or solvation. However, systematic error in the endpoint of the E(N) curve, and thus in the ionization potential, is simultaneously introduced, demonstrating the impact of molecular size on delocalization error.

Influence of molecular size on the density-functional delocalization error

248th National Meeting (2014)

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