Intramolecular basis set superposition error effects on the planarity of benzene and other aromatic molecules: A solution to the problem

Recently, the surprising result that ab initio calculations on benzene and other planar arenes at correlated MP2, MP3, configuration interaction with singles and doubles (CISD), and coupled cluster with singles and doubles levels of theory using standard Pople’s basis sets yield nonplanar minima has been reported. The planar optimized structures turn out to be transition states presenting one or more large imaginary frequencies, whereas single-determinant-based methods lead to the expected planar minima and no imaginary frequencies. It has been suggested that such anomalous behavior can be originated by two-electron basis set incompleteness error. In this work, we show that the reported pitfalls can be interpreted in terms of intramolecular basis set superposition error (BSSE) effects, mostly between the C–H moieties constituting the arenes. We have carried out counterpoise-corrected optimizations and frequency calculations at the Hartree–Fock, B3LYP, MP2, and CISD levels of theory with several basis sets for a number of arenes. In all cases, correcting for intramolecular BSSE fixes the anomalous behavior of the correlated methods, whereas no significant differences are observed in the single-determinant case. Consequently, all systems studied are planar at all levels of theory. The effect of different intramolecular fragment definitions and the particular case of charged species, namely, cyclopentadienyl and indenyl anions, respectively, are also discussed

Direct and indirect subsidies in markets with system goods in the presence of externalities. Preliminary version

This paper derives a model of markets with system goods and two technological standards. An established standard incurs lower unit production costs but causes a negative externality. The paper derives the conditions for policy intervention and compares the effect of direct and indirect cost-reducing subsidies in two markets with system goods in the presence of externalities. If consumers are committed to the technology by purchasing one of the components, direct subsidies are preferable. For a medium-low cost difference between technological standards and a low externality cost it is optimal to provide a direct subsidy only to the first technology adopter. As the higher the externality cost raises, the more technology adopters should be provided with direct subsidies. This effect is robust in all extensions. In the absence of consumers commitment to a technological standard indirect and direct subsidies are both desirable. In this case, the subsidy to the first adopter is lower then the subsidy to the second adopter. Moreover, for the low cost difference between technological standards and low externality cost the fi rst fi rm chooses a superior standard without policy intervention. Finally, a perfect compatibility between components based on different technological standards enhances an advantage of indirect subsidies for medium-high externality cost and cost difference between technological standards. Journal of Economic Literature Classi fication Numbers: C72, D21, D40, H23, L13, L22, L51, O25, O33, O38. Keywords: Technological standards; complementary products; externalities; cost-reducing subsidies; compatibility.