Saddle point localization of molecular wavefunctions

The quantum mechanical description of isomerization is based on bound eigenstates of the molecular potential energy surface. For the near-minimum regions there is a textbook-based relationship between the potential and eigenenergies. Here we show how the saddle point region that connects the two minima is encoded in the eigenstates of the model quartic potential and in the energy levels of the [H, C, N] potential energy surface. We model the spacing of the eigenenergies with the energy dependent classical oscillation frequency decreasing to zero at the saddle point. The eigenstates with the smallest spacing are localized at the saddle point. The analysis of the HCN???HNC isomerization states shows that the eigenstates with small energy spacing relative to the effective (v1, v3, l) bending potentials are highly localized in the bending coordinate at the transition state. These spectroscopically detectable states represent a chemical marker of the transition state in the eigenenergy spectrum. The method developed here provides a basis for modeling characteristic patterns in the eigenenergy spectrum of bound states

The Past and Future of Evolutionary Economics : Some Reflections Based on New Bibliometric Evidence

This document is the Accepted Manuscript version of the following article: Geoffrey M. Hodgson, and Juha-Antti Lamberg, ‘The past and future of evolutionary economics: some reflections based on new bibliometric evidence’, Evolutionary and Institutional Economics Review, first online 20 June 2016. The final publication is available at Springer via doi: http://dx.doi.org/10.1007/s40844-016-0044-3 © Japan Association for Evolutionary Economics 2016The modern wave of ‘evolutionary economics’ was launched with the classic study by Richard Nelson and Sidney Winter (1982). This paper reports a broad bibliometric analysis of ‘evolutionary’ research in the disciplines of management, business, economics, and sociology over 25 years from 1986 to 2010. It confirms that Nelson and Winter (1982) is an enduring nodal reference point for this broad field. The bibliometric evidence suggests that ‘evolutionary economics’ has benefitted from the rise of business schools and other interdisciplinary institutions, which have provided a home for evolutionary terminology, but it has failed to nurture a strong unifying core narrative or theory, which in turn could provide superior answers to important questions. This bibliometric evidence also shows that no strong cluster of general theoretical research immediately around Nelson and Winter (1982) has subsequently emerged. It identifies developmental problems in a partly successful but fragmented field. Future research in ‘evolutionary economics’ needs a more integrated research community with shared conceptual narratives and common research questions, to promote conversation and synergy between diverse clusters of research.Peer reviewedFinal Accepted Versio