Accurate localized resolution of identity approach for linear-scaling hybrid density functionals and for many-body perturbation theory

© 2015 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.A key component in calculations of exchange and correlation energies is the Coulomb operator, which requires the evaluation of two-electron integrals. For localized basis sets, these four-center integrals are most efficiently evaluated with the resolution of identity (RI) technique, which expands basis-function products in an auxiliary basis. In this work we show the practical applicability of a localized RI-variant ('RI-LVL'), which expands products of basis functions only in the subset of those auxiliary basis functions which are located at the same atoms as the basis functions. We demonstrate the accuracy of RI-LVL for Hartree-Fock calculations, for the PBE0 hybrid density functional, as well as for RPA and MP2 perturbation theory. Molecular test sets used include the S22 set of weakly interacting molecules, the G3 test set, as well as the G2-1 and BH76 test sets, and heavy elements including titanium dioxide, copper and gold clusters. Our RI-LVL implementation paves the way for linear-scaling RI-based hybrid functional calculations for large systems and for all-electron many-body perturbation theory with significantly reduced computational and memory cost.

Identity Change Impacts Autobiographical Reconstruction of Identity-Relevant Events: Influences of the Self-System on Remembering

The focus on how one is behaving, feeling, and thinking, provides a powerful source of self-knowledge. How is this self-knowledge utilized in the dynamic reconstruction of autobiographical memories? How, in turn, might autobiographical memories support identity and the self-system? I address these questions through a critical review of the literature on autobiographical memory and the self-system, with a special focus on the self-concept, self-knowledge, and identity. I then outline the methods and results of a prospective longitudinal study examining the effects of an identity change on memory for events related to that identity. Participant-rated memory characteristics, computer-generated ratings of narrative content and structure, and neutral-observer ratings of coherence were examined for changes over time related to an identity-change, as well as for their ability to predict an identity-change. The conclusions from this study are threefold: (1) when the rated centrality of an event decreases, the reported instances of retrieval, as well as the phenomenology associated with retrieval and the number of words used to describe the memory, also decrease; (2) memory accuracy (here, estimating past behaviors) was not influenced by an identity change; and (3) remembering is not unidirectional – characteristics of identity-relevant memories and the life story predict and may help support persistence with an identity (here, an academic trajectory).

The Market for Apples: A Theory of Identity and Consumption

This paper presents an economic model of the effects of identity and social norms on consumption patterns. By incorporating qualitative studies in psychology and sociology, I propose a utility function that features two components – economic (functional) and identity elements. This setup is extended to analyze a market comprising a continuum of consumers, whose identity distribution along a spectrum of binary identities is described by a Beta distribution. I also introduce the notion of salience in the context of identity and consumption decisions. The key result of the model suggests that fundamental economic parameters, such as price elasticity and market demand, can be altered by identity elements. In addition, it predicts that firms in perfectly competitive markets may associate their products with certain types of identities, in order to reduce product substitutability and attain price-setting power.