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.

A Theory and Test of How Speakers with Nonnative Accents are Evaluated in Entrepreneurial Settings

An abundance of research in the social sciences has demonstrated a persistent bias against nonnative English speakers (Giles & Billings, 2004; Gluszek & Dovidio, 2010). Yet, organizational scholars have only begun to investigate the underlying mechanisms that drive the bias against nonnative speakers and subsequently design interventions to mitigate these biases. In this dissertation, I offer an integrative model to organize past explanations for accent-based bias into a coherent framework, and posit that nonnative accents elicit social perceptions that have implications at the personal, relational, and group level. I also seek to complement the existing emphasis on main effects of accents, which focuses on the general tendency to discriminate against those with accents, by examining moderators that shed light on the conditions under which accent-based bias is most likely to occur. Specifically, I explore the idea that people’s beliefs about the controllability of accents can moderate their evaluations toward nonnative speakers, such that those who believe that accents can be controlled are more likely to demonstrate a bias against nonnative speakers. I empirically test my theoretical model in three studies in the context of entrepreneurial funding decisions. Results generally supported the proposed model. By examining the micro foundations of accent-based bias, the ideas explored in this dissertation set the stage for future research in an increasingly multilingual world.