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.

The neural basis of naming impairments in Alzheimer's disease revealed through positron emission tomography.

The naming impairments in Alzheimer's disease (AD) have been attributed to a variety of cognitive processing deficits, including impairments in semantic memory, visual perception, and lexical access. To further understand the underlying biological basis of the naming failures in AD, the present investigation examined the relationship of various classes of naming errors to regional brain measures of cerebral glucose metabolism as measured with 18 F-Fluoro-2-deoxyglucose (FDG) and positron emission tomography (PET). Errors committed on a visual naming test were categorized according to a cognitive processing schema and then examined in relationship to metabolism within specific brain regions. The results revealed an association of semantic errors with glucose metabolism in the frontal and temporal regions. Language access errors, such as circumlocutions, and word blocking nonresponses were associated with decreased metabolism in areas within the left hemisphere. Visuoperceptive errors were related to right inferior parietal metabolic function. The findings suggest that specific brain areas mediate the perceptual, semantic, and lexical processing demands of visual naming and that visual naming problems in dementia are related to dysfunction in specific neural circuits.