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.

Microbial Community Responses to Environmental Perturbation

Microorganisms mediate many biogeochemical processes critical to the functioning of ecosystems, which places them as an intermediate between environmental change and the resulting ecosystem response. Yet, we have an incomplete understanding of these relationships, how to predict them, and when they are influential. Understanding these dynamics will inform ecological principles developed for macroorganisms and aid expectations for microbial responses to new gradients. To address this research goal, I used two studies of environmental gradients and a literature synthesis.

With the gradient studies, I assessed microbial community composition in stream biofilms across a gradient of alkaline mine drainage. I used multivariate approaches to examine changes in the non-eukaryote microbial community composition of taxa (chapter 2) and functional genes (chapter 3). I found that stream biofilms at sites receiving alkaline mine drainage had distinct community composition and also differed in the composition of functional gene groups compared with unmined reference sites. Compositional shifts were not dominated by groups that could benefit from mining associated increases of terminal electron acceptors; two-thirds of responsive taxa and functional gene groups were negatively associated with mining. The majority of subsidies and stressors (nitrate, sulfate, conductivity) had no consistent relationships with taxa or gene abundances. However, methane metabolism genes were less abundant at mined sites and there was a strong, positive correlation between selenate reductase gene abundance and mining-associated selenium. These results highlighted the potential for indirect factors to also play an important role in explaining compositional shifts.

In the fourth chapter, I synthesized studies that use environmental perturbations to explore microbial community structure and microbial process connections. I examined nine journals (2009–13) and found that many qualifying papers (112 of 148) documented structure and process responses, but few (38 of 112 papers) reported statistically testing for a link. Of these tested links, 75% were significant. No particular approach for characterizing structure or processes was more likely to produce significant links. Process responses were detected earlier on average than responses in structure. Together, the findings suggested that few publications report statistically testing structure-process links; but when tested, links often occurred yet shared few commonalities in linked processes or structures and the techniques used for measuring them.

Although the research community has made progress, much work remains to ensure that the vast and growing wealth of microbial informatics data is translated into useful ecological information. In part, this challenge can be approached through using hypotheses to guide analyses, but also by being open to opportunities for hypothesis generation. The results from my dissertation work advise that it is important to carefully interpret shifts in community composition in relation to abiotic characteristics and recommend considering ecological, thermodynamic, and kinetic principles to understand the properties governing community responses to environmental perturbation.