Ground and Electronic Excited States from Pairing Matrix Fluctuation and Particle-Particle Random Phase Approximation

<p>The accurate description of ground and electronic excited states is an important and challenging topic in quantum chemistry. The pairing matrix fluctuation, as a counterpart of the density fluctuation, is applied to this topic. From the pairing matrix fluctuation, the exact electron correlation energy as well as two electron addition/removal energies can be extracted. Therefore, both ground state and excited states energies can be obtained and they are in principle exact with a complete knowledge of the pairing matrix fluctuation. In practice, considering the exact pairing matrix fluctuation is unknown, we adopt its simple approximation --- the particle-particle random phase approximation (pp-RPA) --- for ground and excited states calculations. The algorithms for accelerating the pp-RPA calculation, including spin separation, spin adaptation, as well as an iterative Davidson method, are developed. For ground states correlation descriptions, the results obtained from pp-RPA are usually comparable to and can be more accurate than those from traditional particle-hole random phase approximation (ph-RPA). For excited states, the pp-RPA is able to describe double, Rydberg, and charge transfer excitations, which are challenging for conventional time-dependent density functional theory (TDDFT). Although the pp-RPA intrinsically cannot describe those excitations excited from the orbitals below the highest occupied molecular orbital (HOMO), its performances on those single excitations that can be captured are comparable to TDDFT. The pp-RPA for excitation calculation is further applied to challenging diradical problems and is used to unveil the nature of the ground and electronic excited states of higher acenes. The pp-RPA and the corresponding Tamm-Dancoff approximation (pp-TDA) are also applied to conical intersections, an important concept in nonadiabatic dynamics. Their good description of the double-cone feature of conical intersections is in sharp contrast to the failure of TDDFT. All in all, the pairing matrix fluctuation opens up new channel of thinking for quantum chemistry, and the pp-RPA is a promising method in describing ground and electronic excited states.</p>

Can a Broader Education Narrow the Gap? Evidence on Non-Academic Features of Schooling

<p>Empirical studies of education programs and systems, by nature, rely upon use of student outcomes that are measurable. Often, these come in the form of test scores. However, in light of growing evidence about the long-run importance of other student skills and behaviors, the time has come for a broader approach to evaluating education. This dissertation undertakes experimental, quasi-experimental, and descriptive analyses to examine social, behavioral, and health-related mechanisms of the educational process. My overarching research question is simply, which inside- and outside-the-classroom features of schools and educational interventions are most beneficial to students in the long term? Furthermore, how can we apply this evidence toward informing policy that could effectively reduce stark social, educational, and economic inequalities?</p><p>The first study of three assesses mechanisms by which the Fast Track project, a randomized intervention in the early 1990s for high-risk children in four communities (Durham, NC; Nashville, TN; rural PA; and Seattle, WA), reduced delinquency, arrests, and health and mental health service utilization in adolescence through young adulthood (ages 12-20). A decomposition of treatment effects indicates that about a third of Fast Track’s impact on later crime outcomes can be accounted for by improvements in social and self-regulation skills during childhood (ages 6-11), such as prosocial behavior, emotion regulation and problem solving. These skills proved less valuable for the prevention of mental and physical health problems.</p><p>The second study contributes new evidence on how non-instructional investments – such as increased spending on school social workers, guidance counselors, and health services – affect multiple aspects of student performance and well-being. Merging several administrative data sources spanning the 1996-2013 school years in North Carolina, I use an instrumental variables approach to estimate the extent to which local expenditure shifts affect students’ academic and behavioral outcomes. My findings indicate that exogenous increases in spending on non-instructional services not only reduce student absenteeism and disciplinary problems (important predictors of long-term outcomes) but also significantly raise student achievement, in similar magnitude to corresponding increases in instructional spending. Furthermore, subgroup analyses suggest that investments in student support personnel such as social workers, health services, and guidance counselors, in schools with concentrated low-income student populations could go a long way toward closing socioeconomic achievement gaps.</p><p>The third study examines individual pathways that lead to high school graduation or dropout. It employs a variety of machine learning techniques, including decision trees, random forests with bagging and boosting, and support vector machines, to predict student dropout using longitudinal administrative data from North Carolina. I consider a large set of predictor measures from grades three through eight including academic achievement, behavioral indicators, and background characteristics. My findings indicate that the most important predictors include eighth grade absences, math scores, and age-for-grade as well as early reading scores. Support vector classification (with a high cost parameter and low gamma parameter) predicts high school dropout with the highest overall validity in the testing dataset at 90.1 percent followed by decision trees with boosting and interaction terms at 89.5 percent.</p>