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

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.

Predicting the frequency dispersion of electronic hyperpolarizabilities on the basis of absorption data and thomas-kuhn sum rules

Successfully predicting the frequency dispersion of electronic hyperpolarizabilities is an unresolved challenge in materials science and electronic structure theory. We show that the generalized Thomas-Kuhn sum rules, combined with linear absorption data and measured hyperpolarizability at one or two frequencies, may be used to predict the entire frequency-dependent electronic hyperpolarizability spectrum. This treatment includes two- and three-level contributions that arise from the lowest two or three excited electronic state manifolds, enabling us to describe the unusual observed frequency dispersion of the dynamic hyperpolarizability in high oscillator strength M-PZn chromophores, where (porphinato)zinc(II) (PZn) and metal(II)polypyridyl (M) units are connected via an ethyne unit that aligns the high oscillator strength transition dipoles of these components in a head-to-tail arrangement. We show that some of these structures can possess very similar linear absorption spectra yet manifest dramatically different frequency dependent hyperpolarizabilities, because of three-level contributions that result from excited state-to excited state transition dipoles among charge polarized states. Importantly, this approach provides a quantitative scheme to use linear optical absorption spectra and very limited individual hyperpolarizability measurements to predict the entire frequency-dependent nonlinear optical response. Copyright © 2010 American Chemical Society.

Design, Synthesis, and Photophysical Investigation of Porphyrin-containing Polymer-wrapped Single-walled Carbon Nanotubes

Significant advances in understanding the fundamental photophysical behavior of single-walled carbon nanotubes (SWNTs) have been made possible by the development of ionic, conjugated aryleneethynylene polymers that helically wrap SWNTs with well-defined morphology. My contribution to this work was the design and synthesis of porphyrin-containing polymers and the photophysical investigation of the corresponding polymer-wrapped SWNTs. For these new constructs, the polymer acts as more than just a solubilization scaffold; such assemblies can provide benchmark data for evaluating spectroscopic signatures of energy and charge transfer events and lay the groundwork for further, rational development of polymers with precisely tuned redox properties and electronic coupling with the underlying SWNT. The first design to incorporate a zinc porphyrin into the polymer backbone, PNES-PZn, suffered from severe aggregation in solution and was redesigned to produce the porphyrin-containing polymer S-PBN-PZn. This polymer was utilized to helically wrap chirality-enriched (6,5) SWNTs, which resulted in significant quenching of the porphyrin-based fluorescence. Time-resolved spectroscopy revealed a simultaneous rise and decay of the porphyrin radical cation and SWNT electron polaron spectroscopic signatures indicative of photoinduced electron transfer. A new polymer, S-PBN(b)-Ph2PZn3, was then synthesized which incorporated a meso-ethyne linked zinc porphyrin trimer. By changing the absorption profile and electrochemical redox potentials of the polymer, the photophysical behavior of the corresponding polymer-wrapped (6,5)-SWNTs was dramatically changed, and the polymer-wrapped SWNTs no longer showed evidence for photoinduced electron transfer.

Nowhere Landscape, for Clarinets, Trombones, Percussion, Violins, and Electronics and “The Map and the Territory: Documenting David Dunn’s Sky Drift”

1. nowhere landscape, for clarinets, trombones, percussion, violins, and electronics

nowhere landscape is an eighty-minute work for nine performers, composed of acoustic and electronic sounds. Its fifteen movements invoke a variety of listening strategies, using slow change, stasis, layering, coincidence, and silence to draw attention to the sonic effects of the environment—inside the concert hall as well as the world outside of it. The work incorporates a unique stage set-up: the audience sits in close proximity to the instruments, facing in one of four different directions, while the musicians play from a number of constantly-shifting locations, including in front of, next to, and behind the audience.

Much of nowhere landscape’s material is derived from a collection of field recordings

made by the composer during a road trip from Springfield, MA to Douglas, WY along US- 20, a cross-country route made effectively obsolete by the completion of I-90 in the mid- 20th century. In an homage to artist Ed Ruscha’s 1963 book Twentysix Gasoline Stations, the composer made twenty-six recordings at gas stations along US-20. Many of the movements of nowhere landscape examine the musical potential of these captured soundscapes: familiar and anonymous, yet filled with poignancy and poetic possibility.

2. “The Map and the Territory: Documenting David Dunn’s Sky Drift”

In 1977, David Dunn recruited twenty-six musicians to play his work Sky Drift in the

Anza-Borrego Desert in Southern California. This outdoor performance was documented with photos and recorded with four stationary microphones to tape. A year later, Dunn presented the work in New York City as a “performance/documentation,” playing back the audio recording and projecting slides. In this paper I examine the consequences of this kind of act: what does it mean for a recording of an outdoor work to be shared at an indoor concert event? Can such a complex and interactive experience be successfully flattened into some kind of re-playable documentation? What can a recording capture and what must it exclude?

This paper engages with these questions as they relate to David Dunn’s Sky Drift and to similar works by Karlheinz Stockhausen and John Luther Adams. These case-studies demonstrate different solutions to the difficulty of documenting outdoor performances. Because this music is often heard from a variety of equally-valid perspectives—and because any single microphone only captures sound from one of these perspectives—the physical set-up of these kind of pieces complicate what it means to even “hear the music” at all. To this end, I discuss issues around the “work itself” and “aura” as well as “transparency” and “liveness” in recorded sound, bringing in thoughts and ideas from Walter Benjamin, Howard Becker, Joshua Glasgow, and others. In addition, the artist Robert Irwin and the composer Barry Truax have written about the conceptual distinctions between “the work” and “not- the-work”; these distinctions are complicated by documentation and recording. Without the context, the being-there, the music is stripped of much of its ability to communicate meaning.

Application of Numerical Methods to Study Arrangement and Fracture of Lithium-Ion Microstructure

The focus of this work is to develop and employ numerical methods that provide characterization of granular microstructures, dynamic fragmentation of brittle materials, and dynamic fracture of three-dimensional bodies.

We first propose the fabric tensor formalism to describe the structure and evolution of lithium-ion electrode microstructure during the calendaring process. Fabric tensors are directional measures of particulate assemblies based on inter-particle connectivity, relating to the structural and transport properties of the electrode. Applying this technique to X-ray computed tomography of cathode microstructure, we show that fabric tensors capture the evolution of the inter-particle contact distribution and are therefore good measures for the internal state of and electronic transport within the electrode.

We then shift focus to the development and analysis of fracture models within finite element simulations. A difficult problem to characterize in the realm of fracture modeling is that of fragmentation, wherein brittle materials subjected to a uniform tensile loading break apart into a large number of smaller pieces. We explore the effect of numerical precision in the results of dynamic fragmentation simulations using the cohesive element approach on a one-dimensional domain. By introducing random and non-random field variations, we discern that round-off error plays a significant role in establishing a mesh-convergent solution for uniform fragmentation problems. Further, by using differing magnitudes of randomized material properties and mesh discretizations, we find that employing randomness can improve convergence behavior and provide a computational savings.

The Thick Level-Set model is implemented to describe brittle media undergoing dynamic fragmentation as an alternative to the cohesive element approach. This non-local damage model features a level-set function that defines the extent and severity of degradation and uses a length scale to limit the damage gradient. In terms of energy dissipated by fracture and mean fragment size, we find that the proposed model reproduces the rate-dependent observations of analytical approaches, cohesive element simulations, and experimental studies.

Lastly, the Thick Level-Set model is implemented in three dimensions to describe the dynamic failure of brittle media, such as the active material particles in the battery cathode during manufacturing. The proposed model matches expected behavior from physical experiments, analytical approaches, and numerical models, and mesh convergence is established. We find that the use of an asymmetrical damage model to represent tensile damage is important to producing the expected results for brittle fracture problems.

The impact of this work is that designers of lithium-ion battery components can employ the numerical methods presented herein to analyze the evolving electrode microstructure during manufacturing, operational, and extraordinary loadings. This allows for enhanced designs and manufacturing methods that advance the state of battery technology. Further, these numerical tools have applicability in a broad range of fields, from geotechnical analysis to ice-sheet modeling to armor design to hydraulic fracturing.