Application of the Schwinger multichannel method to multichannel studies of electronically inelastic electron-molecule collisions

We have applied the Schwinger Multichannel Method(SMC) to the study of electronically inelastic, low energy electron-molecule collisions. The focus of these studies has been the assessment of the importance of multichannel coupling to the dynamics of these excitation processes. It has transpired that the promising quality of results realized in early SMC work on such inelastic scattering processes has been far more difficult to obtain in these more sophisticated studies.

We have attempted to understand the sources of instability of the SMC method which are evident in these multichannel studies. Particular instances of such instability have been considered in detail, which indicate that linear dependence, failure of the separable potential approximation, and difficulties in converging matrix elements involving recorrelation or Q-space terms all conspire to complicate application of the SMC method to these studies. A method involving singular value decomposition(SVD) has been developed to, if not resolve these problems, at least mitigate their deleterious effects on the computation of electronically inelastic cross sections.

In conjunction with this SVD procedure, the SMC method has been applied to the study of the H_2 , H_2O, and N_2 molecules. Rydberg excitations of the first two molecules were found to be most sensitive to multichannel coupling near threshold. The (3σ_g → 1π_g ) and (1π_u → 1π_g) valence excitations of the N_2 molecule were found to be strongly influenced by the choice of channel coupling scheme at all collision energies considered in these studies.

Intramolecular conflict : conformation and self-assembly of architecturally complex macromolecules in solution

The solution behavior of linear polymer chains is well understood, having been the subject of intense study throughout the previous century. As plastics have become ubiquitous in everyday life, polymer science has grown into a major field of study. The conformation of a polymer in solution depends on the molecular architecture and its interactions with the surroundings. Developments in synthetic techniques have led to the creation of precision-tailored polymeric materials with varied topologies and functionalities. In order to design materials with the desired properties, it is imperative to understand the relationships between polymer architecture and their conformation and behavior. To meet that need, this thesis investigates the conformation and self-assembly of three architecturally complex macromolecular systems with rich and varied behaviors driven by the resolution of intramolecular conflicts. First we describe the development of a robust and facile synthetic approach to reproducible bottlebrush polymers (Chapter 2). The method was used to produce homologous series of bottlebrush polymers with polynorbornene backbones, which revealed the effect of side-chain and backbone length on the overall conformation in both good and theta solvent conditions (Chapter 3). The side-chain conformation was obtained from a series of SANS experiments and determined to be indistinguishable from the behavior of free linear polymer chains. Using deuterium-labeled bottlebrushes, we were able for the first time to directly observe the backbone conformation of a bottlebrush polymer which showed self-avoiding walk behavior. Secondly, a series of SANS experiments was conducted on a homologous series of Side Group Liquid Crystalline Polymers (SGLCPs) in a perdeuterated small molecule liquid crystal (5CB). Monodomain, aligned, dilute samples of SGLCP-b-PS block copolymers were seen to self-assemble into complex micellar structures with mutually orthogonally oriented anisotropies at different length scales (Chapter 4). Finally, we present the results from the first scattering experiments on a set of fuel-soluble, associating telechelic polymers. We observed the formation of supramolecular aggregates in dilute (≤0.5wt%) solutions of telechelic polymers and determined that the choice of solvent has a significant effect on the strength of association and the size of the supramolecules (Chapter 5). A method was developed for the direct estimation of supramolecular aggregation number from SANS data. The insight into structure-property relationships obtained from this work will enable the more targeted development of these molecular architectures for their respective applications.

Optimal design of building structures using genetic algorithms

A general framework for multi-criteria optimal design is presented which is well-suited for automated design of structural systems. A systematic computer-aided optimal design decision process is developed which allows the designer to rapidly evaluate and improve a proposed design by taking into account the major factors of interest related to different aspects such as design, construction, and operation.

The proposed optimal design process requires the selection of the most promising choice of design parameters taken from a large design space, based on an evaluation using specified criteria. The design parameters specify a particular design, and so they relate to member sizes, structural configuration, etc. The evaluation of the design uses performance parameters which may include structural response parameters, risks due to uncertain loads and modeling errors, construction and operating costs, etc. Preference functions are used to implement the design criteria in a "soft" form. These preference functions give a measure of the degree of satisfaction of each design criterion. The overall evaluation measure for a design is built up from the individual measures for each criterion through a preference combination rule. The goal of the optimal design process is to obtain a design that has the highest overall evaluation measure - an optimization problem.

Genetic algorithms are stochastic optimization methods that are based on evolutionary theory. They provide the exploration power necessary to explore high-dimensional search spaces to seek these optimal solutions. Two special genetic algorithms, hGA and vGA, are presented here for continuous and discrete optimization problems, respectively.

The methodology is demonstrated with several examples involving the design of truss and frame systems. These examples are solved by using the proposed hGA and vGA.

Adsorption of Pb(II) and Cu(II) on α-quartz from aqueous solutions: influence of pH, ionic strength, and complexing ligands

Adsorption of aqueous Pb(II) and Cu(II) on α-quartz was studied as a function of time, system surface area, and chemical speciation. Experimental systems contained sodium as a major cation, hydroxide, carbonate, and chloride as major anions, and covered the pH range 4 to 8. In some cases citrate and EDTA were added as representative organic complexing agents. The adsorption equilibria were reached quickly, regardless of the system surface area. The positions of the adsorption equilibria were found to be strongly dependent on pH, ionic strength and concentration of citrate and EDTA. The addition of these non-adsorbing ligands resulted in a competition between chelation and adsorption. The experimental work also included the examination of the adsorption behavior of the doubly charged major cations Ca(II) and Mg(II) as a function of pH.

The theoretical description of the experimental systems was obtained by means of chemical equilibrium-plus-adsorption computations using two adsorption models: one mainly electrostatic (the James-Healy Model), and the other mainly chemical (the Ion Exchange-Surface Complex Formation Model). Comparisons were made between these two models.

The main difficulty in the theoretical predictions of the adsorption behavior of Cu(II) was the lack of the reliable data for the second hydrolysis constant(*β_2) The choice of the constant was made on the basis of potentiometric titratlons of Cu^(2+)

The experimental data obtained and the resulting theoretical observations were applied in models of the chemical behavior of trace metals in fresh oxic waters, with emphasis on Pb(II) and Cu(II).

Trimethylsilyl anions: stereospecific deoxygenation of epoxides and trimethylsilyldehalogenation of aryl halides

I. Trimethylsilylpotassium reacts with epoxides to give olefins with inversion of stereochemistry. The reaction appears to proceed via the potassium β-silyl alkoxide (2) formed from the S_N2 attack of the silyl anion on the epoxide. Subsequent stereospecific synelimination of 2 affords the olefin of inverted stereo-chemistry. The reaction is convenient and preparatively useful.

The byproduct of the reaction, potassium trimethylsilanolate (17), effectively cleaves hexamethyldisilane to yield trimethylsilylpotassium. Since the latter reagent is generated and reacted in situ with epoxides, the overall reaction can be carried out with less than one equivalent of potassium methoxide.

II. The reaction of aryl halides with trimethylsilyl anions in HMPT provides good yields of aryltrimethylsilanes, useful synthetic intermediates. The choice of metal cation is unimportant. Chlorides and bromides give high yields of silylated products, while iodides give lower yields, with correspondingly increased amounts of reduced products. Arylammonium and arylphosphonium salts also undergo the reaction.

We have permissive evidence for the reaction proceeding via both aryl radical and aryl anion intermediates.

III. Trimethylsilyl and trimethylstannyl methoxycarbene complexes of chromium and tungsten have been prepared. One of these, (CO)_5WC(OMe)SnMe_3, reacts with norbornene at 80° to afford a new olefin polymer. Efforts to effect the alpha-elimination of the nonmetallic carbene ligands have not yet been successful. Reactions of these carbene complexes with acetone have been investigated.

First principles based multiparadigm modeling of electronic structures and dynamics

Electronic structures and dynamics are the key to linking the material composition and structure to functionality and performance.

An essential issue in developing semiconductor devices for photovoltaics is to design materials with optimal band gaps and relative positioning of band levels. Approximate DFT methods have been justified to predict band gaps from KS/GKS eigenvalues, but the accuracy is decisively dependent on the choice of XC functionals. We show here for CuInSe₂ and CuGaSe₂, the parent compounds of the promising CIGS solar cells, conventional LDA and GGA obtain gaps of 0.0-0.01 and 0.02-0.24 eV (versus experimental values of 1.04 and 1.67 eV), while the historically first global hybrid functional, B3PW91, is surprisingly the best, with band gaps of 1.07 and 1.58 eV. Furthermore, we show that for 27 related binary and ternary semiconductors, B3PW91 predicts gaps with a MAD of only 0.09 eV, which is substantially better than all modern hybrid functionals, including B3LYP (MAD of 0.19 eV) and screened hybrid functional HSE06 (MAD of 0.18 eV).

The laboratory performance of CIGS solar cells (> 20% efficiency) makes them promising candidate photovoltaic devices. However, there remains little understanding of how defects at the CIGS/CdS interface affect the band offsets and interfacial energies, and hence the performance of manufactured devices. To determine these relationships, we use the B3PW91 hybrid functional of DFT with the AEP method that we validate to provide very accurate descriptions of both band gaps and band offsets. This confirms the weak dependence of band offsets on surface orientation observed experimentally. We predict that the CBO of perfect CuInSe₂/CdS interface is large, 0.79 eV, which would dramatically degrade performance. Moreover we show that band gap widening induced by Ga adjusts only the VBO, and we find that Cd impurities do not significantly affect the CBO. Thus we show that Cu vacancies at the interface play the key role in enabling the tunability of CBO. We predict that Na further improves the CBO through electrostatically elevating the valence levels to decrease the CBO, explaining the observed essential role of Na for high performance. Moreover we find that K leads to a dramatic decrease in the CBO to 0.05 eV, much better than Na. We suggest that the efficiency of CIGS devices might be improved substantially by tuning the ratio of Na to K, with the improved phase stability of Na balancing phase instability from K. All these defects reduce interfacial stability slightly, but not significantly.

A number of exotic structures have been formed through high pressure chemistry, but applications have been hindered by difficulties in recovering the high pressure phase to ambient conditions (i.e., one atmosphere and room temperature). Here we use dispersion-corrected DFT (PBE-ulg flavor) to predict that above 60 GPa the most stable form of N₂O (the laughing gas in its molecular form) is a 1D polymer with an all-nitrogen backbone analogous to cis-polyacetylene in which alternate N are bonded (ionic covalent) to O. The analogous trans-polymer is only 0.03-0.10 eV/molecular unit less stable. Upon relaxation to ambient conditions both polymers relax below 14 GPa to the same stable non-planar trans-polymer, accompanied by possible electronic structure transitions. The predicted phonon spectrum and dissociation kinetics validate the stability of this trans-poly-NNO at ambient conditions, which has potential applications as a new type of conducting polymer with all-nitrogen chains and as a high-energy oxidizer for rocket propulsion. This work illustrates in silico materials discovery particularly in the realm of extreme conditions.

Modeling non-adiabatic electron dynamics has been a long-standing challenge for computational chemistry and materials science, and the eFF method presents a cost-efficient alternative. However, due to the deficiency of FSG representation, eFF is limited to low-Z elements with electrons of predominant s-character. To overcome this, we introduce a formal set of ECP extensions that enable accurate description of p-block elements. The extensions consist of a model representing the core electrons with the nucleus as a single pseudo particle represented by FSG, interacting with valence electrons through ECPs. We demonstrate and validate the ECP extensions for complex bonding structures, geometries, and energetics of systems with p-block character (C, O, Al, Si) and apply them to study materials under extreme mechanical loading conditions.

Despite its success, the eFF framework has some limitations, originated from both the design of Pauli potentials and the FSG representation. To overcome these, we develop a new framework of two-level hierarchy that is a more rigorous and accurate successor to the eFF method. The fundamental level, GHA-QM, is based on a new set of Pauli potentials that renders exact QM level of accuracy for any FSG represented electron systems. To achieve this, we start with using exactly derived energy expressions for the same spin electron pair, and fitting a simple functional form, inspired by DFT, against open singlet electron pair curves (H₂ systems). Symmetric and asymmetric scaling factors are then introduced at this level to recover the QM total energies of multiple electron pair systems from the sum of local interactions. To complement the imperfect FSG representation, the AMPERE extension is implemented, and aims at embedding the interactions associated with both the cusp condition and explicit nodal structures. The whole GHA-QM+AMPERE framework is tested on H element, and the preliminary results are promising.

I. Efforts toward the synthesis of aliphatic iodonium salts. II. Flourine-19 nuclear magnetic resonance spectroscopy of cyclic and bicyclic systems

The synthesis of iodonium salts of the general formula [C₆H₅IR]⁺X^-, where R is an alkyl group and x- is a stabilizing anion, was attempted. For the choice of R three groups were selected, whose derivatives are known to be sluggish in S_N1 and S_N2 substitutions: cyclopropyl, 7, 7 -dimethyl-1-norbornyl, and 9 -triptycyl. The synthetic routes followed along classical lines which have been exploited in recent years by Beringer and students. Ultimately, the object of the present study was to study the reactions of the above salts with nucleophiles. In none of the three cases, however, was it possible to isolate a stable salt. A thermodynamic argument suggests that this must be due to kinetic instability rather than thermodynamic instability. Only iodocyclopropane and 1-iodoapocamphane formed isolable iododichlorides.

Several methylated 2, 2-difluoronorbornanes were prepared with the intent of correlating fluorine -19 chemical shifts with geometric features in a rigid system. The effect of a methyl group on the shielding of a β -fluorine is dependent upon the dihedral angle; the maximum effect (an upfield shift of the resonance) occurs at 0° and 180°, whereas almost no effect is felt at a dihedral angle of 120°. The effect of a methyl group on a γ -fluorine is to strongly shift the resonance downfield when fluorine and methyl group are in a 1, 3 - diaxial-like relationship. Molecular orbital calculations of fluorine shielding in a variety of molecules were carried out using the formalism developed by Pople; the results are, at best, in modest agreement with experiment.