Spin multiplets: theory and application

2018 Spring.Includes bibliographical references.Transition metal complexes have seen an increased use as photocatalysts for organic reactions in recent literature, mostly involving the Ru(II)(bpy)3 family of catalysts. Due to the rarity of ruthenium in the Earth's crust, alternative catalysts using Earth abundant materials are desirable. Recent literature has shown that chromium based catalysts show great promise as a replacement for ruthenium for some reactions. The mechanisms of these first-row transition metal complexes are significantly more complex than those of the second and third row. The excited state complexities of first-row transition metal complexes are challenges for both experimental and theoretical research. The complexities of the excited states require theoretical methods beyond the standard single reference methods commonly used in the literature. Through the use of recent multi-reference post Hartree Fock (HF) methods as well as a new multi-reference density functional theory (DFT), insights into the character of chromium-based photocatalysts were examined. A new multi-determinant DFT method named few-determinant density functional theory (FD-DFT) was described. FD-DFT incorporates multiple DFT determinants using a finite difference approach to calculate the exchanges between multiple determinants for open shell multiplets. The method is implemented in a generalized bond valence (GVB) wave function, and can be converged through an SCF procedure. The system was benchmarked using oxygen atom and diatomic oxygen as well as atomic systems with more open shell orbitals. The benchmarking shows stability across many different functional choices, and gives good excitation energies with and without SCF convergence. The Cr(III)(AcAc)3 system has been long studied for its unique excited state properties that defy the standard cascade model for excited state relaxation. The tris(1,3-propanedionato)chromium(iii) (Cr(III)(PDO)3) complex was studied as an analog to the Cr(III)(AcAc)3 system to understand the excited state pathway between the initial excited 4T2g state and the long lived 2Eg state. Using the FD-DFT method as well as the multi-reference spectroscopy oriented configuration interaction (SORCI) method, the initial excited state energies were studied compared to previous perturbation theory (PT) approaches. Both SORCI and FD-DFT calculate reasonable 2Eg excitation energies, an improvement over earlier results. The SORCI method was also used to map the potential energy curve between the initial 4T2g excited state and its fully relaxed distorted structure. The pathway agrees with previous experimental and theoretical studies showing that a transitionless path exists between the quartet and doublet states, but spin-orbit coupling calculations suggest that a direct path between the 4T2g and 2Eg is possible rather than needing a internal conversion step to the lowest 2Eg state. Chromium-based photocatalysts have been recently studied in the literature as having a competitive mechanism between the reaction substrate and O2 whereby the O2 quenches the excited catalyst. Using the combined Cr(III)(PDO)3 • O2 system, the likely states by which this quenching event occurs were studied with FD-DFT as well as recent multi-reference PT approaches. Comparing the excited state calculated using the multi-reference based methods to standards DFT calculations shows the inability of single-determinant methods to correctly produce the proper excited state character even when obtaining somewhat reasonable energies. The excited state responsible for the quenching of the excited complex is identified using spin density plots of the CASSCF calculations. The search for suitable first-row transition metals requires a search across possible ligands and metal centers. Using the success of chromium-based catalysts, isoelectronic vanadium catalysts were studied to identify any potential differences between the complexes as well as identify the utility of vanadium-based catalysts. Using a variety of methods, including TDDFT-based absorption spectra, vibrational component plots of the excited state distortions, and SORCI potential energy curves (PEC), the differences between the chromium and vanadium catalysts were examined. It was found that vanadium catalysts absorptions are shifted significantly from chromium complexes and the vanadium excited states disperse the unpaired electron over the complex instead of localizing it on the metal center. The distortions in the chromium-based catalysts have a greater amount of asymmetric vibrational character compared to vanadium, which shows mostly symmetric behavior. Lastly, the SORCI PECs show that, unlike chromium, the doublet curves do not intersect the quartet curves, making a transition to a long lived doublet state a significantly slower process. The results highlight significant differences between the complexes even with ligand structure is controlled

Explicating the Characteristics of STEM Teaching and Learning: A Metasynthesis

This metasynthesis focused on STEM teaching and learning practices in middle and high school classrooms and in informal settings. Research artifacts between 2005 and 2012 were examined. Fifty-eight unique artifacts were classified into four categories: reform-based teaching and learning, informal education, teacher factors, and technology use. Promising pedagogical reform-based practices included inquiry-based learning, engineering design, project-based learning, problem-based learning, and hands-on practices. The most common intervention identified was increasing teacher content knowledge. Even though STEM informal activities attempt to recruit underrepresented or low achieving students, the reality is that access to informal STEM activities is often based on students’ expressed high interest, prior academic achievement, teacher recommendation, time and travel availability and flexibility, and overall levels of ambition or motivation. Positive outcomes, due to technology, appeared to covary with other factors such as teacher content knowledge, the presence of campus support, or active engagement within a learning community

From STEM to STEAM: Students’ Beliefs About the Use of Their Creativity

To be successful in a STEM career, not only STEM knowledge and skills but also creativity is required. Therefore, the arts have been integrated into STEM disciplines and subsequently designated as STEAM education (Sousa & Pilecki, 2013). One example of informal learning environments that STEAM education provided is a summer camp. In this study, middle and highs school students’ use of their creativity in the Project-based Learning (PBL) courses was examined to determine students’ belief about the use of the arts in STEM activities. The results showed that students believed that they used their creativity in eight of the nine classes

Exploring excited states of transition metal photocatalysts with time dependent density functional theory

2018 Spring.Includes bibliographical references.Advances in photocatalysis have led to a rise in interests in more sustainable chemistry. It has been shown that visible light can be harnessed through a photocatalyst to promote conventionally unfavorable chemical transformations. Most of these photoreactions rely on a rare metal photocomplex such as Ru(bpy)32+. However, in order to scale these reactions for industrial purposes, rare metals must be replaced with more earth abundant metals. First row transition metals provide an earth abundant alternative that open up new reaction pathways. Due to the differences between first and second and third row transition metals, catalytic design requires complex knowledge of the photophysics and photochemistry of the complex that is not easily obtained with experimental methods. Electronic structure methods can aid in catalytic design. Density functional theory (DFT) and time dependent density functional theory (TDDFT) are methods capable of calculating large molecular systems. TDDFT is a useful tool in studying excited states, providing excited state energies and intensities, probing the photochemistry of the system. However, DFT/TDDFT are by no means black box calculations, especially when calculating first row transition metal complexes with complicated spin state manifolds. Screening different metal ligand scaffolds requires a high level of benchmarking, ensuring functionals and basis sets are optimal for the given system. A higher level of analysis is required in order to go beyond the electronic spectrum to get at the vibronic character of a system. There is also a coupling between the protonation of a complex and the electronic excited state. Understanding the protonation effects of a system is very useful for tuning a catalyst to a given reaction. In addition, specific binding effects of a solvent must be understood in order to corroborate theoretical and experimental data. All of these factors must be considered when studying the character of metals and their relation to their ligand backbone. This dissertation highlights these issues associated with using TDDFT for photocatalytic development, and derives useful conclusions furthering the development of a first row transition metal photocatalyst

What Enables Human Capital Investment Sharing in Elite Sport?

Sport organizations increasingly cooperate to invest in elite athlete development, sometimes even across national boundaries and industry sectors. This study attempts to explain why organizations decide to cooperatively invest by extending human capital theory. A multiple case study of National Pro Fastpitch (NPF) and Kunlun Red Star Hockey Club (KRS) was conducted, including an analysis of 43 interviews and 305 documents. Organizations decided to invest cooperatively because they believed human capital sharing would allow for levels of investment that would otherwise be prohibitively expensive for individual organizations. Four enabling conditions explain when organizations perceive sharing as more effective than human capital “buying” or “making.” The findings extend human capital theory to explain sharing decisions. The cases and theory provide practical insights for managers investing in athlete development and expanding sports leagues

Characterizing Anharmonic Vibrational Modes of Quinones with Two-Dimensional Infrared Spectroscopy

Two-dimensional infrared (2D IR) spectroscopy was used to study the vibrational modes of three quinonesbenzoquinone, naphthoquinone, and anthraquinone. The vibrations of interest were in the spectral range of 1560–1710 cm^–1, corresponding to the in-plane carbonyl and ring stretching vibrations. Coupling between the vibrational modes is indicated by the cross peaks in the 2D IR spectra. The diagonal and off-diagonal anharmonicities range from 4.6 to 17.4 cm^–1 for the quinone series. In addition, there is significant vibrational coupling between the in-plane carbonyl and ring stretching vibrations. The diagonal anharmonicity, off-diagonal anharmonicity, and vibrational coupling constants are reported for benzoquinone, naphthoquinone, and anthraquinone