Professor Barry Sharpless of Scripps describes the Nobel-prizewinning development of titanium-based catalysts for stereoselective oxidation, the mechanism of their reactions, and their use in preparing esomeprazole. Conformational energy of cyclic alkanes illustrates the use of molecular mechanics.
Although molecular mechanics is imperfect, it is useful for discussing molecular structure and energy in terms of standard covalent bonds. Analysis of the Cambridge Structural Database shows that predicting bond distances to within 1% required detailed categorization of bond types. Early attempts to predict heats of combustion in terms of composition proved adequate for physiology, but not for chemistry. Group- or bond-additivity schemes are useful for understanding heats of formation, especially when corrected for strain. Heat of atomization is the natural target for bond energy schemes, but experimental measurement requires spectroscopic determination of the heat of atomization of elements in their standard states.
After discussing the classic determination of the heat of atomization of graphite by Chupka and Inghram, the values of bond dissociation energies, and the utility of average bond energies, the lecture focuses on understanding equilibrium and rate processes through statistical mechanics. The Boltzmann factor favors minimal energy in order to provide the largest number of different arrangements of "bits" of energy. The slippery concept of disorder is illustrated using Couette flow. Entropy favors "disordered arrangements" because there are more of them than there are of recognizable ordered arrangements.
After discussing the statistical basis of the law of mass action, the lecture turns to developing a framework for understanding reaction rates. A potential energy surface that associates energy with polyatomic geometry can be realized physically for a linear, triatomic system, but it is more practical to use collective energies for starting material, transition state, and product, together with Eyring theory, to predict rates. Free-radical chain halogenation provides examples of predicting reaction equilibria and rates from bond dissociation energies. The lecture concludes with a summary of the semester's topics from the perspective of physical-organic chemistry.
Continuing the discussion of Lewis structures and chemical forces from the previous lecture, Professor McBride introduces the double-well potential of the ozone molecule and its structural equilibrium. The inability for inverse-square force laws to account for stable arrangements of charged particles is prescribed by Earnshaw's Theorem, which may be visualized by means of lines of force. J.J. Thomson circumvented Earnshaw's prohibition on structure by postulating a "plum-pudding" atom. When Rutherford showed that the nucleus was a point, Thomson had to conclude that Coulomb's law was invalid at small distances.
This lecture asks whether it is possible to confirm the reality of bonds by seeing or feeling them. It first describes the work of "clairvoyant" charlatans from the beginning of the twentieth century, who claimed to "see" details of atomic and molecular structure, in order to discuss proper bases for scientific belief. It then shows that the molecular scale is not inconceivably small, and that Newton and Franklin performed simple experiments that measure such small distances. In the last 25 years various realizations of Scanning Probe Microscopy have enabled chemists to "feel" individual molecules and atoms, but not bonds.
Professor McBride introduces the theory behind light diffraction by charged particles and its application to the study of the electron distribution in molecules by x-ray diffraction. The roles of molecular pattern and crystal lattice repetition are illustrated by shining laser light through diffraction masks to generate patterns reminiscent of those encountered in X-ray studies of ordered solids.
Professor McBride uses a hexagonal "benzene" pattern and Franklin's X-ray pattern of DNA, to continue his discussion of X-ray crystallography by explaining how a diffraction pattern in "reciprocal space" relates to the distribution of electrons in molecules and to the repetition of molecules in a crystal lattice. He then uses electron difference density mapping to reveal bonds, and unshared electron pairs, and their shape, and to show that they are only one-twentieth as dense as would be expected for Lewis shared pairs. Anomalous difference density in the carbon-fluorine bond raises the course's second great question, "Compared to what?"
After pointing out several discrepancies between electron difference density results and Lewis bonding theory, the course proceeds to quantum mechanics in search of a fundamental understanding of chemical bonding. The wave function , which beginning students find confusing, was equally confusing to the physicists who created quantum mechanics. The Schrodinger equation reckons kinetic energy through the shape of . When curves toward zero, kinetic energy is positive; but when it curves away, kinetic energy is negative!
Professor McBride expands on the recently introduced concept of the wave function by illustrating the relationship of the magnitude of the curvature of the wave function to the kinetic energy of the system, as well as the relationship of the square of the wave function to the electron probability density. The requirement that the wave function not diverge in areas of negative kinetic energy leads to only certain energies being allowed, a property which is explored for the harmonic oscillator, Morse potential, and the Columbic potential. Consideration of the influence of mass reveals an "isotope effect" on dynamics, on the energy, vibration frequency, and length of bonds.
After showing how a double-minimum potential generates one-dimensional bonding, Professor McBride moves on to multi-dimensional wave functions. Solving Schrodinger's three-dimensional differential equation might have been daunting, but it was not, because the necessary formulas had been worked out more than a century earlier in connection with acoustics. Acoustical "Chladni" figures show how nodal patterns relate to frequencies. The analogy is pursued by studying the form of wave functions for "hydrogen-like" one-electron atoms. Removing normalizing constants from the formulas for familiar orbitals reveals the underlying simplicity of their shapes.
With the emergence of democracies in Europe and the New World at the beginning of the nineteenth century, political philosophers began to re-evaluate the relationship between freedom and equality. Tocqueville, in particular, saw the creation of new forms of social power that presented threats to human liberty. His most famous work, Democracy in America, was written for his French countrymen who were still devoted to the restoration of the monarchy and whom Tocqueville wanted to convince that the democratic social revolution he had witnessed in America was equally representative of France's future.
The changing climate is a phenomenon that will affect us all in the future - with a global increase of 2.1 degrees Fahrenheit over the last century1,decreasing sea ice in the arctic, rising sea levels, and an increase in the frequency of severe weather events, high school students are sure to feel the effects of climate change. While many students may have heard the terms “climate change” and “global warming” in the news, this unit aims to help students develop a scientific understanding as to what is causing these changes. Through a deeper understanding of the scientific basis of climate change, specifically the role of carbon dioxide in climate change, students will be better equipped to explain the changes that they are observing in real time. It is my hope that through this investigation students will become voices of change in their schools and communities, helping to educate others and get involved in climate action.