I. Non-linear effects in a self-consistent calculation of SU_3 symmetry breaking in strong interaction coupling constants. II. Direct-channel reggeization of strong interaction scattering amplitudes

The thesis is divided into two parts. Part I generalizes a self-consistent calculation of residue shifts from SU₃ symmetry, originally performed by Dashen, Dothan, Frautschi, and Sharp, to include the effects of non-linear terms. Residue factorizability is used to transform an overdetermined set of equations into a variational problem, which is designed to take advantage of the redundancy of the mathematical system. The solution of this problem automatically satisfies the requirement of factorizability and comes close to satisfying all the original equations.

Part II investigates some consequences of direct channel Regge poles and treats the problem of relating Reggeized partial wave expansions made in different reaction channels. An analytic method is introduced which can be used to determine the crossed-channel discontinuity for a large class of direct-channel Regge representations, and this method is applied to some specific representations.

It is demonstrated that the multi-sheeted analytic structure of the Regge trajectory function can be used to resolve apparent difficulties arising from infinitely rising Regge trajectories. Also discussed are the implications of large collections of "daughter trajectories."

Two things are of particular interest: first, the threshold behavior in direct and crossed channels; second, the potentialities of Reggeized representations for us in self-consistent calculations. A new representation is introduced which surpasses previous formulations in these two areas, automatically satisfying direct-channel threshold constraints while being capable of reproducing a reasonable crossed channel discontinuity. A scalar model is investigated for low energies, and a relation is obtained between the mass of the lowest bound state and the slope of the Regge trajectory.

Part I. Approximate Hartree-Fock wavefunctions one-electron properties and electronic structure of the water molecule. Part II. Perturbation-variational calculation of the nuclear spin-spin isotope coupling constant in HD

Part I

Several approximate Hartree-Fock SCF wavefunctions for the ground electronic state of the water molecule have been obtained using an increasing number of multicenter s, p, and d Slater-type atomic orbitals as basis sets. The predicted charge distribution has been extensively tested at each stage by calculating the electric dipole moment, molecular quadrupole moment, diamagnetic shielding, Hellmann-Feynman forces, and electric field gradients at both the hydrogen and the oxygen nuclei. It was found that a carefully optimized minimal basis set suffices to describe the electronic charge distribution adequately except in the vicinity of the oxygen nucleus. Our calculations indicate, for example, that the correct prediction of the field gradient at this nucleus requires a more flexible linear combination of p-orbitals centered on this nucleus than that in the minimal basis set. Theoretical values for the molecular octopole moment components are also reported.

Part II

The perturbation-variational theory of R. M. Pitzer for nuclear spin-spin coupling constants is applied to the HD molecule. The zero-order molecular orbital is described in terms of a single 1s Slater-type basis function centered on each nucleus. The first-order molecular orbital is expressed in terms of these two functions plus one singular basis function each of the types e^-r/r and e^-r ln r centered on one of the nuclei. The new kinds of molecular integrals were evaluated to high accuracy using numerical and analytical means. The value of the HD spin-spin coupling constant calculated with this near-minimal set of basis functions is J_HD = +96.6 cps. This represents an improvement over the previous calculated value of +120 cps obtained without using the logarithmic basis function but is still considerably off in magnitude compared with the experimental measurement of J_HD = +43 0 ± 0.5 cps.

Carbon-13 magnetic resonance spectroscopy

High-resolution, natural-abundance ¹³C spectra have been obtained from a wide variety of organic compounds; ¹³C chemical shifts and coupling constants have been correlated with other molecular properties.

Geminal and vicinal, carbon-proton couplings in benzene and the five- and six-membered aromatic heterocycles have been related to the corresponding proton-proton couplings in substituted ethylenes. The carbon-proton coupling constants in benzene are J_CCH = + 1.0, J_CCCH = +7.4 and J_CCCH = -1.1 Hz. Extended Hückel wavefunctions are uniformly poor in explaining the long-range, carbon-proton couplings in aromatic systems.

Couplings between carbon and elements other than hydrogen have been observed in proton decoupled ¹³C spectra. All of the carbons in fluorobenzene and 1-fluoronaphthalene, but only six of the carbons in 2-fluoronaphthalene are coupled to the fluorine. One-bond, carbon-phosphorus coupling in trialkylphosphines is negative, while one-bond, carbon-phosphorus coupling in tetra-alkylphosphonium ions is positive. Atoms which do not use hybrid orbitals to form bonds to carbon (F, P(III), Se, Te) may have negative, one-bond coupling constants because of the failure of the average energy approximation. One-bond couplings between carbon and carbon, silicon, tin, lead and mercury appear to be explainable in terms of an effective nuclear charge and the s-bond order of the metal. Couplings between carbon and nitrogen and phosphorus (IV) have significant negative contributions to the Fermi contact coupling expression, though, within one series, correlations with s-bond order may be valid. Carbon-carbon coupling in cyclopropane derivatives (10-15 Hz) is consistent with a high degree of p character in the interior orbitals. Some two- and three-bond carbon-carbon coupling constants have also been observed.

Substituent effects of hydroxyl groups on the ¹³C chemical shifts of continuous-chain alkanes depend both on steric and electronic factors. The hydroxyl substituent effects in the long-chain, primary alcohols are α = -48.3, β = -10.2, and γ = +6.0 ppm. The upfield γ effect is attributed to steric crowding in the gauche conformations. Additivity of the hydroxyl and carbonyl and alkyl substituent effects in alkyl-substituted cyclohexanols and cyclohexanones has been demonstrated.

Structural and mechanistic study of monoalkyl diazenes. Synthesis, characterization, and reactivity of 1,6-didehydro[10]annulene

Methodology for the preparation of allenes from propargylic hydrazine precursors under mild conditions is described. Oxidation of the propargylic hydrazines, which can be readily prepared from propargylic alcohols, with either of two azo oxidants, diethyl azodicarboxylate (DEAD) or 4-methyl 1,2-triazoline-3,5-dione (MTAD), effects conversion to the allenes, presumably via sigmatropic rearrangement of a monoalkyl diazene intermediate. This rearrangement is demonstrated to proceed with essentially complete stereospecificity. The application of this methodology to the preparation of other allenes, including two that are notable for their reactivity and thermal instability, is also described.

The structural and mechanistic study of a monoalkyl diazene intermediate in the oxidative transformation of propargylic hydrazines to allenes is described. The use of long-range heteronuclear NMR coupling constants for assigning monoalkyl diazene stereochemistry (E vs Z) is also discussed. Evidence is presented that all known monoalkyl diazenes are the E isomers, and the erroneous assignment of stereochemistry in the previous report of the preparation of (Z)-phenyldiazene is discussed.

The synthesis, characterization, and reactivity of 1,6-didehydro[10]annulene are described. This molecule has been recognized as an interesting synthetic target for over 40 years and represents the intersection of two sets of extensively studied molecules: nonbenzenoid aromatic compounds and molecules containing sterically compressed π-systems.The formation of 1,5-dehydronaphthalene from 1 ,6-didehydro[10]annulene is believed to be the prototype for cycloaromatizations that produce 1,4-dehydroaromatic species with the radical centers disposed anti about the newly formed single bond. The aromaticity of this annulene and the facility of its cycloaromatization are also analyzed.

Measurement of the neutron beta decay asymmetry using ultracold neutrons

The free neutron beta decay correlation A₀ between neutron polarization and electron emission direction provides the strongest constraint on the ratio λ = g_A/g_V of the Axial-vector to Vector coupling constants in Weak decay. In conjunction with the CKM Matrix element V_ud and the neutron lifetime τ_n, λ provides a test of Standard Model assumptions for the Weak interaction. Leading high-precision measurements of A₀ and τ_n in the 1995-2005 time period showed discrepancies with prior measurements and Standard Model predictions for the relationship between λ, τ_n, and V_ud. The UCNA experiment was developed to measure A₀ from decay of polarized ultracold neutrons (UCN), providing a complementary determination of λ with different systematic uncertainties from prior cold neutron beam experiments. This dissertation describes analysis of the dataset collected by UCNA in 2010, with emphasis on detector response calibrations and systematics. The UCNA measurement is placed in the context of the most recent τ_n results and cold neutron A₀ experiments.

I. Site effects and exciton structure in molecular crystals - Benzene. II. The first and second triplet states of solid benzene

The effect of intermolecular coupling in molecular energy levels (electronic and vibrational) has been investigated in neat and isotopic mixed crystals of benzene. In the isotopic mixed crystals of C₆H₆, C₆H₅D, m-C₆H₄D₂, p-C₆H₄D₂, sym-C₆H₃D₃, C₆D₅H, and C₆D₆ in either a C₆H₆ or C₆D₆ host, the following phenomena have been observed and interpreted in terms of a refined Frenkel exciton theory: a) Site shifts; b) site group splittings of the degenerate ground state vibrations of C₆H₆, C₆D₆, and sym-C₆H₃D₃; c) the orientational effect for the isotopes without a trigonal axis in both the ¹B_2u electronic state and the ground state vibrations; d) intrasite Fermi resonance between molecular fundamentals due to the reduced symmetry of the crystal site; and e) intermolecular or intersite Fermi resonance between nearly degenerate states of the host and guest molecules. In the neat crystal experiments on the ground state vibrations it was possible to observe many of these phenomena in conjunction with and in addition to the exciton structure.

To theoretically interpret these diverse experimental data, the concepts of interchange symmetry, the ideal mixed crystal, and site wave functions have been developed and are presented in detail. In the interpretation of the exciton data the relative signs of the intermolecular coupling constants have been emphasized, and in the limit of the ideal mixed crystal a technique is discussed for locating the exciton band center or unobserved exciton components. A differentiation between static and dynamic interactions is made in the Frenkel limit which enables the concepts of site effects and exciton coupling to be sharpened. It is thus possible to treat the crystal induced effects in such a fashion as to make their similarities and differences quite apparent.

A calculation of the ground state vibrational phenomena (site shifts and splittings, orientational effects, and exciton structure) and of the crystal lattice modes has been carried out for these systems. This calculation serves as a test of the approximations of first order Frenkel theory and the atom-atom, pair wise interaction model for the intermolecular potentials. The general form of the potential employed was V(r) = Be^-Cr - A/r⁶ ; the force constants were obtained from the potential by assuming the atoms were undergoing simple harmonic motion.

In part II the location and identification of the benzene first and second triplet states (³B_1u and ³E_1u) is given.

I. Nuclear spin-internal-rotation-coupling. II. Fluorine spin-rotation interaction and magnetic shielding in fluorobenzene

Part I.

The interaction of a nuclear magnetic moment situated on an internal top with the magnetic fields produced by the internal as well as overall molecular rotation has been derived following the method of Van Vleck for the spin-rotation interaction in rigid molecules. It is shown that the Hamiltonian for this problem may be written

H_SR = Ῑ · M · Ĵ + Ῑ · M” · Ĵ”

Where the first term is the ordinary spin-rotation interaction and the second term arises from the spin-internal-rotation coupling.

The F¹⁹ nuclear spin-lattice relaxation time (T₁) of benzotrifluoride and several chemically substituted benzotrifluorides, have been measured both neat and in solution, at room temperature by pulsed nuclear magnetic resonance. From these experimental results it is concluded that in benzotrifluoride the internal rotation is crucial to the spin relaxation of the fluorines and that the dominant relaxation mechanism is the fluctuating spin-internal-rotation interaction.

Part II.

The radiofrequency spectrum corresponding to the reorientation of the F¹⁹ nuclear moment in flurobenzene has been studied by the molecular beam magnetic resonance method. A molecular beam apparatus with an electron bombardment detector was used in the experiments. The F¹⁹ resonance is a composite spectrum with contributions from many rotational states and is not resolved. A detailed analysis of the resonance line shape and width by the method of moments led to the following diagonal components of the fluorine spin-rotational tensor in the principal inertial axis system of the molecule:

F/Caa = -1.0 ± 0.5 kHz

F/Cbb = -2.7 ± 0.2 kHz

F/Ccc = -1.9 ± 0.1 kHz

From these interaction constants, the paramagnetic contribution to the F¹⁹ nuclear shielding in C₆H₅F was determined to be -284 ± ppm. It was further concluded that the F¹⁹ nucleus in this molecule is more shielded when the applied magnetic field is directed along the C-F bond axis. The anisotropy of the magnetic shielding tensor, σ_” - σ_⊥, is +160 ± 30 ppm.

Photographic investigations in molecular spectroscopy

The determination of the energy levels and the probabilities of transition between them, by the formal analysis of observed electronic, vibrational, and rotational band structures, forms the direct goal of all investigations of molecular spectra, but the significance of such data lies in the possibility of relating them theoretically to more concrete properties of molecules and the radiation field. From the well developed electronic spectra of diatomic molecules, it has been possible, with the aid of the non-relativistic quantum mechanics, to obtain accurate moments of inertia, molecular potential functions, electronic structures, and detailed information concerning the coupling of spin and orbital angular monenta with the angular momentum of nuclear rotation. The silicon fluori1e molecule has been investigated in this laboratory, and is found to emit bands whose vibrational and rotational structures can be analyzed in this detailed fashion.

Like silicon fluoride, however, the great majority of diatomic molecules are formed only under the unusual conditions of electrical discharge, or in high temperature furnaces, so that although their spectra are of great theoretical interest, the chemist is eager to proceed to a study of polyatomic molecules, in the hope that their more practically interesting structures might also be determined with the accuracy and assurance which characterize the spectroscopic determinations of the constants of diatomic molecules. Some progress has been made in the determination of molecule potential functions from the vibrational term values deduced from Raman and infrared spectra, but in no case can the calculations be carried out with great generality, since the number of known term values is always small compared with the total number of potential constants in even so restricted a potential function as the simple quadratic type. For the determination of nuclear configurations and bond distances, however, a knowledge of the rotational terms is required. The spectra of about twelve of the simpler polyatomic molecules have been subjected to rotational analyses, and a number of bond distances are known with considerable accuracy, yet the number of molecules whose rotational fine structure has been resolved even with the most powerful instruments is small. Consequently, it was felt desirable to investigate the spectra of a number of other promising polyatomic molecules, with the purpose of carrying out complete rotational analyses of all resolvable bands, and ascertaining the value of the unresolved band envelopes in determining the structures of such molecules, in the cases in which resolution is no longer possible. Although many of the compounds investigated absorbed too feebly to be photographed under high dispersion with the present infrared sensitizations, the location and relative intensities of their bands, determined by low dispersion measurements, will be reported in the hope that these compounds may be reinvestigated in the future with improved techniques.

A perturbation procedure for nonlinear oscillations (The dynamics of two oscillators with weak nonlinear coupling)

This thesis considers in detail the dynamics of two oscillators with weak nonlinear coupling. There are three classes of such problems: non-resonant, where the Poincaré procedure is valid to the order considered; weakly resonant, where the Poincaré procedure breaks down because small divisors appear (but do not affect the O(1) term) and strongly resonant, where small divisors appear and lead to O(1) corrections. A perturbation method based on Cole's two-timing procedure is introduced. It avoids the small divisor problem in a straightforward manner, gives accurate answers which are valid for long times, and appears capable of handling all three types of problems with no change in the basic approach.

One example of each type is studied with the aid of this procedure: for the nonresonant case the answer is equivalent to the Poincaré result; for the weakly resonant case the analytic form of the answer is found to depend (smoothly) on the difference between the initial energies of the two oscillators; for the strongly resonant case we find that the amplitudes of the two oscillators vary slowly with time as elliptic functions of ϵ t, where ϵ is the (small) coupling parameter.

Our results suggest that, as one might expect, the dynamical behavior of such systems varies smoothly with changes in the ratio of the fundamental frequencies of the two oscillators. Thus the pathological behavior of Whittaker's adelphic integrals as the frequency ratio is varied appears to be due to the fact that Whittaker ignored the small divisor problem. The energy sharing properties of these systems appear to depend strongly on the initial conditions, so that the systems not ergodic.

The perturbation procedure appears to be applicable to a wide variety of other problems in addition to those considered here.

Capturing protein dynamics with time-resolved luminescence spectroscopy

The presented doctoral research utilizes time-resolved spectroscopy to characterize protein dynamics and folding mechanisms. We resolve millisecond-timescale folding by coupling time-resolved fluorescence energy transfer (trFRET) to a continuous flow microfluidic mixer to obtain intramolecular distance distributions throughout the folding process. We have elucidated the folding mechanisms of two cytochromes---one that exhibits two-state folding (cytochrome cb₅₆₂) and one that has both a kinetic refolding intermediate ensemble and a distinct equilibrium unfolding intermediate (cytochrome c₅₅₂). Our data reveal that the distinct structural features of cytochrome c₅₅₂ contribute to its thermostability.

We have also investigated intrachain contact dynamics in unfolded cytochrome cb₅₆₂ by monitoring electron transfer, which occurs as the heme collides with a ruthenium photosensitizer, covalently bound to residues along the polypeptide. Intrachain diffusion for chemically denatured proteins proceeds on the microsecond timescale with an upper limit of 0.1 microseconds. The power-law dependence (slope = -1.5) of the rate constants on the number of peptide bonds between the heme and Ru complex indicate that cytochrome cb₅₆₂ is minimally frustrated.

In addition, we have explored the pathway dependence of electron tunneling rates between metal sites in proteins. Our research group has converted cytochrome b₅₆₂ to a c-type cytochrome with the porphyrin covalently bound to cysteine sidechains. We have investigated the effects of the changes to the protein structure (i.e., increased rigidity and potential new equatorial tunneling pathways) on the electron transfer rates, measured by transient absorption, in a series of ruthenium photosensitizer-modified proteins.

Synthetic, kinetic and mechanistic studies in early transition metal systems. I. α- and β-hydrogen elimination reactions in derivatives of permethyltitanocene, -zirconocene, and -hafnocene. II. The reactions of aluminum alkyls with derivatives of permethylniobocene

The thermal decomposition of Cp*Ti(CH_3)_2 (Cp*≡ ƞ^5-C_5Me_5) toluene solution follows cleanly first-order kinetics and produces a single titanium product Cp*(C_5Me_4CH_2)Ti(CH_3) concurrent with the evolution of one equivalent of methane. Labeling studies using Cp*_2Ti- (CD_3)_2 and (Cp*-d_(15))_2Ti(CH_3)_2 show the decomposition to be intramolecular and the methane to be produced by the coupling of a methyl group with a hydrogen from the other TiCH_3 group. Activation parameters, ΔH^‡ and ΔS^‡, and kinetic deuterium isotope effects have been measured. The alternative decomposition pathways of α-hydrogen abstraction and a-hydrogen elimination, both leading to a titanium-methylidene intermediate, are discussed.

The insertion of unactivated acetylenes into the metal-hydride bonds of Cp*_2MH_2 (M = Zr, Hf) proceeds rapidly at low temperature to form monoand/ or bisinsertion products, dependent upon the steric bulk of the acetylene substituents. Cp*_2M(H)(C(Me)=CHMe), Cp*_2M(H)(CH=CHCMe_3), Cp*_2M(H)-(CH=CHPh), Cp*_2M(CH=CHPh)_2, Cp*_2M(CH=CHCH_3)_2 and Cp*_2Zr- (CH=CHCH_2CH_3)_2 have been isolated and characterized. To extend the study of unsaturated-carbon ligands, Cp*_2M(C≡CCH_3)_2 have been prepared by treating Cp*_2MCl_2 with LiC≡CCH_3. The reactivity of many of these complexes with carbon monoxide and dihydrogen is surveyed. The mono(2- butenyl) complexes Cp*_2M(H)(C(Me)=CHMe) rearrange at room temperature, forming the crotyl-hydride species Cp*_2M(H)(ƞ^3-C_4H_7). The bis(propenyl) and bis(l-butenyl) zirconium complexes Cp*_2Zr(CH=CHR)_2 (R = CH_3, CH_2CH_3) also rearrange, forming zirconacyclopentenes. Labeling studies, reaction chemistry, and kinetic measurements, including deuterium isotope effects, demonstrate that the unusual 6-hydrogen elimination from an sp^2-hybridized carbon is the first step in these latter rearrangements but is not observed in the former. Details of these mechanisms and the differences in reactivity of the zirconium and hafnium complexes are discussed.

The reactions of hydride- and alkyl-carbonyl derivatives of permethylniobocene with equimolar amounts of trialkylaluminum reagents occur rapidly producing the carbonyl adducts Cp*_2Nb(R)(COAlR'_3) (R = H, CH_3, CH_2CH_3, CH_2CH_2Ph, C(Me)=CHMe; R' = Me, Et). The hydride adduct Cp*_2NbH_3•AlEt_3 has also been formed. In solution, each of these compounds exists in equilibrium with the uncomplexed species. The formation constants for Cp*_2Nb(H)(COA1R'_R) have been measured. They indicate the steric bulk of the Cp* ligands plays a deciding factor in the isolation of the first example of an aluminum Lewis acid bound to a carbonyl-oxygen in preference to a metalhydride. Reactions of Cp*_2Nb(H)CO with other Lewis acids and of the one:one adducts with H_2, CO and C_2H_4 are also discussed.

Cp*_2Nb(H)(C_2H_4) also reacts with equimolar amounts of trialkylaluminum reagents, forming a one:one complex that ^1H NMR spectroscopy indicates contains a Nb-CH_2CH_2-Al bridge. This adduct also exists in equilibrium with the uncomplexed species in solution. The formation constant for Cp*_2N+/b(H)(CH_2CH_2ĀlEt_3) has been measured. Reactions of Cp*_2Nb(H)(C_2H_4) with other Lewis acids and the reactions of Cp*_2N+b(H)- (CH_2CH_2ĀlEt_3) with CO and C_2H_4 are described, as are the reactions of Cp_*2Nb(H)(CH_2=CHR) (R = Me, Ph), Cp*_2Nb(H)(CH_3C≡CCH_3) and Cp*_2Ti-(C_2H_4) with AlEt_3.

Theory of ozone isotopic effects and various electron transfer reactions

Three separate topics, each stimulated by experiments, are treated theoretically in this dessertation: isotopic effects of ozone, electron transfer at interfaces, and intramolecular directional electron transfer in a supramolecular system.

The strange mass-independent isotope effect for the enrichment of ozone, which has been a puzzle in the literature for some 20 years, and the equally puzzling unconventional strong mass-dependent effect of individual reaction rate constants are studied as different aspects of a symmetry-driven behavior. A statistical (RRKM-based) theory with a hindered-rotor transition state is used. The individual rate constant ratios of recombination reactions at low pressures are calculated using the theory involving (1) small deviation from the statistical density of states for symmetric isotopomers, and (2) weak collisions for deactivation of the vibrationally excited ozone molecules. The weak collision and partitioning among exit channels play major roles in producing the large unconventional isotope effect in "unscrambled" systems. The enrichment studies reflect instead the non-statistical effect in "scrambled" systems. The theoretical results of low-pressure ozone enrichments and individual rate constant ratios obtained from these calculations are consistent with the corresponding experimental results. The isotopic exchange rate constant for the reaction ^(16)O + ^(18)O ^(18)O→+ ^(16)O ^(18)O + ^(18)O provides information on the nature of a variationally determined hindered-rotor transition state using experimental data at 130 K and 300 K. Pressure effects on the recombination rate constant, on the individual rate constant ratios and on the enrichments are also investigated. The theoretical results are consistent with the experimental data. The temperature dependence of the enrichment and rate constant ratios is also discussed, and experimental tests are suggested. The desirability of a more accurate potential energy surface for ozone in the transition state region is also noted.

Electron transfer reactions at semiconductor /liquid interfaces are studied using a tight-binding model for the semiconductors. The slab method and a z-transform method are employed in obtaining the tight-binding electronic structures of semiconductors having surfaces. The maximum electron transfer rate constants at Si/viologen^(2-/+) and InP /Me_(2)Fc^(+/O) interfaces are computed using the tight-binding type calculations for the solid and the extended-Huckel for the coupling to the redox agent at the interface. These electron transfer reactions are also studied using a free electron model for the semiconductor and the redox molecule, where Bardeen's method is adapted to calculate the coupling matrix element between the molecular and semiconductor electronic states. The calculated results for maximum rate constant of the electron transfer from the semiconductor bulk states are compared with the experimentally measured values of Lewis and coworkers, and are in reasonable agreement, without adjusting parameters. In the case of InP /liquid interface, the unusual current vs applied potential behavior is additionally interpreted, in part, by the presence of surface states.

Photoinduced electron transfer reactions in small supramolecular systems, such as 4-aminonaphthalimide compounds, are interesting in that there are, in principle, two alternative pathways (directions) for the electron transfer. The electron transfer, however, is unidirectional, as deduced from pH-dependent fluorescence quenching studies on different compounds. The role of electronic coupling matrix element and the charges in protonation are considered to explain the directionality of the electron transfer and other various results. A related mechanism is proposed to interpret the fluorescence behavior of similar molecules as fluorescent sensors of metal ions.

Studies of phonon anharmonicity in solids

Today our understanding of the vibrational thermodynamics of materials at low temperatures is emerging nicely, based on the harmonic model in which phonons are independent. At high temperatures, however, this understanding must accommodate how phonons interact with other phonons or with other excitations. We shall see that the phonon-phonon interactions give rise to interesting coupling problems, and essentially modify the equilibrium and non-equilibrium properties of materials, e.g., thermodynamic stability, heat capacity, optical properties and thermal transport of materials. Despite its great importance, to date the anharmonic lattice dynamics is poorly understood and most studies on lattice dynamics still rely on the harmonic or quasiharmonic models. There have been very few studies on the pure phonon anharmonicity and phonon-phonon interactions. The work presented in this thesis is devoted to the development of experimental and computational methods on this subject.

Modern inelastic scattering techniques with neutrons or photons are ideal for sorting out the anharmonic contribution. Analysis of the experimental data can generate vibrational spectra of the materials, i.e., their phonon densities of states or phonon dispersion relations. We obtained high quality data from laser Raman spectrometer, Fourier transform infrared spectrometer and inelastic neutron spectrometer. With accurate phonon spectra data, we obtained the energy shifts and lifetime broadenings of the interacting phonons, and the vibrational entropies of different materials. The understanding of them then relies on the development of the fundamental theories and the computational methods.

We developed an efficient post-processor for analyzing the anharmonic vibrations from the molecular dynamics (MD) calculations. Currently, most first principles methods are not capable of dealing with strong anharmonicity, because the interactions of phonons are ignored at finite temperatures. Our method adopts the Fourier transformed velocity autocorrelation method to handle the big data of time-dependent atomic velocities from MD calculations, and efficiently reconstructs the phonon DOS and phonon dispersion relations. Our calculations can reproduce the phonon frequency shifts and lifetime broadenings very well at various temperatures.

To understand non-harmonic interactions in a microscopic way, we have developed a numerical fitting method to analyze the decay channels of phonon-phonon interactions. Based on the quantum perturbation theory of many-body interactions, this method is used to calculate the three-phonon and four-phonon kinematics subject to the conservation of energy and momentum, taking into account the weight of phonon couplings. We can assess the strengths of phonon-phonon interactions of different channels and anharmonic orders with the calculated two-phonon DOS. This method, with high computational efficiency, is a promising direction to advance our understandings of non-harmonic lattice dynamics and thermal transport properties.

These experimental techniques and theoretical methods have been successfully performed in the study of anharmonic behaviors of metal oxides, including rutile and cuprite stuctures, and will be discussed in detail in Chapters 4 to 6. For example, for rutile titanium dioxide (TiO₂), we found that the anomalous anharmonic behavior of the B_1g mode can be explained by the volume effects on quasiharmonic force constants, and by the explicit cubic and quartic anharmonicity. For rutile tin dioxide (SnO₂), the broadening of the B_2g mode with temperature showed an unusual concave downwards curvature. This curvature was caused by a change with temperature in the number of down-conversion decay channels, originating with the wide band gap in the phonon dispersions. For silver oxide (Ag₂O), strong anharmonic effects were found for both phonons and for the negative thermal expansion.

Effects of self energy of the ions on the double layer structure and properties at the dielectric interface

Although numerous theoretical efforts have been put forth, a systematic, unified and predictive theoretical framework that is able to capture all the essential physics of the interfacial behaviors of ions, such as the Hofmeister series effect, Jones-Ray effect and the salt effect on the bubble coalescence remain an outstanding challenge. The most common approach to treating electrostatic interactions in the presence of salt ions is the Poisson-Boltzmann (PB) theory. However, there are many systems for which the PB theory fails to offer even a qualitative explanation of the behavior, especially for ions distributed in the vicinity of an interface with dielectric contrast between the two media (like the water-vapor/oil interface). A key factor missing in the PB theory is the self energy of the ion.

In this thesis, we develop a self-consistent theory that treats the electrostatic self energy (including both the short-range Born solvation energy and the long-range image charge interactions), the nonelectrostatic contribution of the self energy, the ion-ion correlation and the screening effect systematically in a single framework. By assuming a finite charge spread of the ion instead of using the point-charge model, the self energy obtained by our theory is free of the divergence problems and gives a continuous self energy across the interface. This continuous feature allows ions on the water side and the vapor/oil side of the interface to be treated in a unified framework. The theory involves a minimum set of parameters of the ion, such as the valency, radius, polarizability of the ions, and the dielectric constants of the medium, that are both intrinsic and readily available. The general theory is first applied to study the thermodynamic property of the bulk electrolyte solution, which shows good agreement with the experiment result for predicting the activity coefficient and osmotic coefficient.

Next, we address the effect of local Born solvation energy on the bulk thermodynamics and interfacial properties of electrolyte solution mixtures. We show that difference in the solvation energy between the cations and anions naturally gives rise to local charge separation near the interface, and a finite Galvani potential between two coexisting solutions. The miscibility of the mixture can either increases or decreases depending on the competition between the solvation energy and translation entropy of the ions. The interfacial tension shows a non-monotonic dependence on the salt concentration: it increases linearly with the salt concentration at higher concentrations, and decreases approximately as the square root of the salt concentration for dilute solutions, which is in agreement with the Jones-Ray effect observed in experiment.

Next, we investigate the image effects on the double layer structure and interfacial properties near a single charged plate. We show that the image charge repulsion creates a depletion boundary layer that cannot be captured by a regular perturbation approach. The correct weak-coupling theory must include the self-energy of the ion due to the image charge interaction. The image force qualitatively alters the double layer structure and properties, and gives rise to many non-PB effects, such as nonmonotonic dependence of the surface energy on concentration and charge inversion. The image charge effect is then studied for electrolyte solutions between two plates. For two neutral plates, we show that depletion of the salt ions by the image charge repulsion results in short-range attractive and long-range repulsive forces. If cations and anions are of different valency, the asymmetric depletion leads to the formation of an induced electrical double layer. For two charged plates, the competition between the surface charge and the image charge effect can give rise to like- charge attraction.

Then, we study the inhomogeneous screening effect near the dielectric interface due to the anisotropic and nonuniform ion distribution. We show that the double layer structure and interfacial properties is drastically affected by the inhomogeneous screening if the bulk Debye screening length is comparable or smaller than the Bjerrum length. The width of the depletion layer is characterized by the Bjerrum length, independent of the salt concentration. We predict that the negative adsorption of ions at the interface increases linearly with the salt concentration, which cannot be captured by either the bulk screening approximation or the WKB approximation. For asymmetric salt, the inhomogeneous screening enhances the charge separation in the induced double layer and significantly increases the value of the surface potential.

Finally, to account for the ion specificity, we study the self energy of a single ion across the dielectric interface. The ion is considered to be polarizable: its charge distribution can be self-adjusted to the local dielectric environment to minimize the self energy. Using intrinsic parameters of the ions, such as the valency, radius, and polarizability, we predict the specific ion effect on the interfacial affinity of halogen anions at the water/air interface, and the strong adsorption of hydrophobic ions at the water/oil interface, in agreement with experiments and atomistic simulations.

The theory developed in this work represents the most systematic theoretical technique for weak-coupling electrolytes. We expect the theory to be more useful for studying a wide range of structural and dynamic properties in physicochemical, colloidal, soft-matter and biophysical systems.

Strategies for the Stereoselective Synthesis of Carbon Quaternary Centers via Transition Metal-Catalyzed Alkylation of Enolate Compounds

Notwithstanding advances in modern chemical methods, the selective installation of sterically encumbered carbon stereocenters, in particular all-carbon quaternary centers, remains an unsolved problem in organic chemistry. The prevalence of all-carbon quaternary centers in biologically active natural products and pharmaceutical compounds provides a strong impetus to address current limitations in the state of the art of their generation. This thesis presents four related projects, all of which share in the goal of constructing highly-congested carbon centers in a stereoselective manner, and in the use of transition-metal catalyzed alkylation as a means to address that goal.

The first research described is an extension of allylic alkylation methodology previously developed in the Stoltz group to small, strained rings. This research constitutes the first transition metal-catalyzed enantioselective α-alkylation of cyclobutanones. Under Pd-catalysis, this chemistry affords all–carbon α-quaternary cyclobutanones in good to excellent yields and enantioselectivities.

Next is described our development of a (trimethylsilyl)ethyl β-ketoester class of enolate precursors, and their application in palladium–catalyzed asymmetric allylic alkylation to yield a variety of α-quaternary ketones and lactams. Independent coupling partner synthesis engenders enhanced allyl substrate scope relative to allyl β-ketoester substrates; highly functionalized α-quaternary ketones generated by the union of our fluoride-triggered β-ketoesters and sensitive allylic alkylation coupling partners serve to demonstrate the utility of this method for complex fragment coupling.

Lastly, our development of an Ir-catalyzed asymmetric allylic alkylation of cyclic β-ketoesters to afford highly congested, vicinal stereocenters comprised of tertiary and all-carbon quaternary centers with outstanding regio-, diastereo-, and enantiocontrol is detailed. Implementation of a subsequent Pd-catalyzed alkylation affords dialkylated products with pinpoint stereochemical control of both chiral centers. The chemistry is then extended to include acyclic β-ketoesters and similar levels of selective and functional group tolerance are observed. Critical to the successful development of this method was the employment of iridium catalysis in concert with N-aryl-phosphoramidite ligands.