On the Ewald method and the quartic Helmholtz free energy of an anharmonic metallic crystal

Thesis (M. Sc.) - Brock University, 1978.

An anharmonic contribution to the Helmholtz free energy O(lambda 6)

The anharmonic contributions of order A6 to the Helmholtz free energy for a crystal in which every atom is on a site of inversion symmetry, have been evaluated The cor~esponding diagrams in the various orders of the perturbation theory have been presented The validity of the expressions given is for high temperatures. Numerical calculations for the diagrams which contribute to the free energy have been worked out for a nearest-n~ighbour central-force model of a facecentered cubic lattice in the high-temperature limit and in the leading term and the Ludwig approximations. The accuracy of the Ludwig approximation in evaluating the Brillouin-zone sums has been investigated. Expansion for all diagrams in the high-temperature limit has been carried out The contribution to the specific heat involves a linear as well as cubic term~ We have applied Lennard-Jones, Morse and Exponential 6 types of potentials. A comparison between the contribution to the free energy of order A6 to that of order A4 has been made.

Anharmonic Helmholtz free energy to O(lambdaâ ´) in the non- leading term approximation /|nby Leslie Wilk. -- 260 St. Catharines, Ont. : [s. n.],

Expressions for the anharmonic Helmholtz free energy contributions up to o( f ) ,valid for all temperatures, have been obtained using perturbation theory for a c r ystal in which every atom is on a site of inversion symmetry. Numerical calculations have been carried out in the high temperature limit and in the non-leading term approximation for a monatomic facecentred cubic crystal with nearest neighbour c entralforce interactions. The numbers obtained were seen to vary by a s much as 47% from thos e obtai.ned in the leading term approximati.on,indicating that the latter approximati on is not in general very good. The convergence to oct) of the perturbation series in the high temperature limit appears satisfactory.

Aspects of the hemes and modulation of hydrogen donors in catalases from bovine liver, yeast, and escherichia coli

Catalase is the enzyme which decomposes hydrogen peroxide to water and oxygen. Escherichia coli contains two catalases. Hydroperoxidase I (HPI) is a bifunctional catalase-peroxidase. Hydroperoxidase II (HPII) is only catalytically active toward H202. Expression of the genes encoding these proteins is controlled by different regimes. HPJI is thought to be a hexamer, having one heme d cis group per enzymatic subunit. HPII wild type protein and heme containing mutant proteins were obtained from the laboratory of P. Loewen (Univ. of Manitoba). Mutants constructed by oligonucleotidedirected mutagenesis were targeted for replacement of either the His128 residue or the Asn201 residue in the vicinity of the HPII heme crevice. His128 is the residue thought to be analogous to the His74 distal axial ligand of the heme in the bovine liver enzyme, and Asn201 is believed to be a residue critical to the function of the enzyme because of its role in orienting and interacting with the substrate molecule. Investigation of the nature of the hemes via absorption spectroscopy of the unmodified catalase proteins and their derived pyridine hemochromes showed that while the bovine and Saccharomyces cerevisiae catalase enzymes are protoheme-containing, the HPII wild type protein contains heme d, and the mutant proteins contain either solely protoheme, or heme d-protoheme mixtures. Cyanide binding studies supported this, as ligand binding was monophasic for the bovine, Saccharomyces cerevisiae, and wild type HPII enzymes, but biphasic for several of the HPII mutant proteins. Several mammalian catalases, and at least two prokaryotic catalases, are known to be NADPH binding. The function of this cofactor appears to be the prevention of inactivation of the enzyme, which occurs via formation of the inactive secondary catalase peroxide compound (compound II). No physiologically plausible scheme has yet been proposed for the NADPH mediation of catalase activity. This study has shown, via fluorescence and affinity chromatography techniques, that NADPH binds to the T (Typical) and A (Atypical) catalases of Saccharomyces cerevisiae, and that wild type HPII apparently does not bind NADPH. This study has also shown that NADPH is unlike any other hydrogen donor to catalase, and addresses its features as a unique donor by proposing a mechanism whereby NADPH is oxidized and catalase is protected from inactivation via the formation of protein radical species. Migration of this radical to a position close to the NADPH is also proposed as an adjunct hypothesis, based on similar electron migrations that are known to occur within metmyoglobin and cytochrome c peroxidase when reacted with H202. Validation of these hypotheses may be obtained in appropriate future experiments.

The importance of hydrogen bonding in the alkylation of phenols

Hydrogen bond assisted alkylation of phenols is compared with the classical base assisted reactions. The influence of solvents on the fluoride assisted reactions is discussed,· with emphasis on the localization of hydrogen bond charge density. Polar aprotic solvents such as DMF favour a-alkylation, and nonpolar aprotic solvents such as toluene favourC-alkylation of phenol. For more reactive and soluble fluorides, such as tetrabu~ylammoniumfluoride, the polar aprotic solvent favours a-alkylation and nonpolar aprotic solvent favours fluorination. Freeze-dried potassium fluoride is a better catalytic agent in hydrogen bond assisted alkylation reactions of phenol than the oven-dried fluoride. The presence of water in the alkylation reactions reduces the expected yield drastically. The tolerance of the reaction to water has also been studied. The use ofa phase transfer catalyst such as tetrabutylammonium bromide in the alkylation reactions of phenol in the presence of potassium fluoride is very effective under anhydrous conditions. Sterically hindered phenols such as 2,6-ditertiarybutyl-4-methyl phenol could not be alkylated even by using the more reactive fluorides, such as tetrabutylammonium fluoride in either polar or nonpolar aprotic solvents. Attempts were also made to alkylate phenols in the presence of triphenylphosphine oxide.

Variational Monte Carlo estimation of the dissociation energy of CuH using correlated sampling

A new approach to treating large Z systems by quantum Monte Carlo has been developed. It naturally leads to notion of the 'valence energy'. Possibilities of the new approach has been explored by optimizing the wave function for CuH and Cu and computing dissociation energy and dipole moment of CuH using variational Monte Carlo. The dissociation energy obtained is about 40% smaller than the experimental value; the method is comparable with SCF and simple pseudopotential calculations. The dipole moment differs from the best theoretical estimate by about 50% what is again comparable with other methods (Complete Active Space SCF and pseudopotential methods).

Planar Topological Defects in Unconventional Superconductors

In this work, we consider the properties of planar topological defects in unconventional superconductors. Specifically, we calculate microscopically the interaction energy of domain walls separating degenerate ground states in a chiral p-wave fermionic superfluid. The interaction is mediated by the quasiparticles experiencing Andreev scattering at the domain walls. As a by-product, we derive a useful general expression for the free energy of an arbitrary nonuniform texture of the order parameter in terms of the quasiparticle scattering matrix. The thesis is structured as follows. We begin with a historical review of the theories of superconductivity (Sec. 1.1), which led the way to the celebrated Bardeen-Cooper- Schrieffer (BCS) theory (Sec. 1.3). Then we proceed to the treatment of superconductors with so-called "unconventional pairing" in Sec. 1.4, and in Sec. 1.5 we introduce the specific case of chiral p-wave superconductivity. After introducing in Sec. 2 the domain wall (DW) model that will be considered throughout the work, we derive the Bogoliubov-de Gennes (BdG) equations in Sec. 3.1, which determine the quasiparticle excitation spectrum for a nonuniform superconductor. In this work, we use the semiclassical (Andreev) approximation, and solve the Andreev equations (which are a particular case of the BdG equations) in Sec. 4 to determine the quasiparticle spectrum for both the single- and two-DW textures. The Andreev equations are derived in Sec. 3.2, and the formal properties of the Andreev scattering coefficients are discussed in the following subsection. In Sec. 5, we use the transfer matrix method to relate the interaction energy of the DWs to the scattering matrix of the Bogoliubov quasiparticles. This facilitates the derivation of an analytical expression for the interaction energy between the two DWs in Sec. 5.3. Finally, to illustrate the general applicability our method, we apply it in Sec. 6 to the interaction between phase solitons in a two-band s-wave superconductor.

Mechanism of tocopherol transfer by human α-tocopherol transfer protein (α-hTTP)

Vitamin E is a well known fat soluble chain breaking antioxidant. It is a general tenn used to describe a family of eight stereoisomers of tocopherols. Selective retention of a-tocopherol in the human circulation system is regulated by the a -Tocopherol Transfer Protein (a-TIP). Using a fluorescently labelled a-tocopherol (NBD-a-Toc) synthesized in our laboratory, a fluorescence resonance energy transfer (FRET) assay was developed to monitor the kinetics of ligand transfer by a-hTTP in lipid vesicles. Preliminary results implied that NBD-a-Toe simply diffused from 6-His-a-hTTP to acceptor membranes since the kinetics of transfer were not responsive to a variety of conditions tested. After a series of trouble shooting experiments, we identified a minor contaminant, E coli. outer membrane porin F (OmpF) that co-purified with 6-His-a-hTTP from the metal affinity column as the source of the problem. In order to completely avoid OmpF contamination, a GST -a-hTTP fusion protein was purified from a glutathione agarose column followed by an on-column thrombin digestion to remove the GST tag. We then demonstrated that a-hTTP utilizes a collisional mechanism to deliver its ligand. Furthennore, a higher rate of a-tocopherol transfer to small unilamellar vesicles (SUV s) versus large unilamellar vesicles (LUV s) indicated that transfer is sensitive to membrane curvature. These findings suggest that ahTTP mediated a-Toc transfer is dominated by the hydrophobic nature of a-hTTP and the packing density of phospholipid head groups within acceptor membranes. Based on the calculated free energy change (dG) when a protein is transferred from water to the lipid bilayer, a model was generated to predict the orientation of a-hTTP when it interacts with lipid membranes. Guided by this model, several hydrophobic residues expected to penetrate deeply into the bilayer hydrophobic core, were mutated to either aspartate or alanine. Utilizing dual polarization interferometry and size exclusion vesicle binding assays, we identified the key residues for membrane binding to be F 165, F 169 and 1202. In addition, the rates of ligand transfer of the u-TTP mutants were directly correlated to their membrane binding capabilities, indicating that membrane binding was likely the rate limiting step in u-TTP mediated transfer of u-Toc. The propensity of u-TTP for highly curved membrane provides a connection to its colocalization with u-Toc in late endosomes.