Isomerism as Manifestation of Intrinsic Symmetry of Molecules: Lunn–Senior’s Theory

This article presents the principal results of the doctoral thesis “Isomerism as internal symmetry of molecules” by Valentin Vankov Iliev (Institute of Mathematics and Informatics), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 15 December, 2008.

The utilization of chiral ion mobility spectrometry for the detection of enantiomeric mixtures and thermally labile compounds

This dissertation utilized electrospray ion mobility mass spectrometry (ESI-IMS-MS) to develop methods necessary for the separation of chiral compounds of forensic interest. The compounds separated included ephedrines and pseudoephedrines, that occur as impurities in confiscated amphetamine type substances (ATS) in an effort to determine the origin of these substances. The ESI-IMS-MS technique proved to be faster and more cost effective than traditional chromatographic methods currently used to conduct chiral separations such as gas and liquid chromatography. Both mass spectrometric and computational analysis revealed the separation mechanism of these chiral interactions allowing for further development to separate other chiral compounds by IMS. Successful separation of chiral compounds was achieved utilizing a variety of modifiers injected into the IMS drift tube. It was found that the modifiers themselves did not need to be chiral in nature and that achiral modifiers were sufficient in performing the required separations. The ESI-IMS-MS technique was also used to detect thermally labile compounds which are commonly found in explosive substances. The methods developed provided mass spectrometric identification of the type of ionic species being detected from explosive analytes as well as the appropriate solvent that enhances detection of these analytes in either the negative or positive ion mode. An application of the developed technique was applied to the analysis of a variety of low explosive smokeless powder samples. It was found that the developed ESI-IMS-MS technique not only detected the components of the smokeless powders, but also provided data that allowed the classification of the analyzed smokeless powders by manufacturer or make. ^

Docking and simulation study of the enantiospecificity of chiral epoxidation reactions catalyzed by chloroperoxidase

Chloroperoxidase (CPO), a 298-residue glycosylated protein from the fungus Caldariomyces fumago, is probably the most versatile heme enzyme yet discovered. Interest in CPO as a catalyst is based on its power to produce enantiomerically enriched products. Recent research has focused its attention on the ability of CPO to epoxidize alkenes in high regioselectivity and enantioselectivity as an efficient and environmentally benign alternative to traditional synthetic routes. There has been little work on the nature of ligand binding, which probably controls the regio- and enantiospecifity of CPO. Consequently it is here that we focus our work. We report docking calculations and computer simulations aimed at predicting the enantiospecificity of CPO-catalyzed epoxidation of three model substrates. On the basis of this work candidate mutations to improve the efficiency of CPO are predicted. In order to accomplish these aims, a simulated annealing and molecular dynamics protocol is developed to sample potentially reactive substrate/CPO complexes.

Numerical study of the enlarged O(5) symmetry of the 3D antiferromagnetic RP^(2) spin model

We investigate by means of Monte Carlo simulation and finite-size scaling analysis the critical properties of the three dimensional O (5) non-linear σ model and of the antiferromagnetic RP^(2) model, both of them regularized on a lattice. High accuracy estimates are obtained for the critical exponents, universal dimensionless quantities and critical couplings. It is concluded that both models belong to the same universality class, provided that rather non-standard identifications are made for the momentum-space propagator of the RP^(2) model. We have also investigated the phase diagram of the RP^(2) model extended by a second-neighbor interaction. A rich phase diagram is found, where most of the phase transitions are of the first order.

Dynamical generation of a gauge symmetry in the double-exchange model

It is shown that a bosonic formulation of the double-exchange model, one of the classical models for magnetism, generates dynamically a gauge-invariant phase in a finite region of the phase diagram. We use analytical methods, Monte Carlo simulations and finite-size scaling analysis. We study the transition line between that region and the paramagnetic phase. The numerical results show that this transition line belongs to the universality class of the antiferromagnetic RP^(2) model. The fact that one can define a universality class for the antiferromagnetic RP^(2) model, different from the one of the O(N) models, is puzzling and somehow contradicts naive expectations about universality.

Multistabilities and symmetry-broken one-color and two-color states in closely coupled single-mode lasers

We theoretically investigate the dynamics of two mutually coupled, identical single-mode semi-conductor lasers. For small separation and large coupling between the lasers, symmetry-broken one-color states are shown to be stable. In this case the light outputs of the lasers have significantly different intensities while at the same time the lasers are locked to a single common frequency. For intermediate coupling we observe stable symmetry-broken two-color states, where both lasers lase simultaneously at two optical frequencies which are separated by up to 150 GHz. Using a five-dimensional model, we identify the bifurcation structure which is responsible for the appearance of symmetric and symmetry-broken one-color and two-color states. Several of these states give rise to multistabilities and therefore allow for the design of all-optical memory elements on the basis of two coupled single-mode lasers. The switching performance of selected designs of optical memory elements is studied numerically.

Fermion Mass Generation without Spontaneous Symmetry Breaking

The conventional mechanism of fermion mass generation in the Standard Model involves Spontaneous Symmetry Breaking (SSB). In this thesis, we study an alternate mechanism for the generation of fermion masses that does not require SSB, in the context of lattice field theories. Being inherently strongly coupled, this mechanism requires a non-perturbative approach like the lattice approach.

In order to explore this mechanism, we study a simple lattice model with a four-fermion interaction that has massless fermions at weak couplings and massive fermions at strong couplings, but without any spontaneous symmetry breaking. Prior work on this type of mass generation mechanism in 4D, was done long ago using either mean-field theory or Monte-Carlo calculations on small lattices. In this thesis, we have developed a new computational approach that enables us to perform large scale quantum Monte-Carlo calculations to study the phase structure of this theory. In 4D, our results confirm prior results, but differ in some quantitative details of the phase diagram. In contrast, in 3D, we discover a new second order critical point using calculations on lattices up to size $ 60^3$. Such large scale calculations are unprecedented. The presence of the critical point implies the existence of an alternate mechanism of fermion mass generation without any SSB, that could be of interest in continuum quantum field theory.

Studies in asymmetric and heterocyclic synthesis: I. chiral ketones II. Quinolones III. Trifluoromethylated pyrones

This thesis is split into three sections based on three different areas of research. In the first section, investigations into the α-alkylation of ketones using a novel chiral auxiliary is reported. This chiral auxiliary was synthesised containing a pyrrolidine ring in the chiral arm and was applied in the preparation of α-alkylated ketones which were obtained in up to 92% ee and up to 63% yield over two steps. Both 3-pentanone and propiophenone based ketones were used in the investigation with a variety of both alkyl and benzyl based electrophiles. The novel chiral auxiliary was also successful when applied to Michael and aldol reactions. A diamine precursor en route to the chiral auxiliary was also applied as an organocatalyst in a Michael reaction, with the product obtained in excellent enantioselectivity. In the second section, investigations into potential anti-quorum sensing molecules are reported. The bacteria Pseudomonas aeruginosa is an antibiotic-resistant pathogen that demonstrates cooperative behaviours and communicates using small chemical molecules in a process termed quorum sensing. A variety of C-3 analogues of the quorum sensing molecules used by P. aeruginosa were synthesised. Expanding upon previous research within the group, investigations were carried out into alternative protecting group strategies of 2-heptyl-4-(1H)- quinolone with the aim of improving the yields of products of cross-coupling reactions. In the third section, investigations into fluorination and trifluoromethylation of 2-pyrones, pyridones and quinolones is reported. The incorporation of a fluorine atom or a trifluoromethyl group into a molecule is important in pharmaceutical drug discovery programmes as it can lead to increased lipophilicity and bioavailability, however late-stage incorporation is rarely reported. Both direct fluorination and trifluoromethylation were attempted. Eight trifluoromethylated 2-pyrones, five trifluoromethylated 2-pyridones and a trifluoromethylated 2-quinolone were obtained in a late-stage synthesis from their respective iodinated precursors using methyl fluorosulfonyldifluoroacetate as a trifluoromethylating reagent.

The development of novel chiral tethers for controlling intramolecular aryl-aryl coupling and their application in the synthesis of gomisin M1 and analogues

The primary focus of this thesis was the development of a novel chiral tether that could be used to control axial chirality around a newly formed aryl-aryl bond, and the extension of this methodology to the model synthesis of gomisin M1. In chapter 1, a review detailing the use of chiral tethers in the synthesis of atropisomers is discussed. The use of a variety of chiral molecules including 1,2-diols, 1,3-diols and other diol-based tethers, as well as amine-based and miscellaneous tethers are detailed. In chapter 2, the rationale behind the design of our novel molecular tethers, along with the subsequent synthesis of three chiral 1,3-diol-based tethers, is outlined. The method by which the enantiopurity of these diols was determined is also reviewed. This chapter also includes the attempted Mitsunobu and intramolecular couplings in the model synthesis of BINOL. Chapter 3 discusses the synthesis of suitable aryl halide substrates, and their employment in the attempted tether-controlled asymmetric model synthesis of gomisin M1. A comprehensive investigation into the attempted intramolecular biaryl coupling of these tethered substrates is also included. The non-stereoselective model synthesis of gomisin M1 is outlined in chapter 4. The installation of the desired biaryl linkage and the subsequent attempted intramolecular McMurry couplings are discussed. The impact of different protecting groups in the molecule on the intramolecular McMurry reaction is also outlined. Chapter 5 details the full experimental procedures, including spectroscopic and analytical data for the compounds prepared during this research.

THE DESIGN AND SYNTHESIS OF SILOXANE PRECURSORS FOR CHIRAL PERIODIC MESOPOROUS ORGANOSILICA MATERIALS

The development of cost-effective and reliable methods for the synthesis and separation of asymmetric compounds is paramount in helping to meet society’s ever-growing demand for chiral small molecules. Of these methods, chiral heterogeneous supports are particularly appealing as they allow for the reuse of the chiral source. One such support, based on the synergy between chiral organic units and structurally stable inorganic silicon scaffolds are periodic mesoporous organosilicas (PMOs). In the work described herein, I examine some of the factors governing the transmission of chirality between chiral dopants and prochiral bulk phases in chiral PMO materials. In particular, the exploration of 1,1’-binaphthalene-bridged chiral dopants with a focus on the point of attachment into the materials. Moreover, the effects of ordering in the materials are examined and reveal that chirality transfer is more facile in materials with molecular-scale order then those containing amorphous walls. Secondly, the issues surrounding the synthesis and purification of aryl-triethoxysilanes as siloxane precursors are addressed. Both the introduction of a two-carbon linker and the direct attachment of allyl and mixed allyldiethoxysilane species are explored. This work demonstrates that allyldiethoxysilanes are ideal, in that they are stable enough to permit facile synthesis, while still being able to hydrolyze completely to produce well-ordered materials. Lastly, the production of new bulk phases for chiral PMO materials is examined by introducing new prochiral nitrogen-containing siloxane precursors. Biphenyldiamine and bipyridine-bridged siloxane precursors are readily synthesized on reasonable scales. Their use as the bulk siloxane precursor in the production of PMO materials however, is precluded by insufficient gelation and additional siloxane precursors are necessary for the production of ordered materials. In addition to the research detailed above that forms the body of this thesis, two short works are appended. The first details the production of polythiophene assemblies mediated through coordination nanospaces, while the second explores the production of N-heterocyclic carbene functionalized gold nanoparticles through ligand exchange.

Total Synthesis of the Antitumor Macrolides, (+)-Brefeldin A and 4‑Epi-Brefeldin A from D‑Glucose: Use of the Padwa Anionic Allenylsulfone [3+2]-Cycloadditive Elimination To Construct Trans-Configured Chiral Cyclopentane Systems

A new synthesis of (+)-brefeldin A is reported via Padwa allenylsulfone [3+2]-cycloadditive elimination. Cycloadduct 13 was initially elaborated into iodide
27, which, following treatment with Zn, gave aldehyde 28 whose C(9) stereocenter was epimerized. Further elaboration into enoate 38 and Julia−Kocienski olefination with 5 subsequently afforded 39, which was deprotected at C(1) and O(15). Yamaguchi macrolactonization of the seco-acid thereafter afforded a macrocycle that underwent O-desilylation and inversion at C(4) to give (+)-brefeldin A following deprotection

The Addition of Allyltrimethylsilane to Cyclic N-Acyliminium Ions Derived from (S)-(+)-Mandelic Acid and Cyclohexyl-Based Chiral Auxiliaries

A adição de aliltrimetilsilano, promovida por TiCl4, a íons N-aciliminios cíclicos de 5- e 6-membros derivados do ácido (S)-(+)-mandélico, (1R,2S)-trans-2-fenil-1-cicloexanol e (1R,2S,5R)-8-fenilmentol ocorreu com baixas a moderadas razões diastereoisoméricas (1:1-6:1) e forneceu as respectivas amidas e carbamatos em bons rendimentos. A melhor diastereosseleção facial foi observada com o uso de (1R,2S,5R)-8-fenilmentol como auxiliar quiral. As amidas e carbamatos 2-substituídos foram convertidos nos alcalóides (S)- e (R)-propil pirrolidina e coniina com eficiente recuperação dos auxiliares quirais.

Symmetry properties of one- and two- electron molecular integrals

The maximum numbers of distinct one- and two-electron integrals that arise in calculating the electronic energy of a molecule are discussed. It is shown that these may be calculated easily using the character table of the symmetry group of the set of basis functions used to express the wave function. Complications arising from complex group representations and from a conflict of symmetry between the basis set and the nuclear configuration are considered and illustrated by examples.

Fast assembly of fock matrices utilising symmetry properties of the basis set

A method of assembling the elements of the Fock matrix is described which is a modification of that due to Dacre. Lists of symmetry equivalent one-electron integrals are used as pointers to abbreviate the process of collecting two-electron integrals into the Fock matrix.