The spin relaxation time, T₁, has been measured at low densities in normal H₂ at 77°K, 196°K, 298°K and 392°K as a function of density using a 96 mHz pulsed N.M.R. spectrometer and a T₁ minimum obtained. The data at 77°K, where only the J=1 rotational state is populated, is fit by the conventional theories, but the results at higher temperatures are not explained by the generalization of the Bloom-Oppenheim⁽⁶⁾ theory. T₁ was also measured as a function of density for a mixture of 54.5% He in at 298°K in an effort to investigate the role of transitions between J states in the relaxation process. The spin relaxation time T₁ was also measured in HD as a function of density in the region of the T₁ minimum at 196°K and 298°K. Since the most recent theory has not been extended to a system of several populated J levels the results are rather inconclusive. T₁ was also measured in CH₄ as a function of density in the region of the T₁ minimum at 196°K and 298°K and information about the rotational coupling constants obtained. From these results it is concluded that measurements of T₁ as a function of density is very useful in testing theories of relaxation and obtaining information on the rotational coupling constants for polyatomic molecules. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

A study of the rates of hindered internal rotation about the C—N bond in N,N-dimethyltrifluoroacetamide and N,N-dimethyldeuteroformamide has been made using the nuclear magnetic resonance spin echo method. A 40 Mc/sec. spin echo spectrometer, which enables measurements to be made of the transverse relaxation time (T₂) from a Carr Purcell sequence of radio-frequency pulses, is described and its performance illustrated. The precision of values obtained is estimated to be of the order of 5%. Equations, derived from a theory developed by Bloom, Reeves and Wells for the dependence of T₂, measured in a Carr Purcell experiment, on pulse intervals in the presence of a suitable exchange process, have been used to extract the kinetic data for the two molecules. The chemical shift, rate constant and natural relaxation time (T2₀) have been calculated from the data by curve fitting procedures using computer techniques, and the experimental verification of the theory has been noted. The accuracy of the rate constants and activation parameters derived is discussed in the light of previous steady state nuclear magnetic resonance studies. The relative merits of the spin echo and steady state methods are examined and the possibility of the occurrence of systematic errors in such studies is investigated. Steady state studies of the proton exchange between methanol and two phenols (meta-cresol and ortho-hydroxyaceto-phenone) and of the ring inversion of N,N-dimethylpiperazine are also presented and the relative merits of the kinetic parameters discussed. / Science, Faculty of / Chemistry, Department of / Graduate

The spin-lattice relaxation time has been studied in normal H₂ as a function of density and temperature in the range 293°K - 700°K. The measurements were made in the region where T₁ α [formula omitted]. The H₂ results have been interpreted using the Bloom-Oppenheim theory in which the transitions between different J states were taken into account. The analysis indicates that the resonant transitions (1,3↔3,1) and quasi-resonant transitions (1,2↔3,0) and (1,4↔3,2) contribute significantly to the relaxation mechanism. The anisotropic inter-molecular potential between the two H₂ molecules which depends on the orientation of both the molecules could be given by quadrupole-quadrupole interaction while the part that depends on the orientation of one of the molecules alone was found to be adequately represented by a Lennard-Jones potential. T₁ was measured in H₂ - He and H₂ - CO₂ mixtures as a function of density and composition in the temperature range 293°K - 700°K. The analysis indicates that the interaction potential for H₂ - He could be adequately described by a Lennard-Jones potential while the dominant interaction for H₂ - CO₂ could be given by quadrupole-quadrupole interaction. There were indications that the dependence of T₁/[formula omitted] in H₂ - He mixture on the percentage of He is non-linear above 150°K. However, this was not found to be the case in H₂ - CO₂ mixtures. T₁ was also measured in CH₄ and CH₄ - He mixture as a function of density and composition in the same temperature range. The data can be fitted by T₁/[formula omitted] = AT⁻ⁿ where n takes the value of 1.5 for pure CH₄ and 0.79 for CH₄ gas infinitely diluted in He. The analysis based on the existing theory for polyatomic gases shows that the intermolecular potential for CH₄ - CH₄ and CH₄ - He could be described by medium range potentials. The results indicate that the dependence of T₁/[formula omitted] on the percentage of He is not linear below 4OO°K. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The longitudinal and transverse nuclear relaxation times, T₁ and T₂, have been measured in normal H₂ gas at 77.5°K in the pressure range 0.05 to 2 atmospheres. In this region T₁ goes through a minimum, and T₂ deviates significantly from a linear dependence on the density. Comparison of the experimental data with existing theory establishes the following results for the J=1 state of orthohydrogen: i. autocorrelation functions of the molecular angular momentum operators are exponential or nearly so, ii. the ratio of the correlation times , Ʈ₁, Ʈ₂, which are associated with operators of the form J₊, and J²₊ respectively, lies within the limits 0.6 ≤ Ʈ₁ / Ʈ₂ ≤ 1, iii. the splitting of the molecular Zeeman levels cannot be neglected as in the original Schwinger theory. T₁ for the proton and deuteron in HD gas and for the deuterons in normal D₂ gas was measured as a function of temperature and pressure in the range 20 to 373°K and 0 to 8 atmospheres. To within experimental error the dependence of T₁ on the density p is linear. In HD below 65°K, when only the J=0 and J=1 states of the molecule are appreciably populated, the temperature dependence of T₁/p is identical for both proton and deuteron, leading to a value of Ʈ₁/Ʈ₂ = 1,07/± 15% for the J=1 state of HD. Above 100°K, T₁/p for the proton is inversely proportional to the temperature, whereas for the deuteron T₁/p is almost temperature independent. The experimental results are interpreted as evidence that in HD gas the process of molecular reorientation is dominated by the anisotropic intermolecular force arising from the separation of the centres of mass and charge of the molecule. In D₂ gas two relaxation times were found, one associated with the S=1 spin state of paradeuterium and the other associated with the S=2 spin state of orthodeuterium. At 40°K (T₁/p)s=₂ appears to go through a minimum; the analogous quantity in H₂ measured by previous workers also goes through a minimum, but at 80°K. This is consistent with interpreting the minimum as a quantum mechanical diffraction effect. The J=2 component of (T₁/p)s=₂ however, does not go through a minimum, which suggests that the intermolecular interactions are significantly different for the J=1 and J=2 states of the molecule. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The cation radical of chlorpromazine in solution was studied in detail by electron spin resonance. The 16 line spectrum was interpreted in terms of a nitrogen atom, two equivalent protons at the first side chain carbon atom, and three almost equivalent protons from the ring system. The relative magnitudes of the splitting constants require many of the spectral lines to be coincident, and the result is the 16 line spectrum observed. Analysis of the splitting constants was done using Huckel molecular orbital calculations, from which it was deduced that the chlorpromazine cation structure is folded about the N-S axis, with an included angle of 104°. The spectral asymmetry observed in sulfuric acid solution was interpreted in terms of random molecular motions causing a fluctuating environment to arise at the nuclear positions. This leads to a modulation effect on the nuclear magnetic moment, and is responsible for linewidth variation. Further broadening due to exchange effects is discussed qualitatively. The asymmetry of the spectra enable the sign of the nitrogen splitting to be estimated -- it was found to be positive. A brief discussion of the electrical properties of chlorpromazine, using HMO calculations, was included, and some discussion of the mechanism of chlorpromazine drug action was also considered for completeness. / Science, Faculty of / Chemistry, Department of / Graduate

Using modern signal averaging techniques, the proton and fluorine spin-lattice relaxation time T₁ has been measured in CH₄, CF₄, CHF₃, CH₃F, and CF₃Cl gases at low densities and 297°K. By measuring the dependence of T₁ on density near the characteristic T₁ minimum, we have been able to obtain new information on the spin-rotation interaction coupling constants in CF₄, CHF₃, and CH₃F. The CH₄ system was used to test the validity of this method since the spin-rotation coupling constants are accurately known for CH₄. The correlation function for the spin-rotation interaction was found to be exponential within experimental error for all of the molecules studied. The temperature dependence of the fluorine T₁ in CHF₃, CH₃F, and CF₄ was investigated at higher densities. The proton T₁ in CHF₃ and CH₃F have also been studied in the same density region and at several temperatures. A very striking density dependence of the proton T₁ in these two symmetric-top molecules was discovered. A plot of T₁/ρ versus ρ shows "steps". Steady-state Overhauser effects have been studied in experiments performed at 297°K in both CHF₃ and CH₃F gases to demonstrate the importance of the intra-molecular magnetic dipolar interaction at moderate densities. This interaction in CHF₃ and CH₃F is found to be responsible for the peculiar density dependence of the proton T₁. A phenomenological interpretation of the above proton results was given using a high temperature approximation relaxation theory in which the correlations between the spin-dependent interactions of the different nuclei and the existence of three distinct molecular symmetry species in CX₃Y molecules were properly accounted for. A detailed molecular theory for polyatomic molecules is still needed to extract information on the anisotropic part of the inter-molecular potential. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The radical anions and ion-pairs of 1,8-dinitro-naphthalene and 1,4,5,8-tetranitronaphthalene have been perpared and the electron spin resonance spectra have been investigated in detail. The spectra were interpreted completely in terms of a set of two equivalent nitrogen atoms and three sets of two equivalent hydrogen atoms for the 1,8-dinitronaphthalene radical, four equivalent nitrogen atoms and four equivalent hydrogen atoms for the 1,4,5, 8-tetranitronaphthalene radical, respectively. The hyper-fine splitting constants obtained are compared with the values derived from molecular orbital calculations. In the ion-pairs of 1,8-dinitronaphthalene the distinct alkali metal hyperfine splitting have been observed The magnitude of the metal hyperfine splitting shows remarkable temperature dependency, and the temperature dependence is interpreted in terms of the cation exchange mechanism b between two nitro groups of 1,8-dinitronaphthalene. In the anion radical of 1,8-dinitronaphthalene as well as in the corresponding ion-pairs, anormalous line width variation has been observed. This behaviour is interpreted in terms of the cation exchange mechanism and supports the hypothesis proposed for the temperature dependence of alkali metal splitting in the ion-pairs of the compound. In the anion radical of 1,4,5,8-tetranitronaphtha-lene the twisting angle of the nitro group from the plane of aromatic ring is estimated to be (35 ±10)° from the observed splitting constants by employing the spin densities obtained with McLachlan method. The temperature dependency of the nitrogen and hydrogen splittings has been determined. The phenomenon is explained in terms of a hindered rotation of.the nitro group in 1,4,5,8-tetranitronaphthalene. From the asymmetry of the spectra it is predicted that the spin density on the nitrogen nucleus is positive. / Science, Faculty of / Chemistry, Department of / Graduate

by Wong Wing Hung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves [70]). / Acknowledgments --- p.iii / Abstract --- p.iv / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- The Coupled-cluster Method --- p.3 / Chapter 2.1 --- Background / Chapter 2.2 --- Basic Idea of the Method / Chapter 2.3 --- Discussion / Chapter Chapter 3 --- Spin-one Heisenberg Antiferromagnet --- p.8 / Paper enclosed： Coupled-cluster / approximation for spin-one / Heisenberg antiferromagnet / Chapter Chapter 4 --- Easy-plane Spin-one Antif erromagnet --- p.10 / Paper enclosed： Coupled-cluster / approximation for the easy-plane / spin-one antif erromagnet / Chapter Chapter 5 --- Conclusion --- p.11 / References --- p.12 / Appendix --- p.13

Chen, Ting = 單個自旋和光子相互作用的理論研究 / 陳婷. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 72-80). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Chen, Ting = Dan ge zi xuan he guang zi xiang hu zuo yong de li lun yan jiu / Chen Ting.

In this dissertation several aspects on one-dimensional edge states in grapheme are studied. First, a background in the history and development of graphitic forms is presented. Then some novel features found in two-dimensional bulk graphene are presented. Here, some focus is given to the chiral nature of the Dirac equation and the symmetries found in the grahene. Magnetism and interactions in graphene is also briefly discussed. Finally, the graphene nanoribbon with its two typical edges: armchair and zigzag is introduced. Gaps due to finite-size effects are studied. Next, the problem of determining the zigzag ground state is presented. Later, we develop this in an attempt to add the Coulomb interaction to the zigzag flat-band states. These nanoribbons can be stimulated with a tight-binding code on a lattice model in which many different effects can be added, including an A/B sublattice asymmetry, spin-orbit coupling and external fields. The lowest Landau level solutions in the different ribbon orientations is of particular current interest. This is done in the context of understanding new physics and developing novel applications of graphene nanoribbon devices. Adding spin-orbit to a graphene ribbon Hamiltonian leads to current carrying electronic states localized on the sample edges. These states can appear on both zigzag and armchair edges in the semi-finite limit and differ qualitatively in dispersion and spin-polarization from the well known zigzag edge states that occur in models that do not include spin-orbit coupling. We investigate the properties of these states both analytically and numerically using lattice and continuum models with intrinsic and Rashba spin-orbit coupling and spin-independent gap producing terms. A brief discussion of the Berry curvature and topological numbers of graphene with spin-orbit coupling also follows.