Trapped ion magnetic resonance: concepts and designs

A novel spectroscopy of trapped ions is proposed which will bring single-ion detection sensitivity to the observation of magnetic resonance spectra. The approaches developed here are aimed at resolving one of the fundamental problems of molecular spectroscopy, the apparent incompatibility in existing techniques between high information content (and therefore good species discrimination) and high sensitivity. Methods for studying both electron spin resonance (ESR) and nuclear magnetic resonance (NMR) are designed. They assume established methods for trapping ions in high magnetic field and observing the trapping frequencies with high resolution (<1 Hz) and sensitivity (single ion) by electrical means. The introduction of a magnetic bottle field gradient couples the spin and spatial motions together and leads to a small spin-dependent force on the ion, which has been exploited by Dehmelt to observe directly the perturbation of the ground-state electron's axial frequency by its spin magnetic moment.

A series of fundamental innovations is described m order to extend magnetic resonance to the higher masses of molecular ions (100 amu = 2x 10^5 electron masses) and smaller magnetic moments (nuclear moments = 10^(-3) of the electron moment). First, it is demonstrated how time-domain trapping frequency observations before and after magnetic resonance can be used to make cooling of the particle to its ground state unnecessary. Second, adiabatic cycling of the magnetic bottle off between detection periods is shown to be practical and to allow high-resolution magnetic resonance to be encoded pointwise as the presence or absence of trapping frequency shifts. Third, methods of inducing spindependent work on the ion orbits with magnetic field gradients and Larmor frequency irradiation are proposed which greatly amplify the attainable shifts in trapping frequency.

The dissertation explores the basic concepts behind ion trapping, adopting a variety of classical, semiclassical, numerical, and quantum mechanical approaches to derive spin-dependent effects, design experimental sequences, and corroborate results from one approach with those from another. The first proposal presented builds on Dehmelt's experiment by combining a "before and after" detection sequence with novel signal processing to reveal ESR spectra. A more powerful technique for ESR is then designed which uses axially synchronized spin transitions to perform spin-dependent work in the presence of a magnetic bottle, which also converts axial amplitude changes into cyclotron frequency shifts. A third use of the magnetic bottle is to selectively trap ions with small initial kinetic energy. A dechirping algorithm corrects for undesired frequency shifts associated with damping by the measurement process.

The most general approach presented is spin-locked internally resonant ion cyclotron excitation, a true continuous Stern-Gerlach effect. A magnetic field gradient modulated at both the Larmor and cyclotron frequencies is devised which leads to cyclotron acceleration proportional to the transverse magnetic moment of a coherent state of the particle and radiation field. A preferred method of using this to observe NMR as an axial frequency shift is described in detail. In the course of this derivation, a new quantum mechanical description of ion cyclotron resonance is presented which is easily combined with spin degrees of freedom to provide a full description of the proposals.

Practical, technical, and experimental issues surrounding the feasibility of the proposals are addressed throughout the dissertation. Numerical ion trajectory simulations and analytical models are used to predict the effectiveness of the new designs as well as their sensitivity and resolution. These checks on the methods proposed provide convincing evidence of their promise in extending the wealth of magnetic resonance information to the study of collisionless ions via single-ion spectroscopy.

Variable-angle electron spectroscopic studies of various polyatomic molecular systems

The complementary techniques of low-energy, variable-angle electron-impact spectroscopy and ultraviolet variable-angle photoelectron spectroscopy have been used to study the electronic spectroscopy and structure of several series of molecules. Electron-impact studies were performed at incident beam energies between 25 eV and 100 eV and at scattering angles ranging from 0° to 90°. The energy-loss regions from 0 eV to greater than 15 eV were studied. Photoelectron spectroscopic studies were conducted using a HeI radiation source and spectra were measured at scattering angles from 45° to 90°. The molecules studied were chosen because of their spectroscopic, chemical, and structural interest. The operation of a new electron-impact spectrometer with multiple-mode target source capability is described. This spectrometer has been used to investigate the spin-forbidden transitions in a number of molecular systems.

The electron-impact spectroscopy of the six chloro-substituted ethylenes has been studied over the energy-loss region from 0-15 eV. Spin-forbidden excitations corresponding to the π → π*, N → T transition have been observed at excitation energies ranging from 4.13 eV in vinyl chloride to 3.54 eV in tetrachloroethylene. Symmetry-forbidden transitions of the type π → np have been oberved in trans-dichloroethyene and tetrachlor oethylene. In addition, transitions to many states lying above the first ionization potential were observed for the first time. Many of these bands have been assigned to Rydberg series converging to higher ionization potentials. The trends observed in the measured transition energies for the π → π*, N → T, and N → V as well as the π → 3s excitation are discussed and compared to those observed in the methyl- and fluoro- substituted ethylenes.

The electron energy-loss spectra of the group VIb transition metal hexacarbonyls have been studied in the 0 eV to 15 eV region. The differential cross sections were obtained for several features in the 3-7 eV energy-loss region. The symmetry-forbidden nature of the ¹A_1g → ¹A_1g, 2t_2g(π) → 3t_2g(π*) transition in these compounds was confirmed by the high-energy, low-angle behavior of their relative intensities. Several low lying transitions have been assigned to ligand field transitions on the basis of the energy and angular behavior of the differential cross sections for these transitions. No transitions which could clearly be assigned to singlet → triplet excitations involving metal orbitals were located. A number of states lying above the first ionization potential have been observed for the first time. A number of features in the 6-14 eV energy-loss region of the spectra of these compounds correspond quite well to those observed in free CO.

A number of exploratory studies have been performed. The π → π*, N → T, singlet → triplet excitation has been located in vinyl bromide at 4.05 eV. We have also observed this transition at approximately 3.8 eV in a cis-/trans- mixture of the 1,2-dibromoethylenes. The low-angle spectrum of iron pentacarbonyl was measured over the energy-loss region extending from 2-12 eV. A number of transitions of 8 eV or greater excitation energy were observed for the first time. Cyclopropane was also studied at both high and low angles but no clear evidence for any spin- forbidden transitions was found. The electron-impact spectrum of the methyl radical resulting from the pyrolysis of tetramethyl tin was obtained at 100 eV incident energy and at 0° scattering angle. Transitions observed at 5.70 eV and 8.30 eV agree well with the previous optical results. In addition, a number of bands were observed in the 8-14 eV region which are most likely due to Rydberg transitions converging to the higher ionization potentials of this molecule. This is the first reported electron-impact spectrum of a polyatomic free radical.

Variable-angle photoelectron spectroscopic studies were performed on a series of three-membered-ring heterocyclic compounds. These compounds are of great interest due to their highly unusual structure. Photoelectron angular distributions using HeI radiation have been measured for the first time for ethylene oxide and ethyleneimine. The measured anisotropy parameters, β, along with those measured for cyclopropane were used to confirm the orbital correlations and photoelectron band assignments. No high values of β similar to those expected for alkene π orbitals were observed for the Walsh or Forster-Coulson-Moffit type orbitals.

Synthesis and characterization of high-spin organic materials: prototypes for the polaronic ferromagnet

The design, synthesis and magnetic characterization of thiophene-based models for the polaronic ferromagnet are described. Synthetic strategies employing Wittig and Suzuki coupling were employed to produce polymers with extended π-systems. Oxidative doping using AsF_5 or I_2 produces radical cations (polarons) that are stable at room temperature. Magnetic characterization of the doped polymers, using SQUID-based magnetometry, indicates that in several instances ferromagnetic coupling of polarons occurs along the polymer chain. An investigation of the influence of polaron stability and delocalization on the magnitude of ferromagnetic coupling is pursued. A lower limit for mild, solution phase I_2 doping is established. A comparison of the variable temperature data of various polymers reveals that deleterious antiferromagnetic interactions are relatively insensitive to spin concentration, doping protocols or spin state. Comparison of the various polymers reveals useful design principles and suggests new directions for the development of magnetic organic materials. Novel strategies for solubilizing neutral polymeric materials in polar solvents are investigated.

The incorporation of stable bipyridinium spin-containing units into a polymeric high-spin array is explored. Preliminary results suggest that substituted diquat derivatives may serve as stable spin-containing units for the polaronic ferromagnet and are amenable to electrochemical doping. Synthetic efforts to prepare high-spin polymeric materials using viologens as a spin source have been unsuccessful.

The importance of spin for observing gravitational waves from coalescing compact binaries with LIGO and Virgo

General Relativity predicts the existence of gravitational waves, which carry information about the physical and dynamical properties of their source. One of the many promising sources of gravitational waves observable by ground-based instruments, such as in LIGO and Virgo, is the coalescence of two compact objects (neutron star or black hole). Black holes and neutron stars sometimes form binaries with short orbital periods, radiating so strongly in gravitational waves that they coalesce on astrophysically short timescales. General Relativity gives precise predictions for the form of the signal emitted by these systems. The most recent searches for theses events used waveform models that neglected the effects of black hole and neutron star spin. However, real astrophysical compact objects, especially black holes, are expected to have large spins. We demonstrate here a data analysis infrastructure which achieves an improved sensitivity to spinning compact binaries by the inclusion of spin effects in the template waveforms. This infrastructure is designed for scalable, low-latency data analysis, ideal for rapid electromagnetic followup of gravitational wave events.

Measurement of the neutron (^3He) spin structure function at low Q^2 : a connection between the Bjorken and Drell-Hearn-Gerasimov sum rules

The spin dependent cross sections, σT_1/2 and σT_3/2 , and asymmetries, A_∥ and A_⊥ for ³He have been measured at the Jefferson Lab's Hall A facility. The inclusive scattering process ³He(e,e)X was performed for initial beam energies ranging from 0.86 to 5.1 GeV, at a scattering angle of 15.5°. Data includes measurements from the quasielastic peak, resonance region, and the deep inelastic regime. An approximation for the extended Gerasimov-Drell-Hearn integral is presented at a 4-momentum transfer Q² of 0.2-1.0 GeV².

Also presented are results on the performance of the polarized ³He target. Polarization of ³He was achieved by the process of spin-exchange collisions with optically pumped rubidium vapor. The ³He polarization was monitored using the NMR technique of adiabatic fast passage (AFP). The average target polarization was approximately 35% and was determined to have a systematic uncertainty of roughly ±4% relative.

Superconductivity, spin-glass properties, and ferromagnetism in amorphous La-Gd-Au alloys

The superconducting and magnetic properties of splat cooled amorphous alloys of composition (La_100-xGd_x)₈₀Au₂₀ (0 ≤ x ≤ 100) have been studied. The La₈₀Au₂₀ alloys are ideal type II super-conductors (critical temperature T_c = 3.5° K ). The concentration range (x less than 1) where superconductivity and spin-glass freezing n1ight coexist has been studied in detail. The spin-glass alloys (0 less than x less than 70) exhibit susceptibility maxima and thermomagnetic history effects. In the absence of complications due to crystal field and enhanced matrix effects, a phenomenological model is proposed in which the magnetic clusters are treated as single spin entities interacting via random forces using the molecular field approach. The fundamental parameters (such as the strength of the forces and the size of clusters) can be deduced from magnetization measurements. The remanent magnetization is shown to arise from an interplay of the RKKY and dipolar forces. Magnetoresistivity results are found to be consistent with the aforementioned picture. The nature of magnetic interactions in an amorphous matrix is also discussed. The moment per Gd atom (7µ_B) is found to be constant and close to that of the crystalline value throughout the concentration range investigated. Finally, a detail study is made of the critical phenomena and magnetic properties of the amorphous ferromagnet: Gd₈₀Au₂₀. The results are compared with recent theories on amorphous magnetism.

Spin dynamics of pulsed nuclear magnetic double resonance in solids

In the first part of this thesis, experiments utilizing an NMR phase interferometric concept are presented. The spinor character of two-level systems is explicitly demonstrated by using this concept. Following this is the presentation of an experiment which uses this same idea to measure relaxation times of off-diagonal density matrix elements corresponding to magnetic-dipole-forbidden transitions in a ^(13)C-^1H, AX spin system. The theoretical background for these experiments and the spin dynamics of the interferometry are discussed also.

The second part of this thesis deals with NMR dipolar modulated chemical shift spectroscopy, with which internuclear bond lengths and bond angles with respect to the chemical shift principal axis frame are determined from polycrystalline samples. Experiments using benzene and calcium formate verify the validity of the technique in heteronuclear (^(13)C-^1H) systems. Similar experiments on powdered trichloroacetic acid confirm the validity in homonuclear (^1H- ^1H) systems. The theory and spin dynamics are explored in detail, and the effects of a number of multiple pulse sequences are discussed.

The last part deals with an experiment measuring the ^(13)C chemical shift tensor in K_2Pt(CN)_4Br_(0.3) • 3H_2O, a one-dimensional conductor. The ^(13)C spectra are strongly affected by ^(14)N quadrupolar interactions via the ^(13)C - ^(14)N dipolar interaction. Single crystal rotation spectra are shown.

An appendix discussing the design, construction, and performance of a single-coil double resonance NMR sample probe is included.

Nonclassical excitation and quantum interference in a three level atom

Non-classical properties and quantum interference (QI) in two-photon excitation of a three level atom (|1〉), |2〉, |3〉) in a ladder configuration, illuminated by multiple fields in non-classical (squeezed) and/or classical (coherent) states, is studied. Fundamentally new effects associated with quantum correlations in the squeezed fields and QI due to multiple excitation pathways have been observed. Theoretical studies and extrapolations of these findings have revealed possible applications which are far beyond any current capabilities, including ultrafast nonlinear mixing, ultrafast homodyne detection and frequency metrology. The atom used throughout the experiments was Cesium, which was magneto-optically trapped in a vapor cell to produce a Doppler-free sample. For the first part of the work the |1〉 → |2〉 → |3〉 transition (corresponding to the 6S_1/2F = 4 → 6P_3/2F' = 5 → 6D_5/2F" = 6 transition) was excited by using the quantum-correlated signal (Ɛ_s) and idler (Ɛ_i) output fields of a subthreshold non-degenerate optical parametric oscillator, which was tuned so that the signal and idler fields were resonant with the |1〉 → |2〉 and |2〉 → |3〉 transitions, respectively. In contrast to excitation with classical fields for which the excitation rate as a function of intensity has always an exponent greater than or equal to two, excitation with squeezed-fields has been theoretically predicted to have an exponent that approaches unity for small enough intensities. This was verified experimentally by probing the exponent down to a slope of 1.3, demonstrating for the first time a purely non-classical effect associated with the interaction of squeezed fields and atoms. In the second part excitation of the two-photon transition by three phase coherent fields Ɛ₁ , Ɛ₂ and Ɛ₀, resonant with the dipole |1〉 → |2〉 and |2〉 → |3〉 and quadrupole |1〉 → |3〉 transitions, respectively, is studied. QI in the excited state population is observed due to two alternative excitation pathways. This is equivalent to nonlinear mixing of the three excitation fields by the atom. Realizing that in the experiment the three fields are spaced in frequency over a range of 25 THz, and extending this scheme to other energy triplets and atoms, leads to the discovery that ranges up to 100's of THz can be bridged in a single mixing step. Motivated by these results, a master equation model has been developed for the system and its properties have been extensively studied.

Excitation energies and decay properties of T = 3/2 states in ^(17)O, ^(17)F and ^(21)Na

The two lowest T = 3/2 levels in ²¹Na have been studied in the ¹⁹F(³He, n), ²⁰Ne (p,p) and ²⁰Ne (p,p’) reactions, and their excitation energies, spins, parities and widths have been determined. In a separate investigation, branching ratios were measured for the isospin-nonconserving particle decays of the lowest T = 3/2 levels in ¹⁷O and ¹⁷F to the ground state and first two excited states of ¹⁶O, by studying the ¹⁵N(³He,n) ¹⁷F*(p) ¹⁶O and ¹⁸O(³He, α)¹⁷O*(n) ¹⁶O reactions.

The ¹⁹F(³He,n) ²¹Na reaction was studied at incident energies between 4.2 and 5.9 MeV using a pulsed-beam neutron-time-of-flight spectrometer. Two T = 3/2 levels were identified at excitation energies of 8.99 ± 0.05 MeV (J > ½) and 9.22 ± 0.015 MeV (J ^π = ½⁺, Γ ˂ 40 keV). The spins and parities were determined by a comparison of the measured angular distributions with the results of DWBA calculations.

These two levels were also obsesrved as isospin-forbidden resonances in the ²⁰Ne(p,p) and ²⁰Ne(p,p’) reactions. Excitation energies were measured and spins, parities, and widths were determined from a single level dispersion theory analysis. The following results were obtained:

E_x = 8.973 ± 0.007 MeV, J ^π = 5/2 ⁺ or 3/2⁺, Γ ≤ 1.2 keV,

^Γp_o = 0.1 ± 0.05 keV; E_x = 9.217 ± 0.007 MeV, J^π = ½ ⁺,

Γ = 2.3 ± 0.5 keV, ^Γp_o = 1.1 ± 0.3 keV.

Isospin assignments were made on the basis of excitation energies, spins, parities, and widths.

Branching ratios for the isospin-nonconserving proton decays of the 11.20 MeV, T = 3/2 level in ¹⁷F were measured by the ¹⁵N(³He,n) ¹⁷ F*(p) ¹⁶O reaction to be 0.088 ± 0.016 to the ground state of ¹⁶O and 0.22 ± 0.04 to the unresolved 6.05 and 6.13 MeV levels of ¹⁶O. Branching ratios for the neutron decays of the analogous T = 3/2 level, at 11.08 MeV in ¹⁷O, were measured by the ¹⁶O(³He, α)¹⁷O*(n)¹⁶O reaction to be 0.91 ± 0.15 to the ground state of ¹⁶O and 0.05 ± 0.02 to the unresolved 6.05 and 6.13 MeV states. By comparing the ratios of reduced widths for the mirror decays, the form of the isospin impurity in the T = 3/2 levels is shown to depend on T_z.

I. Electron spin relaxation studies of manganese(II) complexes in acetonitrile. II. Nuclear spin relaxation studies of bromine in tetrabromomanganese(II) in acetonitrile

Magnetic resonance techniques have given us a powerful means for investigating dynamical processes in gases, liquids and solids. Dynamical effects manifest themselves in both resonance line shifts and linewidths, and, accordingly, require detailed analyses to extract desired information. The success of a magnetic resonance experiment depends critically on relaxation mechanisms to maintain thermal equilibrium between spin states. Consequently, there must be an interaction between the excited spin states and their immediate molecular environment which promote changes in spin orientation while excess magnetic energy is coupled into other degrees of freedom by non-radiative processes. This is well known as spin-lattice relaxation. Certain dynamical processes cause fluctuations in the spin state energy levels leading to spin-spin relaxation and, here again, the environment at the molecular level plays a significant role in the magnitude of interaction. Relatively few electron spin relaxation studies of solutions have been conducted and the present work is addressed toward the extension of our knowledge in this area and the retrieval of dynamical information from line shape analyses on a time scale comparable to diffusion controlled phenomena.

Specifically, the electron spin relaxation of three Mn⁺²3d⁵ complexes, Mn(CH₃CN)₆⁺², MnCl₄^-2 in acetonitrile has been studied in considerable detail. The effective spin Hamiltonian constants were carefully evaluated under a wide range of experimental conditions. Resonance widths of these Mn⁺² complexes were studied in the presence of various excess ligand ions and as a function of concentration, viscosity, temperature and frequency (X-band, ~9.5 Ԍ Hz and K-band, ~35 Ԍ Hz).

A number of interesting conclusions were drawn from these studies. For the Et₄NCl-₄^-2 system several relaxation mechanisms leading to resonance broadening were observed. One source appears to arise through spin-orbit interactions caused by modulation of the ligand field resulting from transient distortions of the complex imparted by solvent fluctuations in the immediate surroundings of the paramagnetic ion. An additional spin relaxation was assigned to the formation of ion pairs [Et₄N⁺…MnCl₄^-2] and it was possible to estimate the dissociation constant for this specie in acetonitrile.

The Bu₄NBr-MnBr₄^-2 study was considerably more interesting. As in the former case, solvent fluctuations and ion-pairing of the paramagnetic complex [Bu₄N⁺…MnBr₄^-2] provide significant relaxation for the electronic spin system. Most interesting, without doubt, is the onset of a new relaxation mechanism leading to resonance broadening which is best interpreted as chemical exchange. Thus, assuming that resonance widths were simply governed by electron spin state lifetimes, we were able to extract dynamical information from an interaction in which the initial and final states are the same

MnBr₄^-2 + Br^- = MnBr₄^-2 + Br^-.

The bimolecular rate constants were obtained at six different temperatures and their magnitudes suggested that the exchange is probably diffusion controlled with essentially a zero energy of activation. The most important source of spin relaxation in this system stems directly from dipolar interactions between the manganese 3d⁵ electrons. Moreover, the dipolar broadening is strongly frequency dependent indicating a deviation between the transverse and longitudinal relaxation times. We are led to the conclusion that the 3d⁵ spin states of ion-paired MnBr₄^-2 are significantly correlated so that dynamical processes are also entering the picture. It was possible to estimate the correlation time, ^Td, characterizing this dynamical process.

In Part II we study nuclear magnetic relaxation of bromine ions in the MnBr4-2-Bu4NBr-acetonitrile system. Essentially we monitor the 79Br and 81Br linewidths in response to the [MnBr4-2]/[Br-] ratio with the express purpose of supporting our contention that exchange is occurring between "free" bromine ions in the solvent and bromine in the first coordination sphere of the paramagnetic anion. The complexity of the system elicited a two-part study: (1) the linewidth behavior of Bu4NBr in anhydrous CH3CN in the absence of MnBr4-2 and (2) in the presence of MnBr4-2. It was concluded in study (1) that dynamical association, Bu4NBr k1= Bu4N+ + Br-, was modulating field-gradient interactions at frequencies high enough to provide an estimation of the unimolecular rate constant, k1. A comparison of the two isotopic bromine linewidth-mole fraction results led to the conclusion that quadrupole interactions provided the dominant relaxation mechanism. In study (2) the "residual" bromine linewidths for both 79Br and 81Br are clearly controlled by quadrupole interactions which appear to be modulated by very rapid dynamical processes other than molecular reorientation. We conclude that the "residual" linewidth has its origin in chemical exchange and that bromine nuclei exchange rapidly between a "free" solvated ion and the paramagnetic complex, MnBr4-2.

A study of T = 2 states in ^(12)B, ^(12)C, ^(20)F and ^(28)Al

The lowest T = 2 states have been identified and studied in the nuclei ¹²C, ¹²B, ²⁰F and and ²⁸Al. The first two of these were produced in the reactions ¹⁴C(p,t)¹²C and ¹⁴C (p,³He)¹²B, at 50.5 and 63.4 MeV incident proton energy respectively, at the Oak Ridge National Laboratory. The T = 2 states in ²⁰F and ²⁸Al were observed in (³He,p) reactions at 12-MeV incident energy, with the Caltech Tandem accelerator.

The results for the four nuclei studied are summarized below:

(1) ¹²C: the lowest T = 2 state was located at an excitation energy of 27595 ± 20 keV, and has a width less than 35 keV.

(2) ¹²B: the lowest T = 2 state was found at an excitation energy of 12710 ± 20 keV. The width was determined to be less than 54 keV and the spin and parity were confirmed to be 0⁺. A second ¹²B state (or doublet) was observed at an excitation energy of 14860 ± 30 keV with a width (if the group corresponds to a single state) of 226 ± 30 keV.

(3) ²⁰F: the lowest T = 2 state was observed at an excitation of 6513 ± 5 keV; the spin and parity were confirmed to be 0⁺. A second state, tentatively identified as T = 2 from the level spacing, was located at 8210 ± 6 keV.

(4) ²⁸Al: the lowest T = 2 state was identified at an excitation of 5997 ± 6 keV; the spin and parity were confirmed to be 0⁺. A second state at an excitation energy of 7491 ± 11 keV is tentatively identified as T = 2, with a corresponding (tentative) spin and parity assignment J^π = 2⁺.

The results of the present work and the other known masses of T = 2 states and nuclei for 8 ≤ A ≤ 28 are summarized, and massequation coefficients have been extracted for these multiplets. These coefficients were compared with those from T = 1 multiplets, and then used to predict the mass and stability of each of the unobserved members of the T = 2 multiplets.

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.

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.

I. Proton magnetic resonance of polynucleotides and transfer RNA. II. Electron spin relaxation studies of manganese (II) complexes in acetonitrile

Part I. Proton Magnetic Resonance of Polynucleotides and Transfer RNA.

Proton magnetic resonance was used to follow the temperature dependent intramolecular stacking of the bases in the polynucleotides of adenine and cytosine. Analysis of the results on the basis of a two state stacked-unstacked model yielded values of -4.5 kcal/mole and -9.5 kcal/mole for the enthalpies of stacking in polyadenylic and polycytidylic acid, respectively.

The interaction of purine with these molecules was also studied by pmr. Analysis of these results and the comparison of the thermal unstacking of polynucleotides and short chain nucleotides indicates that the bases contained in stacks within the long chain poly nucleotides are, on the average, closer together than the bases contained in stacks in the short chain nucleotides.

Temperature and purine studies were also carried out with an aqueous solution of formylmethionine transfer ribonucleic acid. Comparison of these results with the results of similar experiments with the homopolynucleotides of adenine, cytosine and uracil indicate that the purine is probably intercalating into loop regions of the molecule.

The solvent denaturation of phenylalanine transfer ribonucleic acid was followed by pmr. In a solvent mixture containing 83 volume per cent dimethylsulf oxide and 17 per cent deuterium oxide, the tRNA molecule is rendered quite flexible. It is possible to resolve resonances of protons on the common bases and on certain modified bases.

Part II. Electron Spin Relaxation Studies of Manganese (II) Complexes in Acetonitrile.

The electron paramagnetic resonance spectra of three Mn⁺² complexes, [Mn(CH₃CN)₆]⁺², [MnCl₄]^-2, and [MnBr₄]^-2, in acetonitrile were studied in detail. The objective of this study was to relate changes in the effective spin Hamiltonian parameters and the resonance line widths to the structure of these molecular complexes as well as to dynamical processes in solution.

Of the three systems studied, the results obtained from the [Mn(CH₃CN)₆]⁺² system were the most straight-forward to interpret. Resonance broadening attributable to manganese spin-spin dipolar interactions was observed as the manganese concentration was increased.

In the [MnCl₄]^-2 system, solvent fluctuations and dynamical ion-pairing appear to be significant in determining electron spin relaxation.

In the [MnBr₄]^-2 system, solvent fluctuations, ion-pairing, and Br- ligand exchange provide the principal means of electron spin relaxation. It was also found that the spin relaxation in this system is dependent upon the field strength and is directly related to the manganese concentration. A relaxation theory based on a two state collisional model was developed to account for the observed behavior.

Spin wave resonance in ferromagnetic films

The objective of this investigation has been a theoretical and experimental understanding of ferromagnetic resonance phenomena in ferromagnetic thin films, and a consequent understanding of several important physical properties of these films. Significant results have been obtained by ferromagnetic resonance, hysteresis, torque magnetometer, He ion backscattering, and X-ray fluorescence measurements for nickel-iron alloy films.

Taking into account all relevant magnetic fields, including the applied, demagnetizing, effective anisotropy and exchange fields, the spin wave resonance condition applicable to the thin film geometry is presented. On the basis of the simple exchange interaction model it is concluded that the normal resonance modes of an ideal film are expected to be unpinned. The possibility of nonideality near the surface of a real film was considered by means of surface anisotropy field, inhomogeneity in demagnetizing field and inhomogeneity of magnetization models. Numerical results obtained for reasonable parameters in all cases show that they negligibly perturb the resonance fields and the higher order mode shapes from those of the unpinned modes of ideal films for thicknesses greater than 1000 Å. On the other hand for films thinner than 1000 Å the resonance field deviations can be significant even though the modes are very nearly unpinned. A previously unnoticed but important feature of all three models is that the interpretation of the first resonance mode as the uniform mode of an ideal film allows an accurate measurement of the average effective demagnetizing field over the film volume. Furthermore, it is demonstrated that it is possible to choose parameters which give indistinguishable predictions for all three models, making it difficult to uniquely ascertain the source of spin pinning in real films from resonance measurements alone.

Spin wave resonance measurements of 81% Ni-19% Fe coevaporated films 30 to 9000 Å thick, at frequencies from 1 to 8 GHz, at room temperature, and with the static magnetic field parallel and perpendicular to the film plane have been performed. A self-consistent analysis of the results for films thicker than 1000 Å, in which multiple excitations can be observed, shows for the first time that a unique value of exchange constant A can only be obtained by the use of unpinned mode assignments. This evidence and the resonance behavior of films thinner than 1000 Å strongly imply that the magnetization at the surfaces of permalloy films is very weakly pinned. However, resonance measurements alone cannot determine whether this pinning is due to a surface anisotropy, an inhomogeneous demagnetizing field or an inhomogeneous magnetization. The above analysis yields a value of 4πM=10,100 Oe and A = (1.03 ± .05) x 10^-6 erg/cm for this alloy. The ability to obtain a unique value of A suggests that spin wave resonance can be used to accurately characterize the exchange interaction in a ferromagnet.

In an effort to resolve the ambiguity of the source of pinning of the magnetization, a correlation of the ratio of magnetic moment and X-ray film thickness with the value of effective demagnetizing field 4πNM as determined from resonance, for films 45 to 300 Å has been performed. The remarkable agreement of both quantities and a comparison with the predictions of five distinct models, strongly imply that the thickness dependence of both quantities is related to a thickness dependent average saturation magnetization, which is far below 10,100 Oe for very thin films. However, a series of complementary experiments shows that this large decrease of average saturation magnetization cannot be simply explained by either oxidation or interdiffusion processes. It can only be satisfactorily explained by an intrinsic decrease of the average saturation magnetization for very thin films, an effect which cannot be justified by any simple physical considerations.

Recognizing that this decrease of average saturation magnetization could be due to an oxidation process, a correlation of resonance measurements, He ion backscattering, X-ray fluorescence and torque magnetometer measurements, for films 40 to 3500 Å thick has been performed. On basis of these measurements it is unambiguously established that the oxide layer on the surface of purposefully oxidized 81% Ni-19% Fe evaporated films is predominantly Fe-oxide, and that in the oxidation process Fe atoms are removed from the bulk of the film to depths of thousands of angstroms. Extrapolation of results for pure Fe films indicates that the oxide is most likely α-Fe₂O₃. These conclusions are in agreement with results from old metallurgical studies of high temperature oxidation of bulk Fe and Ni-Fe alloys. However, X-ray fluorescence results for films oxidized at room temperature, show that although the preferential oxidation of Fe also takes place in these films, the extent of this process is by far too small to explain the large variation of their average saturation magnetization with film thickness.