C. A. Reilly

Analysis of Complex NMR Spectra. An Iterative Method

A method for analyzing complex NMR spectra, which utilizes an iterative technique on the spin energy levels, is described. We show how the experimental energy levels and their errors are derived from the observed spectrum and the assignment of the various transitions. We discuss several techniques and methods that are helpful in obtaining this assignment. Sum rules for the energy levels and the intensities of the transitions, useful in the analysis, are also pointed out.With the iterative procedure, which uses the eigenvectors of an approximate Hamiltonian, we then calculate the changes in the chemical shielding constants and the spin—spin coupling constants necessary to adjust the approximate energy levels toward the experimental ones. The probable errors in the derived magnetic parameters are also readily determined.

Analysis of Spin‐Spin Multiplets in Nuclear Magnetic Resonance Spectra

A systematic procedure is developed for the analysis of the spin‐spin multiplets that are observed in the high‐resolution NMR (nuclear magnetic resonance) spectra of liquids. It is shown how the symmetry properties of nuclear spin functions can be used to simplify the interpretation of NMR multiplets in terms of the empirical quantities, chemical shifts, and spin‐spin coupling constants. It is also pointed out that when NMR multiplets have been properly interpreted in terms of these empirical quantities, it is then possible to predict theoretically relative intensities of multiplets to the same degree of precision as that involved in the measurement of multiplet frequency separations.As an example the multiplet splittings of the H1 and F19 resonances in 1,1‐difluoroethylene are analyzed using the procedure proposed in the present paper.

Assignment of NMR Spectra with the Aid of Double‐Quantum Transitions

The analysis of complex nuclear magnetic resonance spectra usually requires the assignment of the observed transition to an energy‐level diagram. It is shown that double‐quantum transitions can be used to determine such an assignment. Small frequency shifts of the double‐quantum transitions have been observed and their dependence upon the strength of the applied radio‐frequency field measured and compared with theory. The double‐quantum method is compared to the double resonance method in making an energy‐level assignment using the 60‐Mc/sec spectrum of trivinylphosphine for the purposes of illustration. The analysis has been completed by an algebraic method and by iteration on a computer, and the results checked by recording the 100‐Mc/sec proton spectrum and the 19‐Mc/sec P31 spectrum. The three proton—proton couplings and the three P31 proton couplings all have the same sign.

Ionization of Strong Electrolytes. III. Proton Magnetic Resonance in Nitric, Perchloric, and Hydrochloric Acids

Since the proton magnetic resonance shift in an acid is a colligative property, the derivation of degrees of dissociation requires assumptions which cannot be tested directly. Results derived from measurements of this resonance shift in nitric acid and in perchloric acids are in sufficient agreement with earlier results obtained from a specific property (intensity of Raman lines) to confirm the interpretation of the shift. The value 22 has been found for the thermodynamic dissociation constant of nitric acid, the value 38 for perchloric acid.The association of nitric acid in aqueous solutions containing more than 50 mole percent of acid is reflected in the shift. Differences in the limiting slopes of the resonance shift of the proton in various acids at high dilution are interpreted as due to different influences of the anions on the association of water.

Nuclear Magnetic Resonance Spectra of Some Simple Epoxides

High resolution NMR spectra of four epoxides have been observed at 40 Mcps and analyzed. These epoxides are of the type [Complex chemical formula] where R is a phenyl group (styrene oxide), a cyanide group (glycidonitrile), an acetyl group (1,2‐epoxy‐3‐butanone), and a carboxyl group (glycidic acid). For each molecule the spin‐spin coupling constants and nuclear magnetic screening parameters for the A, B, and C protons were derived from the experimentally determined energy levels. The method for obtaining numerical values for the energy levels from the spectra is described fully. ABK and AA′K approximations as well as an iterative ABC method of solution are described and illustrated.Corresponding coupling constants are found to be about the same in all four molecules with JAB=5.8±0.5 cps, JAC=2.2±0.5 cps and JBC=4.6±0.5 cps. However, the variations from molecule to molecule are considerably greater than the estimated precision of ±0.05 cps. The ABX approximation is shown to be inadequate either for the pr...

Ionization of Strong Electrolytes. VIII. Temperature Coefficient of Dissociation of Strong Acids by Proton Magnetic Resonance

The proton magnetic resonance of nitric and perchloric acid solutions over the entire concentration range has been used for determining the dissociation constants at 0, 25, and 70°C. Excellent agreement with earlier data for nitric acid derived from Raman spectra was obtained.

NMR Spectra of Glycidaldehyde

The NMR spectra of glycidaldehyde were measured at 40 and 60 Mc/sec. [Complex chemical formula] These complicated spectra of four interacting protons were analyzed by two methods: the ABKY approximation and the iterated ABCD solution. The various mathematical techniques developed should prove useful in the analyses of other complicated spin resonance spectra.The following spin‐spin coupling constants, Jij in cycles per second and chemical shifts, δi in parts per million (relative to tetramethylsilane) were found: JABJACJBCJADJBDJCDδAδBδCδD40 Mc/sec5.542.044.90−0.03−0.326.363.0963.1583.3568.92260 Mc/sec5.542.094.87+0.03−0.316.243.0983.1663.3568.922 The first three coupling constants are very close in magnitude to those obtained in other epoxides (in most cases to within 0.5 cps).The magnitude of the coupling constant between the aldehyde proton (D) and the adjacent proton (C) indicates that the D proton of the aldehyde group is probably on a time average, mainly in a plane perpendicular to the epoxide ring...

NMR Spectra of Some Halogenated Propenes

The 40‐Mc/sec nuclear magnetic resonance (NMR) spectra of CF3CF=CF2, cis and trans isomers of CF3CCl=CFCl, and CF3CCl=CF2 have been analyzed in terms of the NMR parameters of the molecules; i.e., the magnetic shielding constants of the various fluorine nuclei and the spin‐spin coupling constants between them.The spectrum of perfluoropropylene, CF3CF=CF2, has been analyzed adequately by a first‐order perturbation treatment. The spectrum of each of the isomers of CF3CCl=CFCl has been analyzed exactly as an AB3 system of spins by the use of the trace relations only. In a previous analysis of the cis‐isomer, a small signal from the trans‐isomer was not identified. This small signal has now been proved to arise from the trans‐isomer. The spectrum of CF3CCl=CF2 has been analyzed by an interative scheme on an electronic computer. Here the nuclei were treated as an ABC3 system of spins.The various magnetic parameters determined by these analyses have been compared with the molecular structures and have been brief...

Ionization of Strong Electrolytes. V. Proton Magnetic Resonance in Sulfuric Acid

The proton magnetic resonance shifts in solutions of sulfuric acid have been measured and degrees of dissociation calculated. The results are consistent with information derived from the intensities of Raman lines.

Ionization of Strong Electrolytes. IV. Nuclear Magnetic Resonance and Dissociation of Trifluoroacetic Acid

Proton and fluorine magnetic resonance of trifluoroacetic acid in water reflects the influence of electrolytic dissociation below a mole fraction 0.5 and of hydration above 0.5. The dissociation constant is estimated to be 1.8.