A new general technique for the investigation of exchange processes in molecular systems is proposed and demonstrated. Applications comprise the study of chemical exchange, of magnetization transfer by inter‐ and intramolecular relaxation in liquids, and of spin diffusion and cross‐relaxation processes in solids.

Investigation of exchange processes by two‐dimensional NMR spectroscopy

In this Account we have compiled a list of reliable bond energies that are based on a set of critically evaluated experiments. A brief description of the three most important experimental techniques for measuring bond energies is provided. We demonstrate how these experimental data can be applied to yield the heats of formation of organic radicals and the bond enthalpies of more than 100 representative organic molecules.

Bond Dissociation Energies of Organic Molecules

The NMR signals of isotopically or chemically dilute nuclear spins S in solids can be enhanced by repeatedly transferring polarization from a more abundant species I of high abundance (usually protons) to which they are coupled. The gain in power sensitivity as compared with conventional observation of the rare spins approaches NII(I+1)γI2/NSS(S+1)γS2, or ∼ 103 for S = 13C, I = 1H in organic solids. The transfer of polarization is accomplished by any of a number of double resonance methods. High‐frequency resolution of the S ‐spin signal is obtained by decoupling of the abundant spins. The experimental requirements of the technique are discussed and a brief comparison of its sensitivity with other procedures is made. Representative applications and experimental results are mentioned.

Proton‐enhanced NMR of dilute spins in solids

About Dendrimers: Structure, Physical Properties, and Applications

(b) Write out the equations for the time dependence of ρ11, ρ22, ρ12 and ρ21 assuming that a light field interaction V = -μ12Ee iωt + c.c. couples only levels |1> and |2>, and that the excited levels exhibit spontaneous decay. (8 marks) (c) Under steady-state conditions, find the ratio of populations in states |2> and |3>. (3 marks) (d) Find the slowly varying amplitude ̃ ρ 12 of the polarization ρ12 = ̃ ρ 12e iωt . (6 marks) (e) In the limiting case that no decay is possible from intermediate level |3>, what is the ground state population ρ11(∞)? (2 marks) 2. (15 marks total) In a 2-level atom system subjected to a strong field, dressed states are created in the form |D1(n)> = sin θ |1,n> + cos θ |2,n-1> |D2(n)> = cos θ |1,n> sin θ |2,n-1>

The Quantum Theory of Light

Diffusion ordered nuclear magnetic resonance spectroscopy: principles and applications

An Improved Diffusion-Ordered Spectroscopy Experiment Incorporating Bipolar-Gradient Pulses

diamide’s behavior on the basis of spectroscopic data should be more straightforward than for 1. Previously reported variabletemperature IH NMR measurements (AG(NH)/A.T) indicated that the intramolecularly hydrogen-bonded and non-hydrogenbonded6 states of 2 are of very similar enthalpy in CD2C12.2a In contrast, when an attempt was made to account for solvation by including three CH2C12 molecules in a “supermolecule” calculation, AM1 predicted the minimum energy intramolecularly hydrogen-bonded conformation of 2 to be 1.9 kcal/mol more enthalpically favorable than the minimum energy non-hydrogen-bonded c~nformat ion .~ In order to provide a more quantitative comparison with the calculations, we have now carried out an IR-based van’t Hoff analysis of the intramolecular hydrogen bonding equilibrium occurring in a 1 mM CH2C12 solution of 2 over the temperature range -69 to 23 OC. Figure 1 shows the N-H stretch region of the IR spectra obtained at high and low temperatures. Both hydrogen-bonded (3340-50 cm-l) and non hydrogen-bonded6 (3443-8 cm-I) bands are observed at each temperature. No hydrogen-bonded N-H stretch band can be detected at any temperature for a 1 mM sample of N-methylcyclohexylactamide (3) in CH,Cl,; therefore, we used this compound to estimate the extinction coefficient of the non-hydrogen-bonded N-H stretch band of 2 as a function of temperature. van’t Hoff analysis (intramolecularly hydrogen-bonded vs non-hydrogen-bonded states; each “state” comprises a set of conformations) indicated that the internally hydrogen-bonded state of 2 is 0.25 f 0.06 kcal/mol less enthalpically favorable and 0.67 f 0.48 eu more entropically favorable than the non-hydrogen-bonded state.’ Since CH2C12 is relatively nonpolar, it is interesting that the internally hydrogen-bonded and non-hydrogen-bonded states of 2 have very similar enthalpies, with the state containing the N-H-O=C interaction slightly less enthalpically favorable. An ideal amide-amide hydrogen bond should be enthalpically superior to any interaction between the amide group and the solvent. The enthalpic similarity of the internally hydrogen-bonded and non-hydrogen-bonded states of 2 may result from at least two factors: (1) the geometry of the seven-membered-ring hydrogen bond is not optimal for the amide-amide interaction (e.g., a nonlinear N-H-0 angle is unavoidable); (2) closure of the hydrogen-bonded ring may involve the development of torsional strain and/or other enthalpically unfavorable interactions. The entropic similarity between the internally hydrogen-bonded and non-hydrogen-bonded states may arise from the fact that these two states enjoy similar degrees of conformational mobility2c and/or from desolvation associated with intramolecular hydrogen bond formation.* (The breadth and asymmetry of the hydrogen-bonded N-H stretch band in Figure 1 is consistent with the existence of multiple hydrogen-bonded ring conformations.) Why does AM1 overestimate the enthalpic favorability of the intramolecularly hydrogen-bonded state of 2? One potential source of error is indicated by the comparison between ab initio and AM1 results for the hydrogen-bonded formamide dimer reported by Novoa and Whangboe3 When interaction energy was examined as a function of the N-H--0 angle, the ab initio calculations predicted that the hydrogen bond energy becomes increasingly unfavorable as the angle decreases below 150°.9 For an N-H-0 angle of 120’ (the smallest angle examined), the ab initio interaction energy was 1.5 kcal/mol less favorable than in the

Diffusion-ordered two-dimensional nuclear magnetic resonance spectroscopy

A PFG NMR experiment for accurate diffusion and flow studies in the presence of eddy currents

Diffusion-ordered 2D NMR (DOSY) experiments have been developed for the analysis of mixtures. These experiments yield conventional chemical shift spectra in one dimension and spectra of diffusion coefficients (or approximate molecular radii) in the other. At the heart of this method are the analysis and display of data obtained with pulsed field gradient (PFG) NMR techniques. At each point on the chemical shift axis, a set of intensities is obtained as a function of K 2 (K=γgδ, whore γ is the magnetogyric ratio and g and δ are the gradient pulse amplitude and duration, respectively)

Charles S. Johnson

Papers

Diffusion ordered nuclear magnetic resonance spectroscopy: principles and applications

An Improved Diffusion-Ordered Spectroscopy Experiment Incorporating Bipolar-Gradient Pulses

Diffusion-ordered two-dimensional nuclear magnetic resonance spectroscopy

A PFG NMR experiment for accurate diffusion and flow studies in the presence of eddy currents

Resolution of discrete and continuous molecular size distributions by means of diffusion-ordered 2D NMR spectroscopy