Designing optimal universal pulses using second-order, large-scale, non-linear optimization.

Recently, RF pulse design using first-order and quasi-second-order pulses has been actively investigated. We present a full second-order design method capable of incorporating relaxation, inhomogeneity in B(0) and B(1). Our model is formulated as a generic optimization problem making it easy to incorporate diverse pulse sequence features.

Exact solution of the CPMG pulse sequence with phase variation down the echo train: application to Râ‚‚ measurements.

An implicit exact algebraic solution of CPMG experiments is presented and applied to fit experiments. Approximate solutions are also employed to explore oscillations and effective decay rates of CPMG experiments. The simplest algebraic approximate solution has illustrated that measured intensities will oscillate in the conventional CPMG experiments and that using even echoes can suppress errors of measurements of Râ‚‚ due to the imperfection of high-power pulses.

Exact solution to the Bloch equations and application to the Hahn echo.

The exact symbolic solution of the Bloch equations is given in the Lagrange form and illustrated with R2 experiments using a Hahn echo. Two different methods are also applied to approximately solve the Bloch equations, we find that splittings with effective-field interpretations are very substantially better than other approximations by comparing the errors. Estimates of transverse relaxation, R2, from Hahn echos are effected by frequency offset and field inhomogeneity.

Problems, artifacts and solutions in the INADEQUATE NMR experiment.

The INADEQUATE experiment can provide unequalled, detailed information about the carbon skeleton of an organic molecule. However, it also has the reputation of requiring unreasonable amounts of sample. Modern spectrometers and probes have mitigated this problem, and it is now possible to get good structural data on a few milligrams of a typical organic small molecule.

Simulation of steady-state NMR of coupled systems using Liouville space and computer algebra methods.

A series of repeated pulses and delays applied to a spin system generates a steady state. This is relatively easy to calculate for a single spin, but coupled systems present real challenges. We have used Maple, a computer algebra program to calculate one- and two-spin symbolically, and larger systems numerically.