SYSTEMATIC DESIGN AND EVALUATION OF MULTIPLE-PULSE EXPERIMENTS IN NUCLEAR-MAGNETIC-RESONANCE SPECTROSCOPY USING A SEMICONTINUOUS BAKER-CAMPBELL-HAUSDORFF EXPANSION

We show that an explicit solution to a semi-continuous analog to the B aker-Campbell-Hausdorff (BCH) problem can be derived by an appropriate combination of the Magnus and BCH expansions. The resulting semi-cont inuous BCH (scBCH) expansion forms a valuable tool for solving the tim e-dependent Schrodinger equation for Hamiltonians with complicated, pi ecewise continuous time dependence. Such Hamiltonians are typical in m ultiple-pulse coherent spectroscopy. Using the scBCH expansion we deri ve a number of general formulas, including relations for permuted puls e sequences. These formulas simplify calculation of the effective Hami ltonian for advanced multiple-pulse experiments and allow for evaluati on of this to considerably higher order than is possible using the Mag nus expansion. This is important for the detailed analysis and systema tic design of multiple-pulse experiments which emphasize some interact ions while effectively suppressing others. The scBCH expansion is appl ied to problems of homonuclear dipolar decoupling in solid-state NMR a nd broadband heteronuclear decoupling in liquid-state NMR. Improved hi gh-order pulse sequences for on- and off-resonance decoupling an intro duced and existing recursive expansion strategies are evaluated within the presented theoretical framework. (C) 1998 American Institute of P hysics. [S0021-9606(98)01634-1].