Gradient duration times, calculation

Hie change is calculated using the Smoluchowski equation (8.15). For the instantaneous deformation, the velodty gradient = dsapldt (dr being the duration time of the deformation) dominates the time evolution of W, so that... 

After a time r, a 180° RF pulse reverses the spin precession. A second gradient pulse of equal duration 8 and magnitude g follows to tag the spins in the same way. If the spins have not changed their position in the sample, the effects of the two applied gradient pulses compensate each other, and aU spins refocus. If the spins have moved due to self-diffusion, the effects of the gradient pulses do not compensate and the echo-amplitude is reduced. The decrease of the amplitude A with the applied gradient is proportional to the movement of the spins and is used to calculate the self-diffusion coefficient. 

Recently, semiempirical molecular-orbital methods have been combined with force-field-based molecular-dynamics techniques into hybrid schemes The interesting part of the system is described by quantum chemistry, while the surroundings are treated by a classical force field. These hybrid schemes allow calculation of the energy and gradients fast enough for molecular dynamics simulations of hundreds of picoseconds (10s time steps) duration to be feasible. This provides sufficient sampling for the calculation of many statistical-mechanical properties. A short synopsis is given of work carried out at ETH Zurich on conformational equilibria in solution, reactions in solution and enzyme reactions. 

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