Other Derivative-Based Dynamics Schemes

Multiparticle collision dynamics describes the interactions in a many-body system in terms of effective collisions that occur at discrete time intervals. Although the dynamics is a simplified representation of real dynamics, it conserves mass, momentum, and energy and preserves phase space volumes. Consequently, it retains many of the basic characteristics of classical Newtonian dynamics. The statistical mechanical basis of multiparticle collision dynamics is well established. Starting with the specification of the dynamics and the collision model, one may verify its dynamical properties, derive macroscopic laws, and, perhaps most importantly, obtain expressions for the transport coefficients. These features distinguish MPC dynamics from a number of other mesoscopic schemes. In order to describe solute motion in solution, MPC dynamics may be combined with molecular dynamics to construct hybrid schemes that can be used to explore a variety of phenomena. The fact that hydrodynamic interactions are properly accounted for in hybrid MPC-MD dynamics makes it a useful tool for the investigation of polymer and colloid dynamics. Since it is a particle-based scheme it incorporates fluctuations so that the reactive and nonreactive dynamics in small systems where such effects are important can be studied. 

Crystal structures of Ln complexes of DTPA and DOTA derivatives show that Ln +-bound diethylenetriamine moieties in these complexes always occur either in the 88 or in the X.X. conformation (Scheme 5.10). In these complexes, the steric interactions are always minimized. Upon coordinated by a metal ion, the central nitrogen atom is chiral. The inversion is precluded if the nitrogen is coordinated to the metal. A common feature of cyclen-based macrocyclic Gd (and other Ln ) is the formation of various isomers which display dynamic behavior (interconvert/exchange) on the NMR time scale in aqueous solution [174,175]. However, the long electronic relaxation time of Gd ion prevents the observation of the NMR spectra of its complexes and its solution structure has been inferred from the H and NMR spectra of its related Ln complexes. 

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