Step dynamics

A variety of techniques have been introduced to increase the time step in molecular dynamics simulations in an attempt to surmount the strict time step limits in MD simulations so that long time scale simulations can be routinely undertaken. One such technique is to solve the equations of motion in the internal degree of freedom, so that bond stretching and angle bending can be treated as rigid. This technique is discussed in Chapter 6 of this book. Herein, a brief overview is presented of two approaches, constrained dynamics and multiple time step dynamics. 

T. Ihle, C. Misbah, O. Pierre-Louis. Equilibrium step dynamics on vicinal surfaces revisited. Phvs Rev B 55 2289, 1998. 

A. Pimpinelli, J. Villain, D. E. Wolf, J. J. Metois, J. C. Heyraud, I. Elkinani, G. Uimin. Equilibrium step dynamics on vicinal surfaces. Surf Sci 295 143, 1993. 

Thus, the isotropic peripheral PCA effectively describes the parallel 2-step dynamics (following the alternating updating of odd- and even- indexed sites) of the following onedimensional Isiug model ... 

Amide Bond Formation as the Final Step-Dynamic Kinetic Resolution... 

Similar schemes to the above can be used in molecular dynamics simulations in other ensembles such as those at constant temperature or constant pressure (see Frenkel and Smit, and Allen and Tildesley (Further reading)). A molecular dynamics simulation is computationally much more intensive than an energy minimization. Typically with modern computers the real time sampled in a simulation run for large cells is of the order of nanoseconds (106 time steps). Dynamical processes operating on longer time-scales will thus not be revealed. 

The titration process has been automated so that batches of samples can be titrated non-manually and the data processed and reported via printouts and screens. One such instrument is the Metrohm 670 titroprocessor. This incorporates a built-in control unit and sample changer so that up to nine samples can be automatically titrated. The 670 titroprocessor offers incremental titrations with variable or constant-volume steps (dynamic or monotonic titration). The measured value transfer in these titrations is either drift controlled (equilibrium titration) or effected after a fixed waiting time pK determinations and fixed end points (e.g. for specified standard procedures) are naturally included. End-point titrations can also be carried out. 

It is interesting to note that there are cases in which the step dynamics is non-universal. We illustrate this point through use of the probability distribution... 

CONDUCTIVITY OF C60 FULLERENE CRYSTALS UNDER MULTI-STEP DYNAMIC COMPRESSION UP TO 300 KBAR... 

Figure 2.10 In situ STM image showing the frazzled appearance of a monatomic step on Ag(lll) substrate 2.22). SystemAg(lll)/10 M CuS04 + 5 x lO M H2SO4at =60 mVvs. SCEandT=298 K. Reprinted from Surface Science Letters, Vol. 327, M. Dietterle, T. Will, D.M. Kolb, Step dynamics at the Ag(lll)-electrolyte interface, p. L495,1995, with kind permission of Elsevier Science.

Giesen M, Dieluweit S (2004) Step dynamics and step-step interactions on the chiral Cu(5, 8, 90) surface. J Mol Catal A Chem 216 263 Image provided courtesy of C. E. Sykes. 

By adapting the proach of Guth and Grosch (6), using an excess of anhydrous sodium sulfate to bind water mentioned above, we have developed a one step dynamic headspace isolation method which gives practical recoveries of Furaneol and Mdtol for quantitative analysis. This new approach (see Figure 1) for the isolation of Furaneol is described below. 

Gratz AJ, Hillner PE, Hansma PK (1993) Step dynamics and spiral growth on calcite. Geochim Cosmochim Acta 57 491-495... 

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