Averaging Named Selections

To average or plot a structural quantity, the structural quantity must first be selected and named by the normal process for creating named selections (select the atoms and then use the menu item Select/Name Selection to give the selected atoms a name). Erom then on the Molecular Dynamics Averages dialog box will show these named selections as possible candidates to be averaged or plotted in addition to energetic quantities described above. 

To average a torsion, select the four atoms of the torsion, name the torsion tor, for example, and then select tor as the quantity to be averaged from the Molecular Dynamics Averages dialog box. 

In addition to being able to plot simple instantaneous values of a quantity x along a trajectory and reporting the average, x , HyperChem can also report information about the deviation of x from its average value. These RMS deviations may have particular significance in statistical mechanics or just represent the process of convergence of the trajectory values. 

If a request for a deviation in a quantity x is made, the instantaneous values that are plotted represent  

The i subscripts emphasize that the averaging is only up to the current step in the trajectory, not necessarily over the whole trajectory  

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Figure 10.58 a The Averaging dialog box files to average are selected by symbols, b The Averaging dialog box files to average are selected by names. 

These results provide clear evidence for the existence of selective heating effects in MAOS involving heterogeneous mixtures. It should be stressed that the standard methods for determining the temperature in microwave-heated reactions, namely with an IR pyrometer from the outside of the reaction vessel, or with a fiber-optic probe on the inside, would only allow measurement of the average bulk temperature of the solvent, not the true reaction temperature on the surface of the solid reagent. 

For the description of a solution of alanine in water two models were compared and combined with one another (79), namely the continuum model approach and the cluster ansatz approach (148,149). In the cluster approach snapshots along a trajectory are harvested and subsequent quantum chemical analysis is carried out. In order to learn more about the structure and the effects of the solvent shell, the molecular dipole moments were computed. To harvest a trajectory and for comparison AIMD (here CPMD) simulations were carried out (79). The calculations contained one alanine molecule dissolved in 60 water molecules. The average dipole moments for alanine and water were derived by means of maximally localized Wannier functions (MLWF) (67-72). For the water molecules different solvent shells were selected according to the three radial pair distributions between water and the functional groups. An overview about the findings is given in Tables II and III. 

Statistical thermodynamics gives us the recipes to perform this average. The most appropriate Gibbsian ensemble for our problem is the canonical one (namely the isochoric-isothermal ensemble N,V,T). We remark, in passing, that other ensembles such as the grand canonical one have to be selected for other solvation problems). To determine the partition function necessary to compute the thermodynamic properties of the system, and in particular the solvation energy of M which we are now interested in, of a computer simulation is necessary [1],... 

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