Relative importance of ensemble

The ability of bimetallic systems to enhance various reactions, by increasing the activity, selectivity, or both, has produced a great deal of interest in understanding the different roles and relative importance of ensemble and electronic effects. Deposition of one metal onto the single-crystal face of another provides an advantage by which the electronic and chemical properties of a well-defined bimetallic surface can be correlated with the atomic structure.5 22 23 Besenbacher et al.24 used this method to study steam reforming (the reverse of the CO methanation process) on Ni(l 11) surfaces... 

The studies reviewed here are part of a continuing effort (4-10) to identify those properties of bimetallic systems which can be related to their superior catalytic properties. A pivotal question to be addressed of bimetallic systems (and of surface impurities in general) is the relative importance of ensemble (steric or local) versus electronic (nonlocal or extended) effects in the modification of catalytic properties. In gathering information to address this question it has been advantageous to simplify the problem by utilizing models of a bimetallic catalyst such as the deposition of metals on single- crystal substrates in the clean environment familiar to surface science. 

The relative importance of fluctuations, e.g. in the membrane area, as is possible in a (N, p, y, T) ensemble, becomes larger when the system that is under investigation is smaller. For macroscopic systems, the fluctuations in such quantities are negligible, but, for some of the modelling techniques that are restricted to small systems, one cannot avoid dealing with it. Of course, for a (N, p, y, T) ensemble in which both the volume and the surface area are allowed... 

Considerable progress has been made in accumulating information on the electronic structure of metals and alloys, on some aspects of the structure of hydrocarbon adsorption complexes, etc. Also, information on the relative importance of the electronic structure effects of alloying—as contrasted to the geometric, ensemble size effects—has grown appreciably. 

Measurements of the infrared spectra of carbon monoxide on supported palladium and Pd-Ag atoms (75a) shed light on the relative importance of the ensemble and ligand effects. Three CO absorption bands were observed on palladium and its alloys at 2060,1960, and 1920 cm-1. 

The most important feature of the information in dipolar couplings is that it is independent of distance. The data can be envisioned as reflecting the relative orientation of pairs of bond vectors, with the intervening distance having no effect (Meiler et al., 2000). Thus dipolar couplings can potentially provide a method for characterizing the structure of denatured proteins, provided that the denatured state ensemble of conformations retains several levels of nonrandomness. 

To model the interaction between CSP and analyte one must account for 1) the shapes of the two molecules in the binary complex, 2) the relative position of the two molecules, i.e. the analyte should be at its proper binding site on or around the CSP, and 3) the orientation of the two molecules with respect to each other. This is just a simple way of saying that some sort of ensemble average is needed wherein a molecular dynamics protocol must ensure adequate sampling of phase space, or, if using a Monte Carlo strategy, a sufficient number of important configurations must be sampled. 

However, there is no unique or optimal measure of accuracy. If MD simulations are performed, the main interest lies in errors connected with the force, while in Monte Carlo (MC) simulations one is concerned with accurate energies. In the simulation of ensemble averages it is the global accuracy, measured, e.g., by root-mean-square quantities, which is important, hi the simulation of rare events local accuracy and maximal errors are relevant as well. Errors in the force can be due to their magnitude or due to their direction. And finally, one might be interested in absolute or relative errors. 

---