Materials discovery searching variable space

Combinatorial chemistry differs from usual Monte Carlo simulations in that several simultaneous searches of the variable space are carried out. That is, in a typical combinatorial chemistry experiment, several samples, e.g., 10,000, are synthesized and screened for figure of merit at one time. With the results of this first round, a new set of samples can be synthesized and screened. This procedure can be repeated for several rounds, although current materials discovery experiments have not systematically exploited this feature. 

The technology for materials discovery is still in the developmental stage, and future progress can still be influenced by theoretical considerations. In this spirit, I assume that the composition and noncomposition variables of each sample can be changed independently, as in spatially addressable libraries (Akporiaye et al., 1998 Pirrung, 1997). This is significant, because it allows great flexibility in how the space can be searched with a limited number of experimental samples. 

Current experiments uniformly tend to perform a grid search on the composition and noncomposition variables. It is preferable, however, to choose the variables statistically from the allowed values. It is also possible to consider choosing the variables in a fashion that attempts to maximize the amount of information gained from the limited number of samples screened, via a quasi-random, low-discrepancy sequence (Niederreiter, 1992 Bratley et al., 1994). Such sequences attempt to eliminate the redundancy that naturally occurs when a space is searched statistically, and they have several favorable theoretical properties. An illustration of these three approaches to materials discovery library design is shown in Fig. 1. 

The space of composition and noncomposition variables to search in materials discovery experiments can be forbiddingly large. Yet, by using Monte Carlo methods, one can achieve an effective search with a limited number of experimental samples. 

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