Prediction of Inorganic Compounds: Experiences and Perspectives
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eir reliability when new data do not easily fit within the framework outlined by the classification rules. An ideal classification scheme must be adaptable to new phenomena, have a flexible structure, and be useful for recognizing new properties. Such a classification scheme will not restrict itself to the narrow boundaries of two-dimensional criteria (two-parameter planes). The search for multidimensional criteria (classification rules) could work with the aid of computer learning techniques in conjunction with databases, e.g., crystallographic, phase diagram, and physical properties. In principle, there are three ways to predict new inorganic compounds and forecast their intrinsic compound properties, based on the knowledge of their constituent component properties: • quantum-mechanical calculations, • two-dimensional criteria (classification rules) found by semi-empirical approaches, and • multidimensional criteria (classification rules) found by computer learning techniques (computational methods for acquiring new knowledge, new skills, and new ways to organize existing knowledge). It should be emphasized that, until recently, the quantum mechanical calculations have failed to bring about a single prediction of new compounds that would be valuable to inorganic materials science. This situation will not change much in the near future. The two-dimensional criteria approach, however, is more efficient, but, in my opinion, not sufficiently flexible and comprehensive. The multidimensional cri-
teria approach (cybernetic) is more suitable for a priori prediction of inorganic compounds. The first experiments using computer learning methods to search for multidimensional criteria for the formation of the binary phases7 have been productive.
Concepts of the Cybernetic Approach The advantages of using computer learning procedures to search for multidimensional criteria are apparent. They consist of (1) analyses of large databases and (2) computer learning methods to locate many and complex criteria. Locating and analyzing such criteria is a computational task. For example, let a certain phenomenon be described by N properties X\,x^..., xH, each of which has k discrete values (Xif, i = 1, 2..., N; j; = 1, 2..., k). If we assume that the formation of a certain type of the crystal structure of a given class of compounds depends on the properties of its constituent chemical elements, then the traditional way of representing the semi-empirical, two-dimensional criteria can be reduced to a Boolean expression that takes the form (x12 & X34) V (xn & Xr, & x32) & NOT (X u & X25 & X37) V (X lk & Xj, &
Xm),
(1)
where x,j is the magnitude of the interval of the change of i properties or algebraic functions of these properties; and &, V, and NOT are respectively the symbols for the conjunction, disjunction, and negation operators. In the case of a semi-empirical analysis of the information, due to human limitations, the number of the simple conjunctions in Expression 1 does not exceed five or six, each conjunction having not more
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