R-category

Since an R-matrix represents an electron or bond redistribution pattern, it can represent not only one specific reaction but a general class of reactions. Because of the properties of R-matrices, they may be grouped in several classes. Brandt, et al (28) have defined an R-category as an equivalence class of chemical reactions which have in common the same electron relocation... 

An irreducible R-matrix is one that does not have a row/column containing all zeroes. Any two chemical reactions which are represented by the same irreducible R-matrix belong to the same R-category. The Brandt categories are characterized by R-matri-ces which may have up to three off-diagonal pairs of positive and negative entries. 

Using these conclusions, we have classified irreducible R-matrices in restricted chemistry into R-categories. The terminology is so chosen as to conform with that of Brandt, et. al. 

The nomenclature for describing an R-category is given by RMMNi, where... 

There are certain existence requirements for an atom set of an R-category. We will refer to valency of an atom, as the number of its designated bonds participating in the R-matrix. Other bonds associated with the atom but not taking part in the reaction are of no concern to us. 

If we enterchange columns and rows C with D but not the labels we will get another product set and hence another R-matrix. Both of these R-matrices, however, belong to the same R-category R224. 

Generally, an R-matrix does not only fit one, but many BE-matrices. Accordingly, an R-matrix does not only represent an individual chemical reaction, but a whole category of reactions which have in common the electron relocation pattern represented by the R-matrix ). An R-category is an equivalence class of chemical reactiois which have in common the same electron relocation pattern and certain features of the participating bond systems. The row/column permutation equivalence of BE-matrices implies that R-matrices represent the same reactions when they are interconverted by row/column... 

R-matrices belong to the same R-category if they are interconverted by reduction or expansion, i.e. by removal or attachment of rows and columns containing only zeros. 

Any two R-matrices R and R belong to the same R-category if there exists an R-matrix R which can be transformed int.o R according to... 

Any two chemical reactions which are represented by the same irreducible R-matrix belong to the same R-category. 

The following reactions (-> ) or their retro-reactions ( ) respectively, are examples for the R-categories listed in Table 1. 

Any two reactions belong to the same RA-type, if they belong to the same R-category, and if their non-zero entries refer to the same components of an associated vector of atoms. 

This hierarchic classification of chemical reactions by their R- and BE-matrices may not only serve as a means of formal ordering of reactions and as a basis of documentation systems, but can also serve as a device in the systematic computer-assisted deductive search for new chemical reactions, by an algorithm which finds all of the mathematically and chemically fitting pairs (B, E) of BE-matrices for a representation R-matrix of an R-category. 

Rather than taking the complete set of all mathematically possible reaction matrices a selection of only three R-matrices is contained in the program. These three R-categories include the majority of all known synthetic reactions and it is believed that most of the reactions which will be discovered in the future will also fall in these three R-categories. So the advantages of the... 

In such cases query entries are processed through reaction generators. These may be the complete set of R-categories, but of course a subset of those can be selected if the application justifies it. Output of the reaction generators is then checked against structure files and matches are output to the user. 

A hierarchy is thereby achieved, that will lead to a reaction file structure, where each entry is referenced through the various levels of specificity up to the R-categories. Queries can be entered at any degree of generality. 

It is worth remarking that the different R-categories govern widely different populations of known reactions. One obvious example is the simple four center reaction of the kind A-B + C-D = A-C + B-D, which is incidentally represented by the simplest R-matrix in closed shell chemistry that has a zero diagonal. 

I" — ildentified benefit or risk category Identified benefit/ risk outcome t [Potential outcomt. or B/R category ... 

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