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COMMENT ⊗ VALID 00005 PAGES C REC PAGE DESCRIPTION C00001 00001 C00003 00002 α|ααMCGRK25αM1FIX25α C00010 00003 APPLICATIONS OF ARTIFICIAL INTELLIGENCE FOR CHEMICAL INFERENCE - XI C00015 00004 APPLICATIONS OF ARTIFICIAL INTELLIGENCE FOR CHEMICAL INFERENCE - XI C00019 00005 APPLICATIONS OF ARTIFICIAL INTELLIGENCE FOR CHEMICAL INFERENCE - XI C00041 ENDMK C⊗; α|ααMCGRK25;αM1FIX25;α; APPLICATIONS OF ARTIFICIAL INTELLIGENCE FOR CHEMICAL INFERENCE - XI Appendix C. Calculation of Loops. There are several rules which must be followed in consideration of loop assignment to ring-superatoms. The minimum (MINLOOPS) and maximum (MAXLOOPS) numbers of loops for a given valence list are designated by equations 5 and 6. n MINLOOPS = max{0,a +1/2(2j - αFCSαF1ja α←.α→p)} (5) 2 max i=2α←pα→.j n MAXLOOPS = min{a , αFCSαF1((i-2)/2)aα←.α→p } (6) 2 j=4α←pα→. MINLOOPS = minimum number of loops MAXLOOPS = maximum number of loops a = number of secondary nodes in degree list 2 j = degree of highest degree item in degree list max j = degree n = highest degree in list a = number of nodes with degree j. j The form of the equations results from the following considerations: 1) Only secondary nodes may be assigned to loops. Nodes of higher degree will always be in the non-loop portion of the ring-superatom. 2) A loop, by definition, must be attached by two bonds to a single node in the resulting ring-superatom. The loop cannot be attached through the free valences. Thus the degree list must possess a sufficient number of quaternary or higher degree nodes to support the loops(s). 3) Each loop must have at least one secondary node, which is the reason MAXLOOPS is restricted to at most the maximum number of secondary nodes in the degree list (Equation 6). 4) There must be available one unsaturation for each loop (this is implicit in the calculation of MINLOOPS and MAXLOOPS) as each loop effectively forms a new ring. 27 APPLICATIONS OF ARTIFICIAL INTELLIGENCE FOR CHEMICAL INFERENCE - XI Partitioning_of_Secondary_Nodes. For each of the possible numbers of loops (0,1, ...) the secondary nodes are removed from the degree list and partitioned among the loops, remembering that the loops are at present indistinguishable and each loop must receive at least one secondary node. In the example (Fig. 2), starting with the degree list (4,0,2), there are three ways of partitioning the four secondary nodes among two loops and the remaining non-looped portion. Removal of the four secondary nodes from the degree list and assignment of two, three or four of them to two loops results in the list specified in Figure 2 as the "reduced degree list". Specification of two loops transforms the two quaternary nodes in the degree list into two secondary nodes. This results from the fact that two valences of a quaternary or higher degree node must be used to support each loop. These are "special" secondary nodes, however, as these particular nodes are the ones which will be connected to loops as the structure is built up. Thus, in the example, any secondary nodes which are found in the reduced degree list will have a loop attached in a subsequent step. The degree list (4,0,2) thus becomes the reduced degree list (2,0,0) in the partition specifying two loops (Fig. 2). Similarly, the partition of one loop for the degree list (3,2,1) results in a reduced degree list of (1,2,0) with the three original secondary nodes partitioned among loop and non-loop portions (Figure 2). If, after the first, second, ... nth loop partition, there remain one or more quaternary or higher degree nodes in the reduced degree list, the list must be tested again for the possibility of additional loops. Each loop partition will generate a new set of structures. The second pass will yield those structures possessing loops on loops, and so forth. One such superatom which would be generated in this manner from a composition of (at least) C U is 15. 6 5 c=c=c=c=c=c 15 The partition of (4,0,2) including one loop results in each case in a reduced degree list (1,0,1). This list is disallowed in the subsequent step, as the vertex-graph for one quaternary node is a daisy (Table II), which requires a minimum of two secondary nodes with which to label the daisy loops (a minimum of one secondary node in the reduced degree list for each loop of the daisy). 28 APPLICATIONS OF ARTIFICIAL INTELLIGENCE FOR CHEMICAL INFERENCE - XI Appendix D A method of construction of structures similar to the generation of acyclic molecules is utilized to join multiple ring-superatoms and remaining atoms. The DENDRAL algorithm for construction of acyclic molecules (3,24) relied on the existence of a unique central atom (or bond) to every molecule. The present acyclic generator uses the same idea. The present algorithm, though simpler in not having to to treat interconnection of atoms or ring-superatoms through multiple bonds, is more complex because of the necessity to deal with the symmetries of the ring-superatoms. D1. Method for the case with even number of total atoms. The superatom partition C U /C U /-/C (partition 7, Table II and 2 2 2 1 2 Figure 2) will be used here to illustrate this procedure. The superatomparts C U and C U have exactly one possible 2 2 2 1 ring-superatom for each (see Table VII). --------------------------------------------------------- Table VII Superatompart Superatom C U -C≡≡C- 2 2 C U >C==C< 2 1 ---------------------------------------- Thus acyclic structures are to be built with -C≡≡C- , >C==C< and two C's. There are an even number atoms and ring-superatoms. The structures to be generated fall into two categories:(a) those with a central bond; (b) those with a central atom. ----------------------- 24) A more complete description of the algorithm is available; see B. G. Buchanan, A. M. Duffield, and A. V. Robertson, in "Mass spectrometry, Techniques and Applications," G. W. A. Milne, ed., John Wiley and Sons, Inc., 1971, p. 121. 29 APPLICATIONS OF ARTIFICIAL INTELLIGENCE FOR CHEMICAL INFERENCE - XI Category A. CENTRAL BOND (see Fig. 3). Step 1. Partition into Two Parts. The atoms and ring-superatoms are partitioned into two parts, with each part having exactly half the total number of items. Each atom or ring-superatom is a single item. Each part has to satisfy equation 7, called the Restriction on Univalents. Restriction on Univalents: n 1+αFCSαF1(i-2)aα←.α→p ≥ 0 (7) i=1 α←pα→.i i = valence a = number of atoms or superatoms of valence i i n = maximum valence in composition There are two ways of partitioning the four items into two parts (Fig. 3). The restriction on univalents is satisfied in each case. The restriction will disallow certain partitions that have "too many" univalents other than hydrogens and therefore is essential only in partitioning compositions that contain any number of non-hydrogen univalents. Step 2. Generate Radicals from Each Part. Using a procedure described in Section C3, radicals are constructed from each part in each partition. Table VIII shows the result of applying this procedure to the example. 30