Using Protochirons for Three-Dimensional Coding of Certain Chemical Structures

For three-dimensional coding (including enantiomerism) of staggered paths and circuits on the diamond lattice, or paths/circuits with angles 90 degrees or 180 degrees on the cubic lattice, use is made of the previously defined paths-3 (paths of length three bonds defining two intersecting planes). The two cases mentioned above are examined and exemplified. In the diamond lattice there are three kinds of diamond-paths-3: one is achiral (Z) and two are chiral and enantiomeric (R and S). In the cubic lattice there are six kinds of orthopaths-3, of which only two are chiral and enantiomeric (R and S) and four are achiral (I, L, U, and Z). The chiral paths-3 are the previously defined protochirons in the respective lattice. Coding ascribes to each bond the letter that would characterize it if it were the central bond of an isolated path-3. To obtain a unique code out of several equally correct ones it is proposed to use the convention of inverse alphabetic priority in the above system of letters.

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