Enumeration of Three-Dimensional Structures Derived from a Dodecahedrane Skeleton under a Restriction Condition. I. The Restricted-Fixed-Point-Matrix (RFPM) Method Based on Restricted Subduced Cycle Indices

Abstract

On the basis of restricted subduced cycle indices with chirality fittingness (RSCI-CFs), the restricted-fixed-point-matrix (RFPM) method has been developed as a new method for the combinatorial enumeration of sterically hindered derivatives of a given skeleton. Such RSCI-CFs are derived from subduced cycle indices with chirality fittingness (SCI-CFs) defined in the unit-subduced-cycle-index (USCI) approach (S. Fujita, "Symmetry and Combinatorial Enumeration in Chemistry," Springer-Verlag (1991)). Thus, the SCI-CFs are combined with territory indicators to give territory discriminants, which are treated by considering a restriction condition that rejects the occupation of any adjacent sites, so as to generate RSCI-CFs. The resulting RSCI-CFs are used to evaluate marks (the numbers of fixed points) in place of the original SCI-CFs and combined with the fixed-point-matrix (FPM) method of the USCI approach to develop the RFPM method. The RFPV method based on RSCI-CFs is applied to enumeration of sterically hindered derivatives of dodecahedrane.