Group-theoretical framework for characterizing the ring flipping of spiro[5.5]undecane derivatives. Pseudo-point groups and subsymmetry-itemized enumeration

The pseudo-point group DD2d for characterizing the flipping of the two cyclohexane rings in spiro[5.5]undecane is defined. Spirane derivatives with a given formula and a given symmetry are enumerated by the unit-subduced-cycle-index (USCI) approach on the basis of the spiro[5.5]undecane skeleton. The symmetry of each derivative corresponds to one of the subgroups of DD2d, which are classified into isoenergetic (isoenergetic-achiral and isoenergetic-chiral) or anisoenergetic (anisoenergetic-achiral and anisoenergetic-chiral) ones. The orbits in the derivative are discussed by the sphericity and chronality.