Fig. 2. Crystal structure and crystal-state packing of (A) n-H1 (CCDC 2165994), (B) c-H1 (CCDC 2158816), (C) n-H2 (CCDC 2165995), and (D) c-H2 (CCDC 2158813). (E) Racemization barrier (kcal mol−1) for c-ExHHel2 calculated at the 6-31g(d,p) level of theory. (F) Crystal structure and crystal-state packing of the Rh-H1 intermediate (CCDC 2158814). [The helical pitch pAI is defined as the centroid-to-centroid distance between the terminal rings A and I of the helical rim of the helicene molecule. The helical diameter dCH is the longest centroid-to-centroid distance between the two rings C and H of the helical rim. The intersecting angle θAI is defined as the angle between the two planes passing through the terminal rings A & I.] (G) (I) Computational calculation of the spring constant value: the distance between the two terminal carbon atoms (red) was allowed hypothetically to expand by a difference up to 2.0 Å, and the respective relative energies were calculated. (II) The variation of relative energy of the neutral and cationic helicenes n-H1 and c-H1 as a function of the increment of the distance between two terminal carbons. (III) The plot of the spring constant k as a function of the inverse of third power of the helical diameter (dh) of the corresponding helicene molecules considering an elliptical cross-section. Computations were performed at the B3LYP/6-311g(2d,p) level of theory.
