Stereochemistry I In Memory of van't Hoff by Boschke F.L.

By Boschke F.L.

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35 IV. Many-turn 43 H e l i c e s - - L o n g C h a i n s of A t o m s . . . . . . . . . . . . 1. G e n e r a l C o n s i d e r a t i o n s ....................................... 30 43 2. C h a r a c t e r i s t i c s of t h e M o t i f s i n [ 2 j - H e l i c e s . . . . . . . . . . . 44 3. C h a r a c t e r i s t i c s of t h e C r o s s S e c t i o n s of [ 2 ~ - H e l i c e s . . . . . . . . 45 4. E f f e c t s of D i f f e r e n c e s of B o n d A n g l e i n E2]-Helices .

Each bond subtends an internal triangle, the areas of which are: ~'A Y B Aa = - ~ - - sin (14a) Ab (14b) - - ~'A/'B " 2 s i n fl whence the total area of one cross section, subtended b y one turn: $'A ~'B At -- t 2 (sin a + sin fi) (14c) where u/t is the number of motifs (u) per turn (t). This term is often expressed as a ratio of integers: u t uc tc (15) where ue is the number of motifs per crystallographic repeat unit and te the number of turns per crystallographic repeat unit. I t is evident that: U Lt = - t (Pa + Pb) (16) and: U Ot = -/- (da + db) (17) whence: H = 6 V~ u rA rB (sin a + sin r) (Pa + Pb) 2 u/t (d~ + rib)3 (18) 4.

20) Harris, M. M. : Progress in Stereochemistry, p. 174. (eds. ~V. K l y n e and P. t3. D. de la Mare), Vol. 2: L o n d o n : 13utterworths 1958. -- Ollis, W. , Sutherland, I. : Chem. , 7966, 402. , Mislow, K. : Proc. Natl. Acad. Sci. S. 70, 3445 (1973). 22) Berry, R. : J. Chem. Phys. 32, 933 (1960). 23) Musher, J. : J. Am. Chem. Soc. 94, 5662 (1972). : Ace. Chem. Res. 4, 288 (1971). : Ace. Chem. Res. 3, 321 (1970). : Chimia 22, 488 (1968), and references cited therein. 27) Casey, J. : Chem. Commun.

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