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For a tutorial article emphasizing symmetry arguments in chemistry: J.D. Dunitz Proc. Natl. Acad. Sci. U.S.A. 93 1996 14260 14266
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Curie, P.1
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5144228088
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note
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6h characteristic of a planar arrangement (e.g., benzene)
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14
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5144226459
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note
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Jean Buridan (1300-1358) was Rector of the University of Paris (the Sorbonne). Curiously the animal mentioned in Buridan's commentary on Aristotle's De Caelo (On the Heavens) is actually a dog not an ass
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5144229170
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Perseus Books New York
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We have learned that some fundamental physical laws may not be entirely symmetric. Parity or space inversion conservation is not a perfect symmetry of nature. In particle physics symmetry breaking is usually connected with the theory of supersymmetry, which relates fermions to bosons in an approach to incorporating gravity into a unified theory with strong and electroweak interactions G. Kane Supersymmetry: Unvealing the Ultimate Laws of Nature 2001 Perseus Books New York
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For some recent essays: F. Wilczek Nature 428 2004 261
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Wilczek, F.1
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E. Witten Nature 429 2004 507 508
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Witten, E.1
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L. Addadi, Z. Berkovitch-Yellin, I. Weissbuch, M. Lahav, and L. Leiserowitz Top. Stereochem. 16 1986 1 85
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Berkovitch-Yellin, Z.2
Weissbuch, I.3
Lahav, M.4
Leiserowitz, L.5
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Collinear electric and magnetic fields do not generate molecular chirality either. Pierre Curie ignored the role of time reversal (T), characteristic of motion-dependent chirality. Time reversal of one of the enantiomorphous states (interconverted by space inversion P) combined with any proper rotation gives rise to a homomorph of the former. Pseudoscalar properties such as natural optical activity and hence chirality are only supported by a T-invariant enantiomorphism that is, T cannot undo the effect of space inversion (P): L.D. Barron J. Am. Chem. Soc. 108 1986 5539 5542
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E. Bauer, G. Hilscher, H. Michor, C. Paul, E.W. Scheidt, A. Gribanov, Yu. Seropegin, H. Noël, M. Sigrist, and P. Rogl Phys. Rev. Lett. 92 2004 027003
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In magnetic superconductors such as metals or alloys, the state wave function can be separated into two parts, one depending only on the spatial coordinates and the other only on the spin coordinates. In crystals with space-inversion (parity) symmetry, the interchange of the spatial coordinates of the electrons gives rise to a state indistinguishable from the original. Therefore, the probability distribution of the electrons in the state wave function remains unaffected. A second interchange gives back the initial quantum state, with a phase factor of +1 or -1, that is, the spatial part must be either symmetric or antisymmetric. If the complete state has to be antisymmetric (electron states have momenta equal in magnitude, but opposite in direction), the spin part of the wave function must be antisymmetric (it must have the opposite symmetry under electron interchange). This implies a spin-singlet state, typical of metals such as aluminum. Conversely, an antisymmetric spatial wave function requires a symmetric spin wave function (corresponding to a spin-triplet state)
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See Ref. 1, p 1193
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(a) See Ref. 1, p 1193
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M.M. Green R.J.M. Nolte E.W. Meijer Wiley New York
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In other words the observable pattern, which has in principle no relation with the intimate structure. In crystallography, the packing may present low symmetry as revealed by the asymmetry of the electron diffraction pattern, although the single crystals be highly symmetric. For an excellent discussion: C. De Rosa M.M. Green R.J.M. Nolte E.W. Meijer Materials-Chirality, Topics in Stereochemistry Vol. 24 2003 Wiley New York 71 155 (especially pp 109-121)
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De Rosa, C.1
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C.A. Orme, A. Noy, A. Wierzbicki, M.T. McBride, M. Grantham, H.H. Teng, P.M. Dove, and J.J. DeYoreo Nature 411 2001 775 779
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Teng, H.H.6
Dove, P.M.7
Deyoreo, J.J.8
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Conglomerate refers to a mechanical mixture of two enantiomers forming a eutectic. The term is reserved for a mixture of macroscopic chiral domains although it is not only confined to crystals but also to two-dimensional conglomerates such as Langmuir films. For chiral morphologies of Langmuir monolayers see: N. Nandi, and D. Vollhardt Chem. Rev. 103 2003 4033 4075 In stark contrast true racemates contain equal numbers of enantiomeric molecules within the unit cell, that is, they are composed of achiral domains containing chiral elements of opposite handedness forming an achiral system
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Chem. Rev.
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Nandi, N.1
Vollhardt, D.2
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Achiral symmetry breaking is also to be discouraged because supramolecular aggregates composed of chiral nonracemic molecules may display no chirality (achiral phases), such as in mesogenic structures; see for instance: H.H.v. Doren, E. Smits, J.M. Pestman, J.B.F.N. Engberts, and R.M. Kellogg Chem. Soc. Rev. 29 2000 183 199
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Kellogg, R.M.5
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See Ref. 1, pp 88-91 and references cited therein
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See Ref. 1, pp 88-91 and references cited therein
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