The algebraic structure of central molecular chirality can be achieved starting from the geometrical representation of bonds of tetrahedral molecules, as complex numbers in polar form, and the empirical Fischer projections used in organic chemistry. A general orthogonal O(4) algebra is derived from which we obtain a chirality index X related to the classification of a molecule as achiral, diastereoisomer or enantiomer. Consequently, the chiral features of tetrahedral chains can be predicted by means of a molecular Aufbau. Moreover, a consistent Schrodinger equation is developed, whose solutions are the bonds of tetrahedral molecules in complex number representation. Starting from this result, the O(4) algebra can be considered as a "quantum chiral algebra". It is shown that the operators of such an algebra preserve the parity of the whole system.
From Fischer projections to quantum mechanics of tetrahedral molecules: new perspectives in chirality
LATTANZI, Alessandra
2005
Abstract
The algebraic structure of central molecular chirality can be achieved starting from the geometrical representation of bonds of tetrahedral molecules, as complex numbers in polar form, and the empirical Fischer projections used in organic chemistry. A general orthogonal O(4) algebra is derived from which we obtain a chirality index X related to the classification of a molecule as achiral, diastereoisomer or enantiomer. Consequently, the chiral features of tetrahedral chains can be predicted by means of a molecular Aufbau. Moreover, a consistent Schrodinger equation is developed, whose solutions are the bonds of tetrahedral molecules in complex number representation. Starting from this result, the O(4) algebra can be considered as a "quantum chiral algebra". It is shown that the operators of such an algebra preserve the parity of the whole system.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
