dorsal/arxiv
View SchemaFrom Fischer projections to quantum mechanics of tetrahedral molecules: new perspectives in chirality
| Authors | S. Capozziello, A. Lattanzi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0411034 |
| URL | https://arxiv.org/abs/quant-ph/0411034 |
| DOI | 10.1016/S0065-3276(05)49005-X |
| Journal | Adv.Quant.Chem.49:227-247,2005 |
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 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 Schroedinger 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.
{
"annotation_id": "cd4afd8a-f6bb-4746-a07d-14c03f4072d3",
"date_created": "2026-03-02T18:02:12.915000Z",
"date_modified": "2026-03-02T18:02:12.915000Z",
"file_hash": "2ea4f242193376832c5c0fbca340fc5f139219ed8cf21014c020812705e1c826",
"private": false,
"record": {
"abstract": "The algebraic structure of central molecular chirality can be achieved\nstarting from the geometrical representation of bonds of tetrahedral molecules,\nas complex numbers in polar form, and the empirical Fischer projections used in\norganic chemistry. A general orthogonal O(4) algebra is derived from which we\nobtain a chirality index related to the classification of a molecule as\nachiral, diastereoisomer or enantiomer. Consequently, the chiral features of\ntetrahedral chains can be predicted by means of a molecular Aufbau. Moreover, a\nconsistent Schroedinger equation is developed, whose solutions are the bonds of\ntetrahedral molecules in complex number representation. Starting from this\nresult, the O(4) algebra can be considered as a quantum chiral algebra. It is\nshown that the operators of such an algebra preserve the parity of the whole\nsystem.",
"arxiv_id": "quant-ph/0411034",
"authors": [
"S. Capozziello",
"A. Lattanzi"
],
"categories": [
"quant-ph",
"hep-th"
],
"doi": "10.1016/S0065-3276(05)49005-X",
"journal_ref": "Adv.Quant.Chem.49:227-247,2005",
"title": "From Fischer projections to quantum mechanics of tetrahedral molecules: new perspectives in chirality",
"url": "https://arxiv.org/abs/quant-ph/0411034"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "a8a7cad3-c898-491c-8ce5-8bad7e9965cb",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}