• Symmetry Measures of the Electron Density


Prof. Santiago Alvarez, Prof. Pere Alemany, Prof. Miquel Llunell

Continuous symmetry measures (CSM), continuous chirality measures (CCM) and continuous shape measures (CShM) provide simple and accurate stereochemical descriptors for molecular structures.  Derived tools, such as shape maps, minimal distortion paths, and generalized polyhedral interconversion coordinates have been developed in our research group.  Their application to large structural data sets has allowed us to redefine the qualitative rules that govern the stereochemical preferences of four- and six-coordinate complexes.

For some stereochemical problems one needs a better description of molecular shape and symmetry than that given by the atomic positions.  To fulfill that need we have proposed an extension of the CSM approach to analyze chemical bonding in terms of the symmetry contents of the electron density, the Hamiltonian or of individual molecular orbitals.

Main Results of Our Research in this Field

SHAPE 2.1 – Our software for obtaining continuous shape measures of coordination polyhedra and derived properties is available for download.

Relevant Publications

P. Alemany, D. Casanova, S. Alvarez, C. Dryzun and D. Avnir.  «Continuous Symmetry Measures: A New Tool in Quantum Chemistry».  Rev. Comput. Chem.201730, 289-352.
S. Alvarez, «Distortion Pathways of Transition Metal Coordination Polyhedra Induced by Chelating Topology».  Chem. Rev.2015115, 13447-13483.  Doi: 10.1021/acs.chemrev.5b00537. Open access.
L. J. K. Cook, R. Mohammed, G. Sherborne, S. Alvarez and M. Halcrow, “Spin-state Behaviour of Iron(II)Dipyrazolylpyridine Complexes. New Insights from Crystallographic and Solution Measurements». Coord. Chem. Rev.2015289-290, 2-12. Doi: 10.1016/j.ccr.2014.08.006.
S. Alvarez, E. Ruiz.  «Self-Assembly of Coordination Compounds: Design Principles», in Supramolecular Chemistry, From Molecules to Nanomaterials, J. W. Steed, P. A. Gale, eds., John Wiley & Sons, Chichester, UK, 20125, 1993-2044.  ISBN 978-0-470-74640-0
S. Alvarez, J. Echeverría.  «New Perspectives on Polyhedral Molecules and their Crystal Structures».  J. Phys. Org. Chem. 201023, 1080-1087.
S. Alvarez.  «Nesting of Fullerenes and Frank-Kasper Polyhedra».  Dalton Trans.2006, 2045-2051.
S. Alvarez, P. Alemany, D. Casanova, J. Cirera, M. Llunell, D. Avnir.  «Shape Maps and Polyhedral Interconversion Paths in Transition Metal Chemistry».  Coord. Chem. Rev.2005249, 1693-1708.
J. Cirera, E. Ruiz, S. Alvarez.  «Continuous Shape Measures as a Stereochemical Tool in Organometallic Chemistry».  Organometallics 200524, 1556-1562.
S. Alvarez, P. Alemany, D. Avnir.  «Continuous Chirality Measures in Transition Metal Chemistry».  Chem. Soc. Rev. 200534, 313-326.
S. Alvarez.  «Polyhedra in (Inorganic) Chemistry».  Dalton Trans. 2005, 2209-2233.
S. Alvarez.  «Poliedros y sus distorsiones en la descripción de la estructura molecular y en el diseño de edificios supramoleculares».  An. Real Soc. Esp. Quím. 200399, 29-44.

All Publications of Continuous Shape and Symmetry Measures. Applications in Structural Chemistry.