Charge density distribution application for

the evaluation of optical properties for tartaric acid crystals.

Mateusz Pitak, Katarzyna Stadnicka

Faculty of Chemistry, Jagiellonian University, ul. Ingardena 3, 30-060 Kraków, Poland

(+)-(2R,3R)-2,3-dihydroxybutanedioic acid, known under the common name L-tartaric acid crystallizes in non-centrosymmetric space group P 2₁. In aqueous solution it shows optical dextro-rotation (+).

A big discrepancy was found between the experimentally determined principal components of the gyration tensor and the optical rotation calculated from the structural data using atom polarizabilities derived from simple model assuming dipol-dipol interactions only [1]. Since the contribution of the molecule itself was estimated as relatively small, the predominating intermolecular contribution was expected to be responsible for the high gyration tensor components. Unfortunately the computations did not include the polarizability arising from the three-dimensional network of very strong intermolecular hydrogen bonds.

The molecule of (2R,3R)-tartaric is chiral with two asymmetric carbon atoms and is able to form strong hydrogen bonds of OH×××O type. In the crystal structure all possible donors are involved in intermolecular hydrogen bonds and one of them can be considered as bifurcated having both intra- and intermolecular components.

The structure and bonding have been studied by low-temperature X-ray diffraction at 85 K and 14 K respectively.

A charge density analysis, including the multipole refinement based on the Hansen – Coppens formalism [2], deformation density, topological analysis of r(r) according to the AIM theory [3] was carried out with the program package XD [4].

The results of the topological analysis of r(r) at the bond critical points enable a quantitative description of the bonds.

Charge density and topological properties for the studied crystal have been undertaken to explore the character and role of both inter- and intra-molecular hydrogen bonds in the structure, and to utilize the polarizability of the electron density at the hydrogen bonds towards the determination of gyration tensor components. The interesting features of the structure are different electron density distributions found for the same functional groups like either hydroxyl or carboxyl groups resulting in decreasing of the molecular symmetry (C₂ ® C₁).

[1] D. Mucha, K. Stadnicka, W. Kaminsky, A. M. Glazer. J. Phys.: Condens. Matter 9

(1997) 10829-10842.

[2] N. K. Hansen, P. Coppens, Acta Cryst. A34 (1978) 909-921

[3] R. F. W. Bader, Atoms in Molecules: A Quantum Theory, Oxford, Calderon

Press,1995.

[4]  T. Koritsanszky,. S.T. Howard, T. Richter, P. Macchi,A. Volkov, C. Gatti, 

P.R. Mallinson, L. J. Farrugia, Z. Su, N.K. Hansen, XD - A Computer 

program package for multipole refinement and Topological Analysis of charge

densities from diffraction data, 2003