Topological study of refractive indices, atomic charges, polar and axial vectors of second rank and optical rotation in α-HgS (cinnabar) at 296 K

Volume 7, Issue 1, February 2022     |     PP. 19-32      |     PDF (397 K)    |     Pub. Date: February 12, 2022
DOI: 10.54647/chemistry15252    83 Downloads     161346 Views  

Author(s)

M. Karppinen, Institute of Chemistry, University of Uppsala, Box 531, Uppsala S-75 121 Sweden.

Abstract
The magnitude and sense of optical rotation are determined from the point charge model in a nonpolar, chiral, covalently bonded and semiconducting α-HgS (cinnabar) crystal. Atomic charges of Hg and S are variables in the iteration of topological equivalence between the inverted ratios of the second electric moments and the corresponding optical refractive indices of the α-HgS crystal. Vector cross products of the wave vector in the propagation direction of light and the second electric moments in the other two semi-axis directions of the quadric specify the handedness of axial vectors of second rank and the refractive indices comprise the magnitudes of them. The calculated axial vectors contain information of optical rotation and the handedness of the dominant component of them reveals the sense of rotational character of the crystal. They are converted to principal gyration tensor components and the magnitude and sense of rotation are computed in the direction of optic axis of the quadric. The sense of optical rotation is opposite to the sense of the helical arrangement of the atoms. The magnitude and sense of optical rotation solely arises from the asymmetric distribution of point charges and electric vectors in the unit cell of α-HgS crystal. The morphological right- and left-handed character of the two enantiomorphs and the absolute structure of α-HgS crystal are discussed.

Keywords
α-HgS (cinnabar),refractive indices,atomic charges, polar and axial vectors of second rank,optical rotation

Cite this paper
M. Karppinen, Topological study of refractive indices, atomic charges, polar and axial vectors of second rank and optical rotation in α-HgS (cinnabar) at 296 K , SCIREA Journal of Chemistry. Volume 7, Issue 1, February 2022 | PP. 19-32. 10.54647/chemistry15252

References

[ 1 ] Fresnel, A., (1824). Bull. Soc. Philomath. Paris, pp. 147-158.
[ 2 ] Born, M., (1922). Z. Phys. 8, 390 - 417.
[ 3 ] Hylleraas, E.A., (1927). Z.Phys. 44, 871.
[ 4 ] Condon, E.U., (1937). Rev.Mod. Phys., 9, 432-457.
[ 5 ] Cotton, F.A. and Wilkinson, G., (1972). Advanced Inorganic Chemistry, 3rd ed. Interscience, New York, 1972.
[ 6 ] Lamure, J., Brusset, H., (1962). Mercure. In: Nouveau Traité de Chimie Minérale, Tome V, Pascal P. Ed., 733-797.
[ 7 ] Auvray, P. and Genet. F., (1973). Bulletin de la Societe Francaise de Mineralogie et de Cristallographie, 96, 218-219.
[ 8 ] Auvray, P., (1976). Bulletin de la Societe Francaise de Mineralogie et de Cristallographie, 99, 373-379.
[ 9 ] Ayrault, I.B., Lefin, F., Langlaois, H., Toudic. Y., Palmier, J.F., (1972). Optics Communications, Volume 5, Issue 4, 239-243.
[ 10 ] Devardajan, V., and Glazer, A., M., (1986). Acta Cryst. A42, 560-569.
[ 11 ] Glazer, A.M. & Stadnicka, K. (1986). J. Appl. Cryst. 19, 108-122.
[ 12 ] Nye, J.F. (1972)., Physical Properties of Crystals. Oxford: Clarendon Press.
[ 13 ] Buckingham, A.D., (1959). Q.Rev. Chem.Soc. 13,183.
[ 14 ] Buckingham, A.D., (1970). Physical Chemistry. An Advanced Treatise. Vol. IV, p.349. New York: Academic Press.
[ 15 ] Farrugia, L. J., (1997). ORTEP-3 for Windows. J. Appl. Cryst. 30, 565.
[ 16 ] W. L. Bond, G. D. Boyd and H. L. Carter Jr., (1967). J. Appl. Phys., 38, 4090-4091 (https://RefractiveIndex.INFO).
[ 17 ] Karppinen. M., (2015). Acta Crystallogr. Sec.B 71, 334-341.
[ 18 ] Karppinen, M., (2020). J.Appl.Crystallogr. 53, 1252-1256.
[ 19 ] Karppinen, M., (2022). SCIREA Journal of Chemistry. (https://doi.org/10.54647chemistry 15232)