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Investigation of the Chirality of Enantiomers through Information Theory

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HPC-UGent: the central High Performance Computing infrastructure of Ghent University
Abstract
In this work [1] we probed the Kullback-Leibler information entropy as a chirality measure, as an extension of previous studies on molecular quantum similarity evaluated for different enantiomers (enantiomers possessing two asymmetric centra in [2], with a single asymmetric carbon atom in [3] and with a chiral axis in [4]). The entropy was calculated using the shape functions of the R and S enantiomers considering one as reference for the other, resulting in an information theory based expression useful for quantifying chirality. It was evaluated for 5 chiral halomethanes possessing one asymmetric carbon atom with H, F, Cl, Br and I as substituents. To demonstrate the general applicability, a study of two halogen-substituted ethanes possessing two asymmetric carbon atoms has been included as well. Avnir’s Continuous Chirality Measure (CCM) [5] has been computed and confronted with the information deficiency. By these means we quantified the dissimilarity of enantiomers and illustrated Mezey’s Holographic Electron Density Theorem in chiral systems [6]. A comparison is made with the optical rotation and with the Carbó similarity index. As an alternative chirality index, we recently also calculated the information deficiency in a way which is consistent with experiments as VCD spectroscopy and optical rotation measurements. The entropy calculates the difference in information between the shape function of one enantiomer and a normalized shape function of the racemate. Comparing the latter index with the optical rotation reveals a similar trend. [1] S. Janssens, A. Borgoo, C. Van Alsenoy, P. Geerlings, J. Phys. Chem. A, 112, 10560 (2008). [2] S. Janssens, C. Van Alsenoy, P. Geerlings, J. Phys. Chem. A, 111, 3143 (2007). [3] G. Boon, C. Van Alsenoy, F. De Proft, P. Bultinck, P. Geerlings, J. Phys. Chem. A, 110, 5114 (2006). [4] S. Janssens, G. Boon, P. Geerlings, J. Phys. Chem. A, 110, 9267 (2006). [5] H. Zabrodsky, D. Avnir, J. Am. Chem. Soc., 117, 462 (1995). [6] P.G. Mezey, Mol. Phys., 96, 169 (1999).
Keywords
Information theory

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Chicago
Janssens, Sara, Alex Borgoo, Patrick Bultinck, Christian Van Alsenoy, and Paul Geerlings. 2009. “Investigation of the Chirality of Enantiomers Through Information Theory.” In Abstracts XIIIth International Congress of Quantum Chemistry, A49–A49. Helsinki, Finland.
APA
Janssens, Sara, Borgoo, A., Bultinck, P., Van Alsenoy, C., & Geerlings, P. (2009). Investigation of the Chirality of Enantiomers through Information Theory. Abstracts XIIIth International Congress of Quantum Chemistry (pp. A49–A49). Presented at the XIIIth International Congress of Quantum Chemistry, Helsinki, Finland.
Vancouver
1.
Janssens S, Borgoo A, Bultinck P, Van Alsenoy C, Geerlings P. Investigation of the Chirality of Enantiomers through Information Theory. Abstracts XIIIth International Congress of Quantum Chemistry. Helsinki, Finland; 2009. p. A49–A49.
MLA
Janssens, Sara, Alex Borgoo, Patrick Bultinck, et al. “Investigation of the Chirality of Enantiomers Through Information Theory.” Abstracts XIIIth International Congress of Quantum Chemistry. Helsinki, Finland, 2009. A49–A49. Print.
@inproceedings{764613,
  abstract     = {In this work [1] we probed the Kullback-Leibler information entropy as a chirality
measure, as an extension of previous studies on molecular quantum similarity evaluated
for different enantiomers (enantiomers possessing two asymmetric centra in [2], with a
single asymmetric carbon atom in [3] and with a chiral axis in [4]). The entropy was
calculated using the shape functions of the R and S enantiomers considering one as
reference for the other, resulting in an information theory based expression useful for
quantifying chirality. It was evaluated for 5 chiral halomethanes possessing one
asymmetric carbon atom with H, F, Cl, Br and I as substituents. To demonstrate the
general applicability, a study of two halogen-substituted ethanes possessing two
asymmetric carbon atoms has been included as well. Avnir{\textquoteright}s Continuous Chirality
Measure (CCM) [5] has been computed and confronted with the information deficiency.
By these means we quantified the dissimilarity of enantiomers and illustrated Mezey{\textquoteright}s
Holographic Electron Density Theorem in chiral systems [6]. A comparison is made
with the optical rotation and with the Carb{\'o} similarity index.
As an alternative chirality index, we recently also calculated the information
deficiency in a way which is consistent with experiments as VCD spectroscopy and
optical rotation measurements. The entropy calculates the difference in information
between the shape function of one enantiomer and a normalized shape function of the
racemate. Comparing the latter index with the optical rotation reveals a similar trend.
[1] S. Janssens, A. Borgoo, C. Van Alsenoy, P. Geerlings, J. Phys. Chem. A, 112, 10560
(2008).
[2] S. Janssens, C. Van Alsenoy, P. Geerlings, J. Phys. Chem. A, 111, 3143 (2007).
[3] G. Boon, C. Van Alsenoy, F. De Proft, P. Bultinck, P. Geerlings, J. Phys. Chem. A,
110, 5114 (2006).
[4] S. Janssens, G. Boon, P. Geerlings, J. Phys. Chem. A, 110, 9267 (2006).
[5] H. Zabrodsky, D. Avnir, J. Am. Chem. Soc., 117, 462 (1995).
[6] P.G. Mezey, Mol. Phys., 96, 169 (1999).},
  author       = {Janssens, Sara and Borgoo, Alex and Bultinck, Patrick and Van Alsenoy, Christian and Geerlings, Paul},
  booktitle    = {Abstracts XIIIth International Congress of Quantum Chemistry},
  keyword      = {Information theory},
  language     = {eng},
  location     = {Helsinki, Finland},
  pages        = {A49--A49},
  title        = {Investigation of the Chirality of Enantiomers through Information Theory},
  year         = {2009},
}