Definite Chirality Measures from Electron Torsion: Application to Helical Molecules
Abstract
The previously given pseudoscalar chirality index based on the electron path torsion [Struct. Chem. 3, 175 (1992)] is modified, and the corresponding positive definite chirality measure is proposed. The approach is applied to helicenes and DNA double-stranded minihelices. In addition, the electronic chirality measure is divided into atomic contributions. It allows to provide an appropriate pictorial presentation of molecular chirality. Several model examples of discrete helix structures are given. They offer an understanding of nontrivial differences in describing molecular chirality by aid of the pseudoscalar torsion invariants and by aid of the positive orbital torsions proposed in the present paper.
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References
M. Petitjean, Entropy 5, 271 (2003).
A. I. Kitaigorodskii, Organic Chemical Cristallography (Consultans Bureau Ets. Inc., New York, 1961).
D. Avnir and H. Zabrodsky, P. G. Mezey, in Encyclopedia of Computational Chemistry, ed-ited by P. v. R. Schleyer (Wiley, Chichester, 1998), vol. 4, p. 2890.
K. Mislow, Top. Stereochem. 22, 1 (1999).
G. Gilat, J. Math. Chem. 15: 197(1994).
N. Weinberg and K. Mislow, Can. J. Chem. 78, 41(2000); G. Millar, N. Weinberg, and K. Mislow, Mol. Phys. 103, 2769 (2005).
A. V. Luzanov and D. Nerukh, J. Math. Chem. 41, 417 (2007).
A V. Luzanov, Int. J. Quantum Chem. 111, 2196 (2011).
R. Natarajan and S. C. Basak, Current Computer-Aided Drug Design 5, 13 (2009).
A. V. Luzanov and E. N. Babich, Struct. Chem. 3, 175 (1992); A. V. Luzanov and E. N. Babich, Theochem. 333, 279 (1995).
A. V. Luzanov, V. V. Ivanov, and R. M. Minyaev, J. Struct. Chem. 39, 261 (1998).
A. V. Luzanov, Funct. Mater. 22 , 355 (2015).
R. Hoffmann, J. Chem. Phys. 39, 1397 (1963); http://www.quantumwise.com/documents/manuals/ATK-2014/ReferenceManual/index.html/chap.atomicdata.html#sect3.atomicdata.huckel.hoffmann.
V. I. Sokolov, Introduction to theoretical stereochemistry (Gordon and Breach, New York, 1991).
D. J. Nelson and C. N. Brammer, J. Chem. Ed. 88, 292 (2011).
M. Gingras, Chem. Soc. Rev. 42, 968 (2013).
S. Grimme, Chem. Phys. Lett. 297, 15 (1998).
O. Katzenelson, J. Edelstein, and D. Avnir, Tetrahedron Asymmetry 11, 2695 (2000)].
H. Laarhoven and J. C. Prinsen, Top. Curr. Chem. 125, 63 (1984).
M. D. Frank-Kamenetski, Unraveling DNA. The most important molecule of life (Addison-Wesley, New York, 1997).
A. Pullman, C. Zakrewska, and D. Perahia, Int. J. Quantum Chem. 16, 395 (1979); D. Perahia and A. Pullman, Theor. Chim. Acta 50, 351 (1979).
T. A. Zubatiuk, O. V. Shishkin, L. Gorb, D. M. Hovorun, and J. Leszczynski, Phys. Chem. Chem. Phys. 15, 18155 (2013).
T. A.Zubatiuk, M. A. Kukuiev, A. S. Korolyova, L. Gorb, A. Nyporko, D. Hovorun, and J. Leszczynski, J. Phys. Chem. B 119 ,12741 (2015).
A. Pietropaolo and M. Parrinello, Chirality 23, 534 (2011).
M. A. Osipov, B. T. Pickup, and D. A. Dunmur, Mol. Phys. 84,1193(1995).
M. Solymosi, R. J. Low, M. Grayson, and M. P. Neal, J. Chem. Phys. 116, 9875 (2002).
R. K. Kondru, P. Wipf, and D. N. Beratan, Science 282, 2247 (1998); R. K. Kondru, P. Wipf, D. N. Beratan, G. K. Friestad, and A. B. Smith, Org. Lett. 2, 1509 (2000).
P. Mukhopadhyay, P. Wipf, and D. N. Beratan, Acc. Chem. Res. 42, 809 (2009).
W. C. Johnson, I. Tinoco, Biopolymers 7, 727(1969).
A.Pietropaolo, in: Ideas in Chemistry and Molecular Sciences: Where Chemistry Meets Life, ed. B. Pignataro.(Wiley-VCH , Weinheim, 2010), p. 293-311.
R.B. King, Ann N Y Acad Sci. 988, 158 (2003).
