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Dipole moment of polyhedral water clusters: mathematical relationships and their application. (English) Zbl 1414.92226
Summary: Polyhedral water clusters are characterized by exponential proton disorder and a complex molecular interaction. Nevertheless, a simple theory has been developed for these systems. It allows predicting classes of the most stable proton configurations that differ in the arrangement of hydrogen atoms (protons) in the hydrogen bonds. The stability for a particular configuration is evaluated on the basis of the analysis of local topological characteristics of the hydrogen bond network. However, the stability of water clusters is determined also by another, clearly non-topological global characteristic: the magnitude of the total dipole moment. In this article we show that the total dipole moment of polyhedral water clusters is proportional to the vector sum of polyhedron edges if their direction coincides with the direction of hydrogen bonds. This makes it possible not to take into account separately the contribution of free (dangling) hydrogen atoms when classifying proton configurations.
MSC:
92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
52C99 Discrete geometry
Software:
TINKER
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References:
[1] Vaida, V., No article title, J. Chem. Phys., 135, 020901, (2011)
[2] Vostrikov, AA; Dubov, DY, No article title, Tech. Phys. Lett., 34, 221-224, (2008)
[3] Liu, K.; Cruzan, JD; Saykally, RJ, No article title, Science, 271, 929-933, (1996)
[4] Gruenloh, CJ; Carney, JR; Arrington, CA; Zwier, TS; Fredericks, SY; Jordan, KD, No article title, Science, 276, 1678-1681, (1997)
[5] Keutsch, FN; Saykally, RJ, No article title, Proc. Natl. Acad. Sci., 98, 10533-10540, (2001)
[6] Maheshwary, S.; Patel, N.; Sathyamurthy, N.; Kulkarni, AD; Gadre, SR, No article title, J. Phys. Chem. A, 105, 10525-10537, (2001)
[7] S. Yoo, S.S. Xantheas, in Handbook of Computational Chemistry, ed. by J. Leszczynski (Springer, Berlin, 2011), p. 761
[8] E.D. Sloan, C.A. Koh, Clathrate Hydrates of Natural Gasses, 3rd edn. (CRC Press, Boca Raton, 2008)
[9] Pauling, L., No article title, J. Am. Chem. Soc., 57, 2680-2684, (1935)
[10] Kirov, MV, No article title, J. Struct. Chem., 34, 557-561, (1994)
[11] Xantheas, SS, No article title, Chem. Phys., 258, 225-231, (2000)
[12] Kirov, MV, No article title, J. Struct. Chem., 37, 84-91, (1996)
[13] Anick, DJ, No article title, J. Mol. Struct. (Theochem), 587, 97-110, (2002)
[14] Chihaia, V.; Adams, S.; Kuhs, WF, No article title, Chem. Phys., 297, 271-287, (2004)
[15] McDonald, S.; Ojamae, L.; Singer, SJ, No article title, J. Phys. Chem., 102, 2824-2832, (1998)
[16] Kirov, MV; Fanourgakis, GS; Xantheas, SS, No article title, Chem. Phys. Lett., 461, 180-188, (2008)
[17] Kuo, J-L; Coe, JV; Singer, SJ, No article title, J. Chem. Phys., 114, 2527-2540, (2001)
[18] Anick, DJ, No article title, J. Chem. Phys., 119, 12442-12456, (2003)
[19] Bernal, JD; Fowler, RH, No article title, J. Chem. Phys., 1, 515-548, (1933)
[20] Fowler, PW; Nikolic, S.; Reyesa, R.; Myrvold, W., No article title, Phys. Chem. Chem. Phys., 17, 23257-23264, (2015)
[21] H.J. Berendsen, J. Postma, W. Van Gunsteren, W.F. Hermans, in Intermolecular forces, ed. by B. Pullman (Springer, Dordrecht, 1981), pp. 331-342
[22] Jorgensen, WL; Chandrasekhar, J.; Madura, JD; Impey, RW; Klein, ML, No article title, J. Chem. Phys., 79, 926-935, (1983)
[23] Mahoney, MW; Jorgensen, WL, No article title, J. Chem. Phys., 112, 8910-8922, (2000)
[24] Dang, LX; Pettitt, BM, No article title, J. Phys. Chem., 91, 3349-3354, (1987)
[25] Ren, P.; Ponder, JW, No article title, J. Phys. Chem. B, 107, 5933-5947, (2003)
[26] L.D. Landau, E.M. Lifschitz, Course of Theoretical Physics: The Classical Theory of Fields (Pergamon Press, Oxford, 2009)
[27] Stillinger, FH; Rahman, A., No article title, J. Chem. Phys., 60, 1545-1557, (1974)
[28] Lieb, EH, No article title, Phys. Rev., 162, 162-172, (1967)
[29] E.W. Weisstein, Wolfram Web Resource. http://mathworld.wolfram.com
[30] J.W. Ponder, TINKER, Software Tools for Molecular Design, Version 6.2 (Washington University School of Medicine, Saint Louis, MO, 2012). http://dasher.wustl.edu/tinker
[31] Fanourgakis, GS; Xantheas, SS, No article title, J. Phys. Chem. A, 110, 4100-4106, (2006)
[32] Kirov, MV, No article title, J. Struct. Chem., 47, 691-698, (2006)
[33] Anick, DJ, No article title, J. Chem. Phys., 132, 164311, (2010)
[34] Kirov, MV, No article title, Phys. Chem. Chem. Phys., 18, 27351-27357, (2016)
[35] Kirov, MV, No article title, Phys. A, 388, 1431-1445, (2009)
[36] Lenz, A.; Ojamäe, L., No article title, Phys. Chem. Chem. Phys., 7, 1905-1911, (2005)
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