Abstract
We study the quantum nature of the protons participating in hydrogen bonds in several ice structures by analyzing the one particle density matrix. We find that in all cases, including ice Ih, the most common form of ice, and the high pressure phases, ice VIII, VII, and X, the system is ground-state dominated. However, while the dynamics is uncorrelated in the structures with standard asymmetric hydrogen bonds, such as ice Ih and VIII, local correlations among the protons characterize ice VII and, to a lesser extent, ice X in the so-called low barrier hydrogen bond regime. The correlations appear along the path to hydrogen bond symmetrization, when quantum fluctuations delocalize the proton on the two bond sides. The correlations derive from a strong requirement for local charge neutrality that favors concerted motion along the bonds. The resulting behavior deviates substantially from mean field theory, which would predict in ice VII coherent tunneling of the proton between the two bond sides, thereby causing an ionization catastrophe. Due to the correlations, the quantum state of the proton is entangled.
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Andreani, C., Colognesi, D., Mayers, J., Reiter, G., Senesi, R.: Adv. Phys. 54, 377 (2005)
Soper, A., Benmore, C.: Phys. Rev. Lett. 101, 65502 (2008)
Morrone, J.A., Car, R.: Phys. Rev. Lett. 101, 017801 (2008)
Bratos, S., Diraison, M., Tarjus, G., Leicknam, J.C.: Phys. Rev. A 45, 5556 (1992)
Ramirez, R., Lopez-Ciudad, T., P, P.K., Marx, D.: J. Chem. Phys. 121, 3973 (2004)
Paesani, F., Iuchi, S., Voth, G.A.: J. Chem. Phys. 127, 074506 (2007)
Habershon, S., Fanourgakis, G.S., Manolopoulos, D.E.: J. Chem. Phys. 129, 074501 (2008)
Beck, T.L.: Free Energy Calculations: Theory and Applications in Chemistry and Biology. Springer, Berlin (2007) (Chap. 11, p. 387)
Lin, L., Morrone, J.A., Car, R., Parrinello, M.: Phys. Rev. B 83, 220302(R) (2011)
Bernal, J., Fowler, R.: J. Chem. Phys. 1, 515 (1933)
Pauling, L.: J. Am. Chem. Soc. 57, 2680 (1935)
Stillinger, F., Schweizer, K.: J. Phys. Chem. 87, 4281 (1983)
Schweizer, K., Stillinger, F.: Phys. Rev. B 29, 350 (1984)
Schweizer, K., Stillinger, F.: J. Chem. Phys. 80, 1230 (1984)
Benoit, M., Marx, D., Parrinello, M.: Nature 392, 258 (1998)
Morrone, J.A., Lin, L., Car, R.: J. Chem. Phys. 130, 204511 (2009)
Neto, A., Pujol, P., Fradkin, E.: Phys. Rev. B 74, 024302 (2006)
Bramwell, S., Gingras, M.: Science 294, 1495 (2001)
Feynman, R., Hibbs, A.: Quantum Mechanics and Path Integrals. McGraw-Hill, New York (1965)
Chandler, D., Wolynes, P.: J. Chem. Phys. 74, 4078 (1981)
Hohenberg, P., Kohn, W.: Phys. Rev. 136, B864 (1964)
Kohn, W., Sham, L.: Phys. Rev. 140, A1133 (1965)
Car, R., Parrinello, M.: Phys. Rev. Lett. 55, 2471 (1985)
Marx, D., Parrinello, M.: J. Chem. Phys. 104, 4077 (1996)
Tuckerman, M., Marx, D., Klein, M., Parrinello, M.: J. Chem. Phys. 104, 5579 (1996)
Marx, D., Tuckerman, M., Martyna, G.: Comput. Phys. Commun. 118, 166 (1999)
Morrone, J.A., Srinivasan, V., Sebastiani, D., Car, R.: J. Chem. Phys. 126, 234504 (2007)
Benoit, M., Marx, D.: Chem. Phys. Chem. 6, 1738 (2005)
Robertson, J., Ubbelohde, A.: Proc. R. Soc. Lond. Ser. A 170, 222 (1939)
Lin, L., Morrone, J.A., Car, R., Parrinello, M.: Phys. Rev. Lett. 105, 110602 (2010)
Bove, L.E., Klotz, S., Paciaroni, A., Sacchetti, F.: Phys. Rev. Lett. 103, 165901 (2009)
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Lin, L., Morrone, J.A. & Car, R. Correlated Tunneling in Hydrogen Bonds. J Stat Phys 145, 365–384 (2011). https://doi.org/10.1007/s10955-011-0320-x
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DOI: https://doi.org/10.1007/s10955-011-0320-x