Dynamics of proton tunneling in Hydrogen-Bonded systems through Green's function formalism

Luca Nanni*    -  University of Ferrara, Italy

(*) Corresponding Author
DOI: 10.21580/jnsmr.v10i1.20095
This study proposes a new theoretical model based on Green's function formalism for studying proton tunneling via hydrogen bonding. This approach allows calculating the tunneling probability and the tunneling energy that proton transfer occurs along a given path inferred a priori. The method is extended to multiple protons tunneling, characterizing the behaviour of some biological molecules. Specifically, the cases of the proton transfer in the Fujicurin A molecule and the double proton tunneling in the Guanine-Cytosine base-pair are investigated. The new approach is an alternative to those present in the literature. It allows straightforwardly predicting the mechanisms of intramolecular and intermolecular proton transfers involving the rearrangement of conjugated electrons.

Keywords: Green function; path integral method; proton tunneling; hydrogen bonding

  1. Angiolari, F., Huppert, S., Pietrucci, F., & Riccardo, S. (2023). Environmental and Nuclear Quantum Effects on Double Proton Transfer in the Guanine–Cytosine Base Pair. Journal of Physical Chemistry Letters, 14(22), 5102–5108. https://doi.org/https://doi.org/10.1021/acs.jpclett.3c00747.
  2. Baradaran, M., & Panahi, H. (2017). Exact Solutions of a Class of Double-Well Potentials: Algebraic Bethe Ansatz. Advances in High Energy Physics. https://doi.org/https://doi.org/10.1155/2017/8429863
  3. Barton, G. (2005). Elements of Green’s Functions and Propagation. A Clarendon Press Publication.
  4. Beardon, A. F., & Minda, D. (2003). On the Pointwise Limit of Complex Analytic Functions. The American Mathematical Monthly, 110(4), 289–297. https://doi.org/https://doi.org/10.2307/3647878
  5. Bountis, T. (1992). Proton Transfer in Hydrogen-Bonded Systems (NATO Scien).
  6. Butenhoff, T. J., & Moore, C. B. (1988). Hydrogen atom tunneling in the thermal tautomerism of porphine imbedded in a n-hexane matrix. American Chemical Society, 110(25), 8336–8341. https://doi.org/https://doi.org/10.1021/ja00233a009
  7. Cheng, Y.-H., Zhu, Y.-C., Kang, W., Li, X., & Fang, W. (2022). Determination of concerted or stepwise mechanism of hydrogen tunneling from isotope effects: Departure between experiment and theory. The Journal of Chemical Physics, 156(12). https://doi.org/https://doi.org/10.1063/5.0085010.
  8. Faulder, P. F., Tresadern, G., Chohan, K. K., Scrutton, N. S., Sutcliffe, M. J., Hillier, I. H., & Burton, N. A. (2001). QM/MM Studies Show Substantial Tunneling for the Hydrogen-Transfer Reaction in Methylamine Dehydrogenase. Journal of American Chemical Society, 123(35), 8604–8605. https://doi.org/https://doi.org/10.1021/ja016219a
  9. Fiedler, L., Gao, J., & Truhlar, D. G. (2011). Polarized Molecular Orbital Model Chemistry. 1. Ab Initio Foundations. Journal of Chemical Theory and Computation, 7(4), 852–856. https://doi.org/https://doi.org/10.1021/ct1006373
  10. Fillaux, F., Cousson, A., & Gutmann, M. J. (2007). Evidence for Coherent Proton Tunneling in a Hydrogen Bond Network. Pure and Applied Chemistry, 79(6), 1023–1039. https://doi.org/https://doi.org/10.1351/pac200779061023
  11. Golo, V. L., & Volkov, Y. S. (2003). Tunneling of protons and tautomeric transitions in base pairs of DNA. International Journal of Modern Physics C, 14(01), 133–156. https://doi.org/https://doi.org/10.1142/S0129183103004280
  12. Hans-Heinrich Limbach, Hennig, J., Gerritzen, D., & Rumpel, H. (1982). Primary kinetic HH/HD/DH/DD isotope effects and proton tunnelling in double proton-transfer reactions. Faraday Discuss. Chem. Soc., 74, 229–243. https://doi.org/DOI https://doi.org/10.1039/DC9827400229
  13. Herrera, W. J., Vinck-Posada, H., & Paez, S. G. (2021). Green’s functions in quantum mechanics courses. Physics Education. https://doi.org/https://doi.org/10.1119/5.0065733
  14. Horsewill, A. J., Jones, N. H., & Caciuffo, R. (2001). Evidence for Coherent Proton Tunneling in a Hydrogen Bond Network. Science, 291(5501), 100–103. https://doi.org/DOI: 10.1126/science.291.5501.100
  15. Jana, K., & Ganguly, B. (2018). DFT studies on quantum mechanical tunneling in tautomerization of three-membered rings. Physical Chemistry Chemical Physics, 44(20), 28049–28058. https://doi.org/https://doi.org/10.1039/C8CP03963A.
  16. Klinman, J. P., & Kohen, A. (2013). Hydrogen tunneling links protein dynamics to enzyme catalysis. Annual Reviews of Biochemistry, 82, 471–496. https://doi.org/10.1146/annurev-biochem-051710-133623
  17. Krishtalik, L. I. (2000). Review: The mechanism of the proton transfer: an outline. Biochimica et Biophysica Acta, 1458(1), 6–27. https://doi.org/https://doi.org/10.1016/S0005-2728(00)00057-8
  18. Kumar, A., & Sevilla, M. D. (2009). Influence of Hydration on Proton Transfer in the Guanine−Cytosine Radical Cation (G•+−C) Base Pair: A Density Functional Theory Study. Journal of Physical Chemistry B, 113(33), 11359–11361. https://doi.org/https://doi.org/10.1021/jp903403d.
  19. Lambert, C. J. (2021). Quantum Transport in Nanostructures and Molecules: An introduction to molecular electronics. IOP Publishing.
  20. Limbach, H.-H., Lopez, J. M., & Kohen, A. (2006). Arrhenius curves of hydrogen transfers: tunnel effects, isotope effects and effects of pre-equilibria. Philos Trans R Soc Lond B Biol Sci., 361(1472), 1399–1415. https://doi.org/https://doi.org/10.1098/rstb.2006.1872
  21. Linderberg, J. (2004). Propagators in quantum chemistry. Wiley-Interscience.
  22. Marais, A., Adams, B., Ringsmuth, A. K., Ferretti, M., Gruber, J. M., Hendrikx, R., Schuld, M., Smith, S. L., Sinayskiy, I., Krüger, T. P. J., Petruccione, F., & Grondelle, R. van. (2018). The future of quantum biology. Journal of the Royal Society Interface, 15(20180640). https://doi.org/https://doi.org/10.1098/rsif.2018.0640
  23. Matsui, H. (2022). Lorentzian path integral for quantum tunneling and WKB approximation for wave-function. General Relativity and Quantum Cosmology, 82(426). https://doi.org/https://doi.org/10.1140/epjc/s10052-022-10374-1
  24. McMahon, R. J. (2003). Chemical Reactions Involving Quantum Tunneling. Science, 2994(5608), 833–883. https://doi.org/DOI: 10.1126/science.1080715
  25. Meng, X., Guo, J., Peng, J., Chen, J., Wang, Z., Shi, J.-R., Li, X.-Z., Wang, E.-G., & Jiang, Y. (2015). Direct visualization of concerted proton tunnelling in a water nanocluster. Nature Physics Volume, 11, 235–239. https://doi.org/https://doi.org/10.1038/nphys3225
  26. Nanni, L. (2022). The product arbitrariness of generalised functions and its role in quantum field theory. Journal of Physics Communications, 6(3). https://doi.org/https://doi.org/10.1088/2399-6528/ac5d07.
  27. Onuchic, J. N., de Andrade, P. C. P., & Beratan, D. N. (1991). Electron tunneling pathways in proteins: A method to compute tunneling matrix elements in very large systems. The Journal of Chemical Physics, 95(2), 1131–1138. https://doi.org/https://doi.org/10.1126/science.1334572.
  28. Pinotsi, D., Grisanti, L., Mahou, P., Gebauer, R., Kaminski, C. F., Hassanali, A., & Schierle, G. S. K. (2016). Proton Transfer and Structure-Specific Fluorescence in Hydrogen Bond-Rich Protein Structures. Journal of American Chemical Society, 138(9), 3046–3057. https://doi.org/https://doi.org/10.1021/jacs.5b11012
  29. Ranaghan, K. E., Morris, W. G., Masgrau, L., Senthilkumar, K., Johannissen, L. O., Scrutton, N. S., Harvey, J. N., Manby, F. R., & Mulholland, A. J. (2017). Ab Initio QM/MM Modeling of the Rate-Limiting Proton Transfer Step in the Deamination of Tryptamine by Aromatic Amine Dehydrogenase. Journal of Physical Chemistry B, 121(42), 9785–9798. https://doi.org/https://doi.org/10.1021/acs.jpcb.7b06892
  30. Sapse, A.-M. (1998). Molecular orbital calculations for biological systems. Oxford academics books.
  31. Sarai, A., & DeVault, D. (1986). Proton tunneling. Methods in Enzymology, 127, 79–91.
  32. Scheiner, S., Redfern, P., & Hillenbrand, E. A. (1986). Factors influencing proton positions in biomolecules. International Journal of Quantum Chemistry, 29, 817–827. https://doi.org/https://doi.org/10.1002/qua.560290420
  33. Schreiner, P. R., Wagner, J. P., Reisenauer, H. P., Gerbig, D., Ley, D., Sarka, J., Császár, A. G., Vaughn, A., & Allen, W. D. (2015). Domino Tunneling. Journal of American Chemical Society, 137(24), 7828–7834. https://doi.org/https://doi.org/10.1021/jacs.5b03322
  34. Seremet, V. D. (2022). Handbook of Green’s Functions and Matrices.
  35. Setten, M. J. van, Caruso, F., Sharifzadeh, S., Ren, X., Scheffler, M., Liu, F., Lischner, J., Lin, L., Deslippe, J. R., Louie, S. G., Yang, C., Weigend, F., Neaton, J. B., Evers, F., & Rinke, P. (2015). GW100: Benchmarking G0W0 for Molecular Systems. Journal of Chemical Theory and Computation, 11(12), 5665–5687. https://doi.org/https://doi.org/10.1021/acs.jctc.5b00453
  36. Sieber, M. (2007). Wavefunctions, Green’s functions and expectation values in terms of spectral determinants. Chaotic Dynamics. https://doi.org/https://doi.org/10.1088/0951-7715/20/11/013
  37. Slocombe, L., Sacchi, M., & Al-Khalili, J. (2022). An open quantum systems approach to proton tunnelling in DNA. Communications Physics, 5(109). https://doi.org/https://doi.org/10.1038/s42005-022-00881-8
  38. Sole, J., González-Lafont, À., & Lluch, J. M. (2020). A protocol to obtain multidimensional quantum tunneling corrections derived from QM(DFT)/MM calculations for an enzyme reaction. Physical Chemistry Chemical Physics, 46. https://doi.org/https://doi.org/10.1039/D0CP05265E
  39. Soler-Polo, D., Mendieta-Moreno, J. I., Trabada, D. G., Mendieta, J., & Ortega, J. (2019). Proton Transfer in Guanine-Cytosine Base Pairs in B-DNA. Journal of Chemical Theory and Computation, 15(12), 6984–6991. https://doi.org/https://doi.org/10.1021/acs.jctc.9b00757.
  40. Stuke, A., Kunkel, C., Golze, D., Todorović, M., Margraf, J. T., Reuter, K., Rinke, P., & Oberhofer, H. (2020). Atomic structures and orbital energies of 61,489 crystal-forming organic molecules. Scientific Data, 7(58). https://doi.org/https://doi.org/10.1038/s41597-020-0385-y.
  41. Takaya, D., Watanabe, C., Nagase, S., Kamisaka, K., Okiyama, Y., Moriwaki, H., Yuki, H., Sato, T., Kurita, N., Yagi, Y., Takagi, T., Kawashita, N., Takaba, K., Ozawa, T., Takimoto-Kamimura, M., Tanaka, S., Fukuzawa, K., & Honma, T. (2021). FMODB: The World’s First Database of Quantum Mechanical Calculations for Biomacromolecules Based on the Fragment Molecular Orbital Method. Journal of Chemical Information and Modeling, 61, 777–794. https://doi.org/https://doi.org/10.1021/acs.jcim.0c01062.
  42. Tanaka, H., Kuwahata, K., Tachikawa, M., & Udagawa, T. (2022). Low-Barrier Hydrogen Bond in Fujikurin A–D: A Computational Study. ACS Omega, 7(16), 14244–14251. https://doi.org/https://doi.org/10.1021/acsomega.2c00857.
  43. Tikhonov, D. S. (2022). A simplistic computational procedure for tunneling splittings caused by proton transfer. Structural Chemistry, 33, 351–362. https://doi.org/https://doi.org/10.1007/s11224-021-01845-4.
  44. Unke, O. T., Chmiela, S., Sauceda, H. E., Gastegger, M., Poltavsky, I., Schütt, K. T., Tkatchenko, A., & Müller, K.-R. (2021). Machine Learning Force Fields. Chemical Review, 121(16), 10142–10186. https://doi.org/https://doi.org/10.1021/acs.chemrev.0c01111
  45. Vshivtsev, A. S., Korolev, A. F., Kruglov, K. G., & Tatarintsev, A. V. (1998). Potential model for tunnel proton transfer in hydrogen bond theory. Russian Physics Journal, 41, 399–407. https://doi.org/https://doi.org/10.1007/BF02766496.
  46. Werner, H.-J., Knowles, P. J., Knizia, G., Manby, F. R., & Schütz, M. (2011). Molpro: a general-purpose quantum chemistry program package. WIREs Computational Molecular Science. https://doi.org/https://doi.org/10.1002/wcms.82

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