Determining the Height of Energy Barriers of the Cyclohexene Molecule Using Stochastic Approximation

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Resumo

The Monte Carlo method (stochastic approximation) is used for calculating the relative values of density of the states of the cyclohexene molecule in the space of Cremer–Pople coordinates. Using this data, the heights of the energy barriers separating the molecule stereoisomers are estimated.

Sobre autores

A. Teplukhin

Institute of Mathematical Problems of Biology—Branch of the Keldysh Institute of Applied Mathematics, Russian Academy of Sciences

Autor responsável pela correspondência
Email: tepl@impb.ru
142290, Pushchino, Moscow oblast, Russia

Bibliografia

  1. Eliel E.L., Allinger N.L., Angyal S.J., Morrison G.A. Conformational Analysis. New York: Interscience-Wiley, 1965.
  2. Leach A.R. Molecular Modeling: Principles and Applications. Harlow: Pearson Education Ltd., 2001.
  3. Hinchliffe A. Molecular Modelling for Beginners. Chichester: John Wiley & Sons Ltd, 2008.
  4. Jensen F. Introduction to Computational Chemistry. Chichester: John Wiley & Sons Ltd, 2007.
  5. Teplukhin A.V. Parametrization of the torsion potential in all-atom models of hydrocarbon molecules using a simplified expression for the deformation energy of valence bonds and angles // J. Struct. Chem. 2021. V. 62. P. 1653.
  6. Metropolis N., Rosenbluth A.W., Rosenbluth M.N., Teller A.H., Teller E. Equation of state calculations by fast computing machines // J. Chem. Phys. 1953. V. 21. P. 1087.
  7. Liang F., Liu C., Carroll R.J. Advanced Markov Chain Monte Carlo Methods: Learning from Past Samples. Chichester: John Wiley & Sons Ltd, 2010.
  8. Singh S., Chopra M., de Pablo J.J. Density of States–Based Molecular Simulations // Annu. Rev. Chem. Biomol. Eng. 2012. V. 3. P. 369.
  9. Janke W., Paul W. Thermodynamics and structure of macromolecules from flat-histogram Monte Carlo simulations // Soft Matter. 2016. V. 12. P. 642.
  10. Wang F., Landau D.P. Efficient, multiple-range random walk algorithm to calculate the density of states // Phys. Rev. Lett. 2001. V. 86. P. 2050.
  11. Landau D.P., Tsai S.-H., Exler M. A new approach to Monte Carlo simulations in statistical physics: Wang-Landau sampling // Am. J. Phys. 2004. P. 72. P. 1294.
  12. Yan Q., de Pablo J.J. Fast calculation of the density of states of a fluid by Monte Carlo simulations // Phys. Rev. Lett. 2003. V. 90. P. 035701.
  13. Belardinelli R.E., Pereyra V.D. Fast algorithm to calculate density of states // Phys. Rev. E. 2007. V. 75. P. 046701.
  14. Belardinelli R.E., Pereyra V.D. Wang-Landau algorithm: A theoretical analysis of the saturation of the error // J. Chem. Phys. 2007. V. 127. P. 184105.
  15. Liang F., Liu C., Carroll R.J. Stochastic approximation in Monte Carlo computation // J. Am. Statist. Assoc. 2007. V. 102. P. 305.
  16. Robbins H., Monro S. A Stochastic Approximation Method // Ann. Math. Statist. 1951. V. 22. P. 400.
  17. Wasan M.T. Stochastic Approximation. New York: Cambridge University Press, 1969.
  18. Lai T.L. Stochastic approximation // Ann. Statist. 2003. V. 31. P. 391.
  19. Werlich B., Shakirov T., Taylor M.P., Paul W. Stochastic approximation Monte Carlo and Wang–Landau Monte Carlo applied to a continuum polymer model // Comput. Phys. Commun. 2015. V. 186. P. 65.
  20. Zablotskiy S.V., Martemyanova J.A., Ivanov V.A., Paul W. Stochastic approximation Monte Carlo algorithm for calculation of diagram of states of a single flexible-semiflexible copolymer chain // Polym. Sci. ser. A. 2016. V. 58. P. 899.
  21. Shakirov T., Paul W. Folded alkane chains and the emergence of the lamellar crystal // J. Chem. Phys. 2019. V. 150. P. 084903.
  22. Teplukhin A.V. Monte Carlo calculation of thermodynamic and structural characteristics of liquid hydrocarbons // J. Struct. Chem. 2021. V. 62. P. 70.
  23. Allen F.H., Kennard O., Watson D.G., Brammer L., Orpen A.G., Taylor R. Tables of bond lengths determined by X-ray and neutron diffraction. Part 1. Bond lengths in organic compounds // J. Chem. Soc. Perkin Trans. 2. 1987. P. S1.
  24. Cornell W.D., Cieplak P., Bayly C.I., Gould I.R., Merz K.M., Ferguson D.M., Spellmeyer D.C., Fox T., Cald-well J.W., Kollman P.A. A second generation force field for the simulation of proteins, nucleic acids, and organic molecules // J. Am. Chem. Soc. 1995. V. 117. P. 5179.
  25. Jorgensen W.L., Maxwell D.S., Tirado-Rives J. Development and testing of the OPLS all-atom force field on conformational energetics and properties of organic liquids // J. Am. Chem. Soc. 1996. V. 118. P. 11225.
  26. Kilpatrick J.E., Pitzer K.S., Spitzer R. The thermodynamics and molecular structure of cyclopentane // J. Am. Chem. Soc. 1947. V. 69. P. 2483.
  27. Cremer D., Pople J.A. A general definition of ring puckering coordinates // J. Am. Chem. Soc. 1975. V. 97. P. 1354.
  28. Essén H., Cremer D. On the relationship between the mean plane and the least-squares plane of an N-membered puckered ring // Acta Cryst. B. 1984. V. 40. P. 418.
  29. Cremer D. On the correct usage of the Cremer-Pople puckering parameters as quantitative descriptors of ring shapes – a reply to recent criticism by Petit, Dillen and Geise // Acta Cryst. B. 1984. V. 40. P. 498.
  30. Sega M., Autieri E., Pederiva F. Pickett angles and Cremer–Pople coordinates as collective variables for the enhanced sampling of six membered ring conformations // Mol. Phys. 2011. V. 109. P. 141.
  31. Cremer D., Szabo K.J. Ab initio studies of six-membered rings: Present status and future developments // In: Conformational Behavior of Six-Membered Rings: Analysis, Dynamics, and Stereoelectronic Effects / Ed. E. Juaristi. New York: Wiley-VCH, 1995. Ch. 3. P. 59.
  32. McDonald I.R., Singer K. Machine calculation of thermodynamic properties of a simple fluid at supercritical temperatures // J. Chem. Phys. 1967. V. 47. P. 4766.
  33. Chung K.L. Markov chains: With Stationary Transition Probabilities. Berlin: Springer-Verlag, 1967.
  34. Feller W. An Introduction to Probability Theory and its Applications. V. 1. New York: John Wiley & Sons Ltd, 1968.
  35. Hastings W.K. Monte Carlo sampling methods using Markov chains and their applications // Biometrika. 1970. V. 57. P. 97.
  36. Stirzaker D. Stochastic Processes and Models. New York: Oxford University Press, 2005.
  37. Wood W.W., Parker F.R. Monte Carlo equation of state of molecules interacting with the Lennard-Jones potential. I. A supercritical isotherm at about twice the critical temperature // J. Chem. Phys. 1957. V. 27. P. 720.
  38. Fisher I.Z. Applications of the Monte Carlo method in statistical physics // Sov. Phys. Usp. 1960. V. 2. P. 783.
  39. Peskun P.H. Optimum Monte-Carlo sampling using Markov chains // Biometrika. 1973. V. 60. P. 607.
  40. Wichmann B.A., Hill I.D. Generating good pseudo-random numbers // Comput. Statist. Data Anal. 2006. V. 51. P. 1614.
  41. Nevel’son M.B., Has’minskiῐ R.Z. Stochastic Approximation and Recursive Estimation. Providence: American Mathematical Society, 1976.
  42. Anet F.A.L., Haq M.Z. Ring inversion in cyclohexene // J. Am. Chem. Soc. 1965. V. 87. P. 3147.
  43. Scharpen L.H., Wollrab J.E., Ames D.P. Microwave spectrum, structure, and dipole moment of cyclohexene // J. Chem. Phys. 1968. V. 49. P. 2368.
  44. Chiang J.F., Bauer S.H. The molecular structure of cyclohexene // J. Am. Chem. Soc. 1969. V. 91. P. 1898.
  45. Naumov V.A., Dashevskii V.G., Zaripov N.M. Refinement of the molecular structure of cyclohexene // J. Struct. Chem. 1970. V. 11. P. 736.
  46. Rivera-Gaines V.E., Leibowitz S.J., Laane J. Far-infrared spectra, two-dimensional vibrational potential energy surface, and conformation of cyclohexene and its isotopomers // J. Am. Chem. Soc. 1991. V. 113. P. 9742.
  47. Saebø S., Cordell F.R., Boggs J.E. Structures and conformations of cyclopentane, cyclopentene, and cyclopentadiene // J. Mol. Struct. (Theochem). 1983. V. 104. P. 221.
  48. Anet F.A.L., Freedberg D.I., Storer J.W., Houk K.N. On the potential energy surface for ring inversion in cyclohexene and related molecules // J. Am. Chem. Soc. 1992. V. 114. P. 10969.
  49. Shishkina S.V., Shishkin O.V., Leszczynski J. Three-stage character of ring inversion in cyclohexene // Chem. Phys. Lett. 2002. V. 354. P. 428.

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Declaração de direitos autorais © А.В. Теплухин, 2023