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Some (Important?) Unsolved Mathematical Problems in Molecular Simulation

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Many-Electron Approaches in Physics, Chemistry and Mathematics

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Abstract

This short contribution presents some, in the author’s opinion, unsolved or unsatisfactorily solved mathematical questions in molecular simulation and related topics. Many such questions exist and the particular choice made here aims to emphasize some specific questions that, again in the author’s opinion, would have important and immediate consequences on the current practice of molecular simulation.

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References

  1. Benzi, M., Boito, P., Razouk, N.: Decay properties of spectral projectors with applications to electronic structure. SIAM Rev. 55, 3–64 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  2. Breuer, H.P., Petruccione, F.: The Theory of Open Quantum Systems. Oxford University Press, Oxford (2002)

    MATH  Google Scholar 

  3. Cancès, E., Defranceschi, M., Kutzelnigg, W., Le Bris, C., Maday, Y.: Computational quantum chemistry: a primer. In: Handbook of Numerical Analysis, Special Volume: Computational Chemistry, North Holland, Amsterdam (2003)

    Google Scholar 

  4. Cancès, E., Le Bris, C., Lions, P.-L.: Molecular simulation and related topics: some open mathematical problems. Nonlinearity 21, T165–T176 (2008)

    Article  ADS  MATH  Google Scholar 

  5. Cancès, E., Le Bris, C.: Mathematical modeling of point defects in materials science. M3AS 23(10), 1795–1859 (2013)

    MATH  Google Scholar 

  6. Catto, I., Le Bris, C., Lions, P.-L.: The Mathematical Theory of Thermodynamic Limits: Thomas-Fermi Type Models. Oxford University Press, Oxford Mathematical Monographs (1998)

    Google Scholar 

  7. Le Bris, C.: Computational chemistry from the perspective of numerical analysis. Acta Numer. 14, 363–444 (2005)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  8. Le Bris, C.: Mathematical and numerical analysis for molecular simulation: accomplishments and challenges. In: Proceedings of the International Congress of Mathematicians Madrid 2006, pp. 1507–1522. EMS (2006)

    Google Scholar 

  9. Le Bris, C., Lions, P.-L.: From atoms to crystals: a mathematical journey Bull. Amer. Math. Soc. 42, 291–363 (2005)

    Article  MATH  Google Scholar 

  10. Le Bris, C., Lelièvre, T., Luskin, M., Perez, D.: A mathematical formalization of the parallel replica dynamics. Monte-Carlo Methods Appl. 18, 119–146 (2012)

    MATH  MathSciNet  Google Scholar 

  11. Resta, R.: Electrical polarization and orbital magnetization: the modern theories. J. Phys. Condens. Matter 22, 123201–123220 (2010)

    Article  ADS  Google Scholar 

  12. Schulz-Baldes, H., Teufel, S.: Orbital polarization and magnetization for independent particles in disordered media. Commun. Math. Phys. 319, 649–681 (2013)

    Article  ADS  MATH  MathSciNet  Google Scholar 

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Acknowledgments

The author is grateful to E. Cancès, V. Ehrlacher, F. Legoll, T. Lelièvre, G. Stoltz for their remarks on a preliminary version of the manuscript.

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Correspondence to Claude Le Bris .

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Le Bris, C. (2014). Some (Important?) Unsolved Mathematical Problems in Molecular Simulation. In: Bach, V., Delle Site, L. (eds) Many-Electron Approaches in Physics, Chemistry and Mathematics. Mathematical Physics Studies. Springer, Cham. https://doi.org/10.1007/978-3-319-06379-9_13

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