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
Benzi, M., Boito, P., Razouk, N.: Decay properties of spectral projectors with applications to electronic structure. SIAM Rev. 55, 3–64 (2013)
Breuer, H.P., Petruccione, F.: The Theory of Open Quantum Systems. Oxford University Press, Oxford (2002)
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)
Cancès, E., Le Bris, C., Lions, P.-L.: Molecular simulation and related topics: some open mathematical problems. Nonlinearity 21, T165–T176 (2008)
Cancès, E., Le Bris, C.: Mathematical modeling of point defects in materials science. M3AS 23(10), 1795–1859 (2013)
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)
Le Bris, C.: Computational chemistry from the perspective of numerical analysis. Acta Numer. 14, 363–444 (2005)
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)
Le Bris, C., Lions, P.-L.: From atoms to crystals: a mathematical journey Bull. Amer. Math. Soc. 42, 291–363 (2005)
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)
Resta, R.: Electrical polarization and orbital magnetization: the modern theories. J. Phys. Condens. Matter 22, 123201–123220 (2010)
Schulz-Baldes, H., Teufel, S.: Orbital polarization and magnetization for independent particles in disordered media. Commun. Math. Phys. 319, 649–681 (2013)
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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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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DOI: https://doi.org/10.1007/978-3-319-06379-9_13
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