Molecular simulation and related topics: Some open mathematical problems

Nonlinearity

Volumn 21, Issue 9, 2008, Pages

  Cancès, Eric ^a,b   Le Bris, C ^a,b   Lions, P L ^c,d  

^a UNIVERSITÉ PARIS EST   (France)

^b INRIA ROCQUENCOURT   (France)

^c l'alimentation et l'Environnement   (France)

^d UNIVERSITÉ PARIS DAUPHINE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 51849119130     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/21/9/T03     Document Type: Article

References (31)

1. Aftalion A, Blanc X and Nier F 2006 Lowest Landau level functional and Bargmann spaces for Bose-Einstein condensates J. Funct. Anal. 241 661-702
2. Barrault M, Cancès E, Hager W and Le Bris C 2007 Multilevel domain decomposition for electronic structure calculations J. Comput. Phys. 222 86-109
3. Blanc X and Le Bris C 2002 Periodicity of the infinite-volume ground state of a one-dimensional quantum model Nonlinear Anal. Theory, Methods, Appl. 48 791-803
4. Blanc X, Le Bris C and Lions P-L 2007 Atomistic to continuum limits for computational materials science Math. Modelling Numer. Anal. 41 391-426
5. Cancès E, Defranceschi M, Kutzelnigg W, Le Bris C and Maday Y 2003 Computational quantum chemistry: a primer Handbook of Numerical Analysis, Special Volume: Computational Chemistry vol I (Amsterdam: North Holland)
6. Cancès E, Galicher H and Lewin M 2006 Computing electronic structures: a new multiconfiguration approach for excited states J. Comput. Phys. 212 73-98
7. Cancès E, Jourdain B and Lelièvre T 2006 Quantum Monte Carlo simulation of fermions Math. Models Methods Appl. Sci. 16 1403-40
8. Cancès E, Legoll F and Stoltz G 2007 Theoretical and numerical comparison of some sampling methods for molecular dynamics Math. Modelling Numer. Anal. 41 351-89
9. Catto I, Le Bris C and Lions P-L 1998 The Mathematical Theory of Thermodynamic Limits: Thomas-Fermi Type Models (Oxford Mathematical Monographs) (Oxford: Oxford University Press)
10. Dellago C, Bolhuis P G and Geissler P L 2002 Transition path sampling Adv. Chem. Phys. 123 1-78
11. Friesecke G and Theil F 2006 A proof of crystallization in two dimensions Commun. Math. Phys. 262 209-36 (see also works in preparation by G Friesecke)
12. Golab J T, Yeager D L and Jørgensen P 1985 Multiple stationary point representation in MCSCF calculations Chem. Phys. 93 83-100
13. Hales T C 1992 The sphere packing problem J. Comput. Appl. Math. 44 41-76
14. Hewitt E and Savage L J 1955 Symmetric measures on Cartesian products Trans. Am. Math. Soc. 80 470-501
15. Hohenberg P and Kohn W 1964 Inhomogeneous electron gas Phys. Rev. B 136 864-71
16. Hylleraas E A and Undheim B 1930 Numerische Berechnung der 2 S-Terme von Ortho- und Par-Helium Z. Phys. 65 759-72
17. Jørgensen P, Olsen P and Yeager D L 1981 Generalizations of Newton-Raphson and multiplicity independent Newton-Raphson approaches in multiconfigurational Hartree-Fock theory J. Chem. Phys. 75 5802-15
18. Kohn W and Sham L J 1965 Self-consistent equations including exchange and correlation effects Phys. Rev. 140 A1133-8
19. Le Bris C 2005 Computational chemistry from the perspective of numerical analysis Acta Numer. 14 363-444
20. Le Bris C 2006 Mathematical and numerical analysis for molecular simulation: accomplishments and challenges Proc. Int. Congr. Mathematicians (Madrid, 2006) pp 1507-22 (EMS)
21. Le Bris C and Lions P-L 2005 From atoms to crystals: a mathematical journey Bull. Am. Math. Soc. 42 291-363
22. Lewin M 2004 Solutions of the multiconfiguration equations in quantum chemistry Arch. Ration Mech. Anal. 171 83-114
23. Lieb E H 1983 Density functionals for Coulomb systems Int. J. Quantum Chem. 24 243-77
24. Lieb E H and Simon B 1977 The Hartree-Fock theory for Coulomb systems Commun. Math. Phys. 53 185-94
25. Lions P-L 1987 Solutions of Hartree-Fock equations for Coulomb systems Commun. Math. Phys. 109 33-97
26. Lions P-L 2007-2008 Course at College de France, Academic year 2007-2008 video downloadable at http://www.college-de-france.fr/default/EN/all/college_en/
27. MacDonald J K L 1933 Successive approximations by the Rayleigh-Ritz variation method Phys. Rev. 43 830-3
28. Olla S, Varadhan S R S and Yau H T 1993 Hydrodynamic limit for a Hamiltonian system with weak noise Commun. Math. Phys. 155 523-60
29. Solovej J P 2003 The ionization conjecture in Hartree-Fock theory Ann. Math. 158 509-76
30. Stuart A M, Voss J and Wiberg P 2004 Conditional path sampling of SDEs and the Langevin MCMC Commun. Math. Sci. 2 685-97
31. Zhislin G M 1960 Discussion of the spectrum of Schrödinger operators for systems of many particles Trudy Moskovskogo Mat. Obscestva 9 81-120 (in Russian)