Eric CANCES


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Research:

Fields of research: 
  • Mathematical and numerical analysis of electronic structure models for quantum chemistry and materials science
  • Molecular dynamics and exploration of potential energy surfaces
  • Laser control of quantum processes
  • Multiscale modelling 
Visit the website of our Molecular and Multiscale Modeling group. 

PhD thesis (1998): Molecular Simulation and Environmental Effects: A Mathematical and Numerical Perspective

Habilitation thesis (2003): Contributions to the mathematical and numerical study of some models arising in molecular and multiscale simulations


Teaching:

Professor at the Ecole des Ponts - ParisTech: 
  • Numerical Analysis (1997-2005) 
  • Analysis (since 1999) 
  • Quantum Physics (1999-2001) 
  • Modelling in engineering problems (2000-2002)
Associate professor at the Ecole Polytechnique: 
  • Numerical analysis and optimization (since 2004) 
University of Paris-Dauphine: 
  • DEA EDPA - Equations aux Dérivées Partielles et Applications: Mathematical and numerical analysis of Quantum Chemistry models (2000-2004) 
University Pierre and Marie Curie (Paris 6): 
  • M2 Mathématiques de la modélisation: Molecular simulation (since 2005)


Scientific awards:

Le Rivot Prize 1992 from the French Academy of Sciences
Ecole des Ponts PhD prize 1998
Blaise Pascal Prize 2009 from SMAI and the French Academy of Sciences


Editorial activities:

ESAIM: Proceedings (ESAIM: Proc), Editor-in-Chief, with P. Del Moral and J.-F. Gerbeau, 2006-2011
Mathematical Modelling and Numerical Analysis (M2AN), 2006-
SIAM Journal of Scientific Computing (SISC), 2008-
Communications in Mathematical Sciences (CMS), 20011-


Publications:

Books, book chapters, survey articles: 
  • E. Cancès, SCF algorithms for Hartree-Fock electronic calculations, in Lecture Notes in Chemistry 74 (Springer 2000) 17-43.
  • E. Cancès, M. Defranceschi, W. Kutzelnigg, C. Le Bris and Y. Maday, Computational quantum chemistry: a primer, in: Handbook of numerical analysis. Volume X: special volume: computational chemistry, Ph. Ciarlet and C. Le Bris eds (North-Holland, 2003) 3-270.  
  • E. Cancès, C. Le Bris and Y. Maday, Méthodes mathématiques en chimie quantique, Springer 2006.
  • E. Cancès, Integral equation approaches for continuum models, in: Continuum solvation models in Chemical Physics, From theory to applications, B. Mennucci and R. Cammi, eds (Wiley 2007) 29-48.
  • E. Cancès, C. Le Bris and P.-L. Lions, Molecular simulation and related topics: some open mathematical problems, Nonlinearity 21 (2008) T165-T176.
  • E. Cancès, M. Lewin and G. Stoltz, The microscopic origin of the macroscopic dielectric permittivity of crystals, in: Lecture Notes in Computational Science and Engineering 82 (Springer 2011).
 
Electronic structure of materials:
  • E Cancès, A. Deleurence and M. Lewin, A new approach to the modeling of local defects in crystals: The reduced Hartree-Fock case, Comm. Math. Phys. 281 (2008) 129-177.
  • E. Cancès, A. Deleurence and M. Lewin, Non-perturbative embedding of local defects in crystalline materials, J. Phys.: Condens. Matter 20 (2008) 294213.
  • E. Cancès and M. Lewin, The dielectric permittivity of crystals in the reduced Hartree-Fock approximation, Arch. Ration. Mech. Anal. 197 (2010) 139-177.
  • E. Cancès and V. Ehrlacher, Local defects are always neutral in the Thomas-Fermi-von Weiszńcker theory of crystals, Arch. Ration. Mech. Anal. 202 (2011) 933-973.
  • E. Cancès and G. Stoltz, A mathematical formulation of the random phase approximation for crystals, Ann. Inst. Henri Poincaré 29 (2012) 887-925.
  • E. Cancès, S. Lahbabi and M. Lewin, Mean-field models for disordered crystals, J. Math. Pures App., in press.

Numerical analysis of eigenvalue problems:
  • E. Cancès, R. Chakir and Y. Maday, Numerical analysis of nonlinear eigenvalue problems, J. Sci. Comput. 45 (2010) 90-117.
  • W. Hager, G. Bencteux, E. Cancès and C. Le Bris, Analysis of a quadratic programming decomposition algorithm, SIAM J. Numer. Anal. 47 (2010) 4517-4539.
  • E. Cancès, R. Chakir and Y. Maday, Numerical analysis of the planewave discretization of orbital-free and Kohn-Sham models, M2AN (highlight article) 46 (2012) 341-388.
  • E. Cancès, V. Ehrlacher and Y. Maday, Periodic Schr÷dinger operators with local defects and spectral pollution, SIAM J. Numer. Anal. 46 (2012) 3016-3035.
  • E. Cancès, V. Ehrlacher and Y. Maday, Non-consistent approximations of self-adjoint eigenproblems: applications to the supercell method, arXiv 1205.0331

Greedy algorithms:
  • E. Cancès, V. Ehrlacher and T. Lelièvre, Convergence of a greedy algorithm for high-dimensional convex nonlinear problems, Math. Mod. and Meth. in App. Sci. 21 (2011) 2433-2467.
  • E. Cancès, V. Ehrlacher and T. Lelièvre, Greedy algorithms for high-dimensional non-symmetric linear problems, arXiv:1210.6688

Mathematical analysis of electronic structure models:
  • E. Cancès and C. Le Bris, On the perturbation methods for some nonlinear quantum chemistry models, Math. Mod. and Meth. in App. Sci. 8 (1998) 55-94.  
  • E. Cancès and C. Le Bris, On the time-dependent Hartree-Fock equations coupled with a classical nuclear dynamics, Math. Mod. and Meth. in App. Sci. 9 (1999) 963-990. 
  • X. Blanc and E. Cancès,  Nonlinear instability of density-independent orbital-free kinetic energy functionals, J. Chem. Phys. 122 (2005) 214106.
  • E. Cancès, M. Lewin and G. Stoltz, The electronic ground-state energy problem: A new reduced density matrix approach, J. Chem. Phys. 125 (2006) 064101.
  • E. Cancès, B. Jourdain and T. Lelièvre, Quantum Monte Carlo simulation of fermions. A mathematical analysis of the fixed node approximation, Math. Mod. and Meth. in App. Sci. 16 (2006) 1403-1440.
  • A. Anantharaman and E. Cancès, Existence of minimizers for Kohn-Sham models in quantum chemistry, Ann. Inst. Henri Poincaré 26 (2009) 2425-2455.
 
Algorithms for electronic structure calculations:
  •  E. Cancès and C. Le Bris, On the convergence of SCF algorithms for the Hartree-Fock equations, M2AN 34 (2000) 749-774.
  • E. Cancès and C. Le Bris Can we outperform the DIIS approach for electronic structure calculations?, Int. J. Quantum Chem. 79 (2000) 82-90.   
  • E. Cancès, SCF algorithms for Kohn-Sham models with fractional occupation numbers, J. Chem. Phys. 114 (2001) 10616-16622.
  • K.N. Kudin, G.E. Scuseria and E. Cancès, A black-box self-consistent field convergence algorithm: one step closer, J. Chem. Phys. 116 (2002) 8255-8261.
  • E. Cancès, C. Le Bris, Y. Maday, and G. Turinici, Towards reduced basis approaches in ab initio electronic structure computations, Journal of Scientific Computing 17 (2002) 461-469.
  • E. Cancès, K.N. Kudin, G.E. Scuseria and G. Turinici, Quadratically convergent algorithm for fractional occupation numbers, J. Chem. Phys. 118 (2003) 5364-5368.
  • E. Cancès, Galicher and M. Lewin, Computing electronic structures: A new multiconfiguration approach for excited states, J. Comput. Phys. 212 (2006) 73-98.
  • E. Cancès, M. Caffarel, T. Lelièvre, A. Scemama and G. Stoltz, An efficient sampling algorithm for Variational Monte Carlo , J. Chem. Phys. 125 (2006) 114105 .
  • M. Barrault, E. Cancès, W.W. Hager and C. Le Bris, Multilevel domain decomposition for electronic structure calculations , J. Comput. Phys. 222 (2007) 86-109.
  • E. Cancès and K. Pernal, Projected gradient algorithms for Hartree-Fock and density-matrix functional theory, J. Chem. Phys. 128 (2008) 134108.

Optimized effective potential:
  • A. Ben Haj Yedder, E. Cancès and C. Le Bris, Mathematical remarks on the optimized effective potential problem, Int. Diff. Eq. 17 (2004) 331-368.
  • A.F. Izmaylov, V.N. Staroverov, G.E. Scuseria, E.R. Davidson, G. Stoltz and E. Cancès, The effective local potential method: Implementation for molecules and relation to approximate optimized effective potential techniques, J. Chem. Phys. 126 (2007) 084107.
  • E. Cancès, G. Stoltz, V.N. Staroverov, G.E. Scuseria, and E.R. Davidson, Local exchange potentials for electronic structure calculations, MathematicS In Action 2 (2009) 1-42.

Implicit solvation models:
  • E. Cancès, B. Mennucci and J. Tomasi, A new integral equation formalism for the polarizable continuum model: theoretical background and applications to isotropic and anisotropic dielectrics, J. Chem. Phys. 101 (1997) 10506-10517. 
  • B. Mennucci, E. Cancès and J. Tomasi, Evaluation of solvent effects in isotropic and anisotropic dielectrics, and in ionic solutions with a unified integral equation method: theoretical bases, computational implementation and numerical applications, J. Phys. Chem. 107 (1997) 3032-3041.
  • C. Amovilli, V. Barone, R. Cammi, E. Cancès, M. Cossi, B. Mennucci, C. S. Pomelli and J. Tomasi, Recent advances in the description of solvent effects with the polarizable continuum model, Adv. Quantum Chem. 32 (1998) 227. 
  • E. Cancès and B. Mennucci, New applications of integral equation methods for solvation continuum models: ionic solutions and liquid crystals, J. Math. Chem. 23 (1998) 309-326. 
  • E. Cancès and B. Mennucci, Analytical derivatives for geometry optimization in solvation continuum models I: Theory, J. Chem. Phys. 109 (1998) 249-259. 
  • E. Cancès, B. Mennucci and J. Tomasi, Analytical derivatives for geometry optimization in solvation continuum models II: Numerical applications, J. Chem. Phys. 109 (1998) 260-266.
  • E. Cancès, C. Le Bris, B. Mennucci and J. Tomasi, Integral Equation Methods for Molecular Scale Calculations in the liquid phase, Math. Mod. and Meth. in App. Sci 9 (1999) 35-44. 
  • J. Tomasi, B. Mennucci and E. Cancès, The IEF version of the PCM solvation method: an overview of a new method addressed to study molecular solutes at the QM ab initio level, J. Mol. Struct. THEOCHEM 464 (1999) 211.
  • E. Cancès and B. Mennucci, The escaped charge problem in solvation continuum models, J. Chem. Phys. 115 (2001) 6130-6135.
  • F. Lipparini, G. Scalmani, B. Mennucci, E. Cancès, M. Caricato, and M.J. Frisch, A variational formulation of the polarizable continuum model, J. Chem. Phys. 133 (2010) 014106.

Localization of electrons in molecules:
  • E. Cancès, R. Keriven, F. Lodier and A. Savin, How electrons guard the space: shape optimization with probability distribution criteria, Theoret. Chem. Acc. 111 (2004) 373-380.
  • A. Gallegos, R. Carbo-Dorca, F. Lodier, E. Cancès and A. Savin, Maximal probability domains in linear molecules, J. Comput. Chem. 26 (2005) 455-460.

Molecular dynamics and exploration of potential energy surfaces
  • (with F. Castella, Ph. Chartier, E. Faou, C. Le Bris, F. Legoll and G. Turinici) High order integration formulae with error bounds for statistical average calculations by molecular dynamics simulations, J. Chem. Phys. 121 (2004) 10346.
  • (with F. Castella, Ph. Chartier, E. Faou, C. Le Bris, F. Legoll and G. Turinici) Long-time averaging using symplectic solvers with application to molecular dynamics,  Numer. Math. 100 (2005) 211-232.
  • (with F. Legoll and G. Stoltz) Theoretical and numerical comparison of some sampling methods for molecular dynamics, Preprint IMA 2040 (2005).
  • (with M.-C. Marinica, F. Legoll, K. Minoukadeh and F. Willaime) Some improvements of the ART method for finding transition pathways on potential energy surfaces, J. Chem. Phys. 130 (2009) 114711.

Laser control of molecular processus:
  • (with A. Ben-Haj-Yedder and C. Le Bris) Optimal laser control of chemical reactions using automatic differentiation, Proceedings of Automatic Differentiation 2000: From Simulation to Optimization, Springer-Verlag  (2001) 203-213. 
  • (with A. Auger,  C. Dion, A. Ben Haj Yedder, A. Keller, C. Le Bris  and  O. Atabek) Optimal laser control of chemical reactions: methodology and results, Math. Mod. and Meth. in App. Sci. 12 (2002) 1281-1315.
  • (with A. Ben Haj-Yedder, A. Auger, C. M. Dion, A. Keller, C. Le Bris, and O. Atabek) Numerical optimization of laser fields to control molecular orientation, Phys. Rev. A 66 (2002) 063401.
  • (with C. Dion, A. Ben Haj Yedder, C. Le Bris, A. Keller and  O. Atabek) Optimal laser control of orientation: the kicked molecule, Phys. Rev. A 65 (2002) 063408.

Multiscale models for complex fluids: 
  • (with I. Catto and Y. Gati) Mathematical analysis of a nonlinear parabolic equation arising in the modelling of non-newtonian flows, SIAM J. Math. Anal. 37 (2005) 60-82.
  • (with I. Catto, Y. Gati and C. Le Bris) A micro-macro model describing Couette flows of concentrated suspensions, SIAM J. Multiscale Modeling and Simulation 4 (2005) 1041-1058.
  • (with C. Le Bris) Convergence to equilibrium of a multiscale model for suspensions, DCDS-B 6 (2006) 449-470.
  • (with M. Belhadj,  J.-F. Gerbeau and A. Mikelic) Homogenization approach to filtration through a fibrous medium, NHM 2 (2007) 529-550.  


 
CERMICS - Ecole des Ponts ParisTech
6 & 8 avenue Blaise Pascal, Cité Descartes, Champs-sur-Marne
77455 Marne-la-Vallée Cedex 2, France
Tel : +33 1 64 15 35 69
Fax : +33 1 64 15 35 86
cances@cermics.enpc.fr