Eric CANCES


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Research:

Main research fields
  • Mathematical analysis of electronic structure models for quantum chemistry and materials science
  • Algorithms for electronic structure calculation
  • Numerical analysis of linear and nonlinear eigenvalue problems
  • Implicit solvent models
  • Molecular dynamics and exploration of potential energy surfaces
             Visit the website of our Molecular and Multiscale Modeling group!

Other research interests
  • Laser control of molecular processes
  • Greedy algorithms
  • Shape optimization
  • Multiscale models

Teaching:

Professor at the Ecole des Ponts - ParisTech: 
  • Mathematical models and methods for engineers (since 2015) 
  • Analysis (1999-2014)
  • Fourier analysis and signal processing (2003-2008)
  • Modeling in engineering problems (2000-2002)
  • Quantum physics (1999-2001) 
  • Numerical analysis (1997-2005)
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)

Training:

Ecole Polytechnique (1989-1992)
Ecole des Ponts (1992-1995)
University Pierre and Marie Curie (1994-1995)
PhD thesis in Mathematics, Ecole des Ponts (1998): Molecular simulation and environmental effects: a mathematical and numerical perspective
Habilitation thesis in Mathematics, University Paris Dauphine (2003): Contributions to the mathematical and numerical study of some models arising in molecular and multiscale simulations

Distinctions:

Le Rivot prize 1992 (French Academy of Sciences)
Best PhD award 1998 (Ecole des Ponts - ParisTech)
Blaise Pascal prize 2009 (SMAI and the French Academy of Sciences)
Ordway visiting professor 2013-2014 (University of Minnesota)
Invited lecturer at ICM 2014 (International Congress of Mathematicians, Seoul)


Editorial activities:

Co-editor-in-Chief of ESAIM: Proceedings (ESAIM: Proc), with P. Del Moral and J.-F. Gerbeau, 2006-2011

Member of the editorial boards of
  • Mathematical Modelling and Numerical Analysis (M2AN), since 2006 
  • SIAM Journal of Scientific Computing (SISC), since 2008
  • Communications in Mathematical Sciences (CMS), since 2011
  • Multiscale Modeling and Simulation: A SIAM interdisciplinary journal (MMS), since 2013


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).
  • E. Cancès and C. Le Bris, Mathematical modeling of point defects in materials science, M3AS 23 (2013) 1795–1859.
  • E. Cancès, Mathematical perspective on Quantum Monte Carlo methods, in: Many-Electron Approaches in Physics, Chemistry and Mathematics: A Multidisciplinary View, V. Bach and L. Delle Site eds (Springer 2014) 393–409.
  • E. Cancès, Mathematical models and numerical methods for electronic structure calculation, ICM Proceedings 2014.
  • E. Cancès, Electronic structure calculations (solid state physics), in: Princeton Companion to Applied Mathematics, Nicholas Higham ed (Princeton University Press, 2015) 847-851.
  • E. Cancès, Self-consistent field (SCF) algorithms, in: Encyclopedia of Applied and Computational Mathematics, B. Engquist ed (Springer, 2015), 1310-1316.
Mathematical analysis of electronic structure models for quantum chemistry and materials science:
  • 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.
  • 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.
  • 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.
  • 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, 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.
  • A. Anantharaman and E. Cancès, Existence of minimizers for Kohn-Sham models in quantum chemistry, Ann. Inst. Henri Poincaré 26 (2009) 2425-2455.
  • 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 Weiszäcker 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. 100 (2013) 241–274.
  • E. Cancès and N. Mourad, A mathematical perspective on density functional perturbation theory, Nonlinearity 27 (2014) 1999–2033.
  • E. Cancès and N. Mourad, Existence of optimal norm–conserving pseudopotentials for Kohn–Sham models, Comm. Math. Sci. 14 (2016) 1315–1352.
  • E. Cancès, D. Gontier and G. Stoltz, A mathematical analysis of the GW0 method for computing electronic excited energies of molecules, Rev. Math. Phys. 28 (2016) 1650008.
    Algorithms for electronic structure calculation:
    •  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 .
    • 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.
    • 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.
    • E. Cancès, G. Dusson, Y. Maday, B. Stamm and M. Vohralík, A perturbation–method–based post–processing for the planewave discretization of Kohn–Sham models, J. Comput. Phys. 307 (2016) 446–459.
    • G. Tritsaris, S. Shirodkar, E. Kaxiras, P. Cazeaux, M. Luskin, P. Plechác, and E. Cancès, Perturbation theory for weakly coupled two–dimensional layers, J. Mater. Res. 31 (2016) 959–966.
    Numerical analysis of linear and nonlinear 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 Schrödinger 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, Numer. Math. 28 (2014) 663–706.
    • E. Cancès, G. Dusson, Y. Maday, B. Stamm and M. Vohralík, A perturbation–method–based a posteriori estimator for the planewave discretization of nonlinear Schrödinger equations, Comptes Rendus Mathématique 352 (2014) 941–946
    • E. Cancès, R. Chakir, L. He and Y. Maday, Two–grid methods for a class of nonlinear elliptic eigenvalue problems, IMA J. Numer. Anal., in press.
    Implicit solvent 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.
    • E. Cancès, Y. Maday and B. Stamm, Domain decomposition for implicit solvation models, J. Chem. Phys., 139 (2013) 054111.
    • F. Lipparini, B. Stamm, E. Cancès, Y. Maday and B. Mennucci, Fast domain decomposition algorithm for continuum solvation models: energy and first derivatives, J. Chem. Theory Comput. 9 (2013) 3637–3648.
    • F. Lipparini, L. Lagardère, G. Scalmani, B. Stamm, E. Cancès, Y. Maday, J.–P. Piquemal, M. Frisch, and B. Mennucci, Quantum calculations in solution for large to very large molecules: a new linear scaling QM/continuum approach, J. Chem. Phys. Lett. 5 (2014) 953–958.
    • F. Lipparini, G. Scalmani, L. Lagardère, B. Stamm, E. Cancès, Y. Maday, J.–P. Piquemal, M. Frisch, and B. Mennucci, Quantum, classical and hybrid QM/MM calculations in solution: General implementation of the ddCOSMO linear scaling strategy, J. Chem. Phys. 141 (2014) 184108.
    • B. Stamm, E. Cancès, F. Lipparini and Y. Maday, A new discretization for the Polarizable Continuum Model within the domain decomposition paradigm, J. Chem. Phys. 144 (2016) 054101.
    Molecular dynamics and exploration of potential energy surfaces
    • E. Cancès, 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.
    • E. Cancès, 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.
    • E. Cancès, F. Legoll and G. Stoltz, Theoretical and numerical comparison of some sampling methods for molecular dynamics, Preprint IMA 2040 (2005).
    • E. Cancès, 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.
    • F. Lipparini, L. Lagardère, B. Stamm, E. Cancès, M. Schnieders, P. Y. Ren, Y. Maday and J.–P. Piquemal, Scalable evaluation of the polarization energy and associated forces in polarizable molecular dynamics: I. towards massively parallel direct space computations, J. Chem. Theory Comput. 10 (2014) 1638–1651.
    • L. Lagardère, F. Lipparini, E. Polack, B. Stamm, E. Cancès, M. Schnieders, P. Ren, Y. Maday and J.–P. Piquemal, Scalable evaluation of polarization energy and associated forces in polarizable molecular dynamics: II. Towards massively parallel computations using smooth particle mesh Ewald, J. Chem. Theory Comput. 11 (2015) 2589–2599.
    • F. Lipparini, L. Lagardère, C. Raynaud, B. Stamm, E. Cancès, B. Mennucci, M. Schnieders, P. Y. Ren, Y. Maday and J.–P. Piquemal, Polarizable molecular dynamics in a polarizable continuum solvent, J. Chem. Theory Comput. 11 (2015) 623–634.
    • I.G. Tejada, L. Brochard, T. Lelièvre, G. Stoltz, F. Legoll and E. Cancès, Coupling a reactive potential with a harmonic approximation for atomistic simulations of material
      failure, Comp. Meth. Appl. Mech. Eng. 305 (2016) 422–440.
    Laser control of molecular processes:
    • A. Ben-Haj-Yedder, E. Cancès 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. 
    • A. Auger,  C. Dion, A. Ben Haj Yedder, A. Keller, E. Cancès, 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.
    • A. Ben Haj-Yedder, A. Auger, C. M. Dion, E. Cancès, A. Keller, C. Le Bris, and O. Atabek, Numerical optimization of laser fields to control molecular orientation, Phys. Rev. A 66 (2002) 063401.
    • C. Dion, A. Ben Haj Yedder, E. Cancès, C. Le Bris, A. Keller and  O. Atabek, Optimal laser control of orientation: the kicked molecule, Phys. Rev. A 65 (2002) 063408.
    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, ESAIM: Proc. 41 (2013) 95–131.
    • E. Cancès, V. Ehrlacher and T. Lelièvre, Greedy algorithms for high–dimensional eigenvalue problems, Constr. Approx. 40 (2014) 387–423.
    Shape optimization:
    • 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.
    • G. Allaire, E. Cancès and J.-L. Vié, Second-order shape derivatives along normal trajectories, governed by Hamilton-Jacobi equations, Struct. Multidisc Opt., in press.
    Multiscale models: 
    • E. Cancès, 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.
    • E. Cancès, 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.
    • E. Cancès and C. Le Bris, Convergence to equilibrium of a multiscale model for suspensions, DCDS-B 6 (2006) 449-470.
    • M. Belhadj,  E. Cancès, J.-F. Gerbeau and A. Mikelic, Homogenization approach to filtration through a fibrous medium, NHM 2 (2007) 529-550.  
    • E. Cancès, V. Ehrlacher, F. Legoll and B. Stamm, An embedded corrector problem to approximate the homogenized coefficients of an elliptic equation, Comptes Rendus Mathématique, 353 (2015) 801–806.