Eric CANCES

Organization: Ecole des Ponts ParisTech
and INRIA Paris
Research Unit: CERMICS
Team: Molecular and Multiscale Modeling
Phone: +33 1 64 15 35 69
E-mail: cancesATcermicsDOTenpcDOTfr
Address:

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

Abstract: French, English
Full report: PhD thesis

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

Full report (in French): Habilitation thesis

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.