solving the schrödinger equation with random walks

Submission : 13769
Thesis proposal CSC 2015
Thesis supervisor:
Prof. Michel Caffarel
E-mail address:
[email protected]
PhD School name:
Physics, Chemistry & Material Sciences (SDM)
Research Laboratory:
Lab. of Quantum Chemistry and Physics
Laboratory website:
Scientific domain:
Subject short description:
To be capable of performing high-level quantum simulations of matter is one of the
grand challenges of contemporary science and technology. Many important
applications and scientific fields are concerned: therapeutic effects of
bio-molecules (drug design in silico), nano-sciences, catalysis, novel materials with
exciting functionalities, etc.
From a mathematical point of view, to be able to construct accurate solutions of a
Partial Differential Equation such as the Schrӧdinger equation defined in a very
large dimensional space (whose dimension scales with the number of electrons) is
an extremely difficult task. During the last fifty years, much effort has been
devoted to this problem and two major approaches have emerged: the so-called
post-Hartree-Fock (post-HF) and Density Functional Theories (DFT). The first ones
are known to be particularly accurate but, unfortunately, they suffer from a
pathological scaling of the computational effort as a function of the electron
number. The DFT methods (1998 Nobel prize in chemistry) are clearly nowadays
the most popular approaches: They lead to useful results for (very) large systems
but, unfortunately, suffer from a lack of control of the error in results.
In the last years, our group has been active in the development of an alternative
approach based on the use of probabilistic approaches for simulating the
Schrӧdinger equation (quantum Monte Carlo methods, QMC). Such methods are
particularly attractive since, in sharp contrast with the two standard methods, they
have much less practical limitations (although some work is still needed to make it
a “black-box” type approach). In addition, the algorithms can be very easily
parallelized, a fundamental property regarding the present/future evolution of
computer architectures (massively parallel machines, grid computing, etc.).
The major part of the scientific activity of our group is devoted to the development,
application, and diffusion of quantum Monte Carlo techniques within the
theoretical chemistry community. Our present activities include i.) the
development of multi-scale wave functions adapted to large and complex molecular
systems ii.) the efficient computation of important observables such as the energy
gradients (geometry optimizations, chemical reactivity, and dynamical studies) or
the electronic charge densities iii) the application of QMC to realistic systems: for
example, we have very recently performed some convincing large-scale simulations
of the amyloid-β (Aβ) peptide at work in the Alzheimer disease (use of the 80 000
compute nodes of the CURIE petaflops platform). Here, we propose to the
interested student to work in any of the subjects investigated in our group. The
PhD thesis work may thus be oriented indifferently toward theoretical,
computational/software aspects, or applications on realistic and challenging
chemical problems.
Two major publications in the domain of PhD:
Some selected publications of the group on the subject:
R. Assaraf and M. Caffarel, Phys. Rev. Lett. 83, 4682 (1999); R. Assaraf, M.
Caffarel, and A. Khelif,
Phys. Rev. E. 61, 4566 (2000); R. Assaraf and M. Caffarel, J. Chem. Phys. 113, 4028
R. Assaraf and M. Caffarel J. Chem. Phys. 119, 10536 (2003); A. Scemama, P.
Chaquin, and M. Caffarel,
J. Chem. Phys. 121, 1725 (2004); M. Caffarel, J.P. Daudey, J.L. Heully, and A.
J. Chem. Phys. 123, 094102 (2005); A. Scemama, T. Lelièvre, G. Stoltz, E. Cancès,
M. Caffarel,
J. Chem. Phys. 125, 114105 (2006); R. Assaraf, M. Caffarel, and A. Khelif,
J. Phys. A : Math. Theor. 40, 1181 (2007); R. Assaraf, M. Caffarel, and A. Scemama,
Phys. Rev. E 75, 035701 (2007); M. Caffarel, R. Hernandez-Lamoneda, A.
Scemama, and A. Ramirez-Solis,
Phys. Rev. Lett. 99, 153001 (2007); M. Caffarel, A. Scemama, and A. Ramirez-Solis,
J. Phys. Chem. 113, pp 9014-9021 (2009);
T. Bouabça, M. Caffarel, N. Ben Amor, and D. Maynau J. Chem. Phys. 130, 114107
M. Caffarel, A. Scemama, and A. Ramirez-Solis Theor Chem Acc 126, 275 (2010);
T. Bouabça,B. Braida,
and M. Caffarel, J. Chem. Phys. 133, 044111 (2010); R. Assaraf, M. Caffarel, and A.
Phys. Rev. Lett. 106, 150601 (2011); M. Caffarel Quantum Monte Carlo Methods in
Encyclopedia of Applied and Computational Mathematics, Ed. Bjorn Engquist,
Springer, (2012);
A. Scemama, M. Caffarel, E. Oseret and W. Jalby, Lecture Notes in Computer
Vol. 7851 p.118-127 (2013); A. Scemama, M. Caffarel, E. Oseret, and W. Jalby, J.
Comp. Chem. 34,
938-951 (2013); E. Giner, A. Scemama, and M. Caffarel, Can. J. Chem. 91(9),
879-885 (2013);
A. Scemama, T. Applencourt, E. Giner, and M. Caffarel (2014) arXiv:1409.3671
E. Giner, A. Scemama, and M. Caffarel, (2014) arXiv:1408.3672
M. Caffarel, E. Giner, A. Scemama, and A. Ramirez-Solis (2014) arXiv:1405.4082
Keywords: Quantum Monte Carlo, Theoretical Chemistry, Electronic
Structure Theory, Ab initio Methods, High-Performance Computing (HPC)
Expected collaboration in China:
First name and family name of the laboratory director:
Fernand Spiegelman
Address of the laboratory director:
CNRS and Université Paul Sabatier IRSAMC 118 route de Narbonne 31 Toulouse
Signature and stamp of the laboratory director:
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