[[File:Photo_dumas.jpg|330px|left]]

Directeur de Recherches au Centre National de la Recherche Scientifique [http://www.cnrs.fr/ (CNRS)] 
Lab. de Chimie et Physique Quantiques [http://www.lcpq.ups-tlse.fr"(LCPQ)] 
Université Paul Sabatier [http://www.ups-tlse.fr/" (UPS)] and University of Toulouse [http://www.univ-toulouse.fr/ (UT)] 
Phone: +33 5 61 55 60 46 
Fax: +33 5 61 55 60 65 
E-mail: [mailto:caffarel@irsamc.ups-tlse.fr caffarel@irsamc.ups-tlse.fr] 
Mail:
CNRS-Lab. de Chimie et Physique Quantiques 
IRSAMC Université Paul Sabatier,
118 route de Narbonne 
31062 Toulouse Cedex (FRANCE) 
 
 
 

RESEARCH INTERESTS

N-body quantum problem in physics and chemistry

TEACHING

* Advanced numerical course: "Simulating Complex Systems of Physics" (20 hrs) M2R Physique de la Matière, Université de Toulouse

* "Exploring nuclear configuration space" (6 hrs) M2I Physique et Chimie pour le Vivant et la Santé [http://masterpcvs.ups-tlse.fr/ (PCVS)]

SCIENTIFIC COMMUNITY INVOLVEMENT

* Head of the [http://www.edsdm.ups-tlse.fr/ Doctoral school in Physics, Chemistry, and Material Sciences], University of Toulouse

* In charge of the CNRS-Groupement De Recherche (GDR)[http://gdrcorelec.ups-tlse.fr/ Méthodes corrélées pour la structure électronique]

* Board member of the [http://www.univ-toulouse.fr/recherche/college-doctoral/15-ecoles-doctorales Doctoral College of University of Toulouse]

* Board member of the Labex NEXT

[http://qmcchem.ups-tlse.fr/files/caffarel/publications.html '''COMPLETE PUBLICATION LIST ''']

PUBLICATIONS PER CATEGORY

Reviews 

* M. Caffarel, Encyclopedia of Applied and Computational Mathematics, ed. Bjorn Engquist, Springer (2011).
* [http://qmcchem.ups-tlse.fr/files/caffarel/barcelone_2007.pdf '''Fixed-Node Quantum Monte Carlo for Chemistry'''] M. Caffarel and A. Ramirez-Solis, in The proceedings of the 14th International Conference: "Recent Progress in Many-Body Theories", edited by Jordi Boronat, Gregory Astrakharchik, and Ferran Mazzanti, World Scientific (2008).
* [http://qmcchem.ups-tlse.fr/files/caffarel/Report_Caffarel.pdf '''A few aspects of QMC for molecules'''] M. Caffarel, R. Assaraf, A. Khelif, A. Scemama, A. Ramirez-Solis, in "Mathematical and Numerical Aspects of Quantum Chemistry Problems", Mathematisches Forschunginstitut Oberwolfach, p.7 Report No.47/2006 (2006).
* [http://qmcchem.ups-tlse.fr/files/caffarel/iciam.pdf '''A pedagogical introduction to quantum Monte Carlo'''] M. Caffarel, R. Assaraf in Mathematical models and methods for ''ab initio'' Quantum Chemistry in Lecture Notes in Chemistry, eds. M. Defranceschi and C.Le Bris, Springer p.45 (2000)
* [http://qmcchem.ups-tlse.fr/files/caffarel/Review_1989.pdf'''Stochastic methods in quantum mechanics'''] M. Caffarel in ''Numerical Determination of the Electronic Structure of Atoms, Diatomic and Polyatomic Molecules'' (Kluwer Academic Publishers, 1989), pp.85-105.

 Methodology: General Aspects 

* [http://qmcchem.ups-tlse.fr/files/caffarel/j_stat_phys_1986.pdf'''Treatment of the Schroedinger Equation Through a Monte Carlo Method Based upon the Generalized Feynman-Kac Formula'''] M. Caffarel and P. Claverie, J. Stat. Phys. vol. 43, 797 (1986)
* [http://dx.doi.org/10.1063/1.454227'''Development of a pure diffusion quantum Monte Carlo method using a full generalized Feynman-Kac formula. I. Formalism'''] M. Caffarel and P. Claverie, J. Chem. Phys. vol. 88, 1088 (1988)
* [http://dx.doi.org/10.1063/1.454228'''Development of a pure diffusion quantum Monte Carlo method using a full generalized Feynman-Kac formula. II. Application to simple systems'''] M. Caffarel and P. Claverie, J. Chem. Phys. vol. 88, 1100(1988)
* [http://dx.doi.org/10.1103/PhysRevLett.71.2159'''Comment on Feynman-Kac Path-Integral Calculation of the Ground-State Energies of Atoms'''] M. Caffarel, D.M. Ceperley, and M.H. Kalos, Phys. Rev. Lett. vol. 71, 2159 (1993)
* [http://localhost '''Diffusion Monte Carlo Methods with a fixed number of walkers'''] R. Assaraf, M. Caffarel, and A. Khelif, Phys. Rev. E. vol. 61, 4566 (2000)
* [http://dx.doi.org/10.1063/1.2354490 '''An efficient sampling algorithm for variational Monte Carlo'''] A. Scemama, T. Lelièvre, G. Stoltz, E. Cancès, M. Caffarel, J. Chem. Phys, Vol. 125, pp. 114105 (2006)

 Zero-Variance Zero-Bias principle and its Applications (Forces) 

* [http://dx.doi.org/10.1103/PhysRevLett.83.4682'''Zero-variance principle for Monte Carlo algorithms'''] R. Assaraf and M. Caffarel, Phys. Rev. Lett. vol. 83, 4682 (1999)
* [http://dx.doi.org/10.1063/1.1286598'''Computing forces with quantum Monte Carlo'''] R. Assaraf and M. Caffarel, J. Chem. Phys. vol. 113, 4028 (2000)
* [http://dx.doi.org/10.1063/1.1621615'''Zero-Variance Zero-Bias Principle for Observables in quantum Monte Carlo: Application to Forces'''] R. Assaraf and M. Caffarel J. Chem. Phys. vol. 119, 10536 (2003)
* [http://link.aps.org/abstract/PRE/v75/e035701 '''Improved Monte Carlo estimators for the one-body density'''] R. Assaraf, M. Caffarel, A. Scemama, Phys. Rev. E. Rapid communications, Vol. 75, pp. 035701 (2007)

 Trial wavefunctions 

* [http://qmcchem.ups-tlse.fr/files/caffarel/book_Flad.pdf '''Quantum Monte Carlo calculations with multi-reference trial wave functions'''] H.J. Flad, M. Caffarel, and A. Savin in Recent Advances in Quantum Monte Carlo Methods, ed. World Scientific Publishing (1997)
* [http://dx.doi.org/10.1063/1.3457364 '''Multi-Jastrow trial wavefunctions for electronic structure calculations with quantum Monte Carlo'''] T. Bouabça, B. Braida, and M. Caffarel, J. Chem. Phys. 133, 044111 (2010).

 Electron Pair Localization Function 

* [http://dx.doi.org/10.1007/s00214-009-0713-y '''The lithium-thiophene interaction: a critical study using highly-correlated electronic structure approaches of quantum chemistry'''] M. Caffarel, A. Scemama, A. Ramirez-Solis Theoretical Chemistry Accounts 126(3) 275, (2010).
* [http://dx.doi.org/10.1021/jp902028g '''Bond breaking and bond making in tetraoxygen: analysis of the O2(X3Sigma(g)-) + O2(X3Sigma(g)-) <==> O4 reaction using the electron pair localization function'''] A. Scemama, M. Caffarel, A. Ramírez-Solís J. Phys. Chem. A 113(31) 9014–9021 (2009)
* [http://dx.doi.org/10.1063/1.1765098 '''Electron pair localization function, a practical tool to visualize electron localization in molecules from quantum Monte Carlo data'''] A. Scemama, P. Chaquin, M. Caffarel J. Chem. Phys., vol 121, pp. 1725-1735 (2004)

 Maximum probability domains 

* [http://dx.doi.org/10.1002/jcc.20526 '''Maximum probability domains from quantum Monte Carlo calculations'''] A. Scemama, M. Caffarel, A. Savin J. Comp. Chem., Vol. 28, pp. 442-454 (2006)
* [http://dx.doi.org/10.1142/S0219633605001581 '''Investigating the volume maximizing the probability of finding N electrons from variational Monte Carlo data'''] A. Scemama, J. Theor. Comp. Chem., Vol. 4, No. 2 pp. 397-409 (2005)

 QMC for vibrational levels 

* [http://dx.doi.org/10.1063/1.456123'''Quantum Monte Carlo method for some model and realistic coupled anharmonic oscillators'''] M. Caffarel, P. Claverie, C. Mijoule, J. Andzelm, and D.R. Salahub, J. Chem. Phys. vol. 90, 990 (1989)

 Implementation of large-scale QMC simulations 

* [http://qmcchem.ups-tlse.fr/files/caffarel/jcc.pdf '''Quantum Monte Carlo for large chemical systems: Implementing efficient strategies for petascale platforms and beyond'''] A.Scemama, M. Caffarel, E. Oseret, and W. Jalby submitted to J.Comp.Chem.
* [http://qmcchem.ups-tlse.fr/files/caffarel/kobe.pdf '''QMC=Chem: a quantum Monte Carlo program for large-scale simulations in chemistry at the petascale level and beyond'''] A. Scemama, M. Caffarel, E. Oseret and W. Jalby VECPAR 2012 in press.

 Perturbation Theory with QMC. Applications to interaction energies and polarizabilities 

* [http://dx.doi.org/10.1103/PhysRevA.43.2139 '''Quantum Monte Carlo-Perturbation Calculations of Interaction Energies'''] M. Caffarel and O. Hess, Phys. Rev. A vol. 43, 2139 (1991)
* [http://qmcchem.ups-tlse.fr/files/caffarel/Obernai.pdf '''Computing Response Properties with Quantum Monte Carlo'''] M. Caffarel and O. Hess in AIP Conference Proceedings No 239, Advances in Biomolecular Simulations Obernai, France 1991 pp. 20-32
* [http://dx.doi.org/10.1103/PhysRevA.47.3704 '''Evaluating Dynamic Multipole Polarizabilities and van Der Waals Dispersion Coefficients of two-electron Systems with a Quantum Monte Carlo Calculation: A Comparison with some ''Ab Initio'' Calculations'''] M. Caffarel, M. Rérat, and C. Pouchan, Phys. Rev. A vol.47, 3704 (1993)
* [http://dx.doi.org/10.1063/1.471209'''A quantum Monte Carlo perturbational study of the He-He interaction'''] C. Huiszoon and M. Caffarel, J. Chem. Phys. vol. 104, 4621 (1996)
* [http://localhost '''Dynamic Polarizabilities andvvan der Waals Coefficients of the 2^1S and 2^3S MetastablevStates of Helium'''] M. Rérat, M. Caffarel, and C. Pouchan, Phys. Rev A vol. 48, 161 (1993).

 Perturbation Theory with SAPT 

* [http://localhost '''Second-order exchange effects in intermolecular interactions. The water dimer'''] O. Hess, M. Caffarel, C. Huiszoon, and P. Claverie, J. Chem. Phys. 92, 6049 (1990).
* [http://localhost '''The water dimer. Comparison of results obtained by both ab initio supermolecule and SAPT methods. Derivation of simplified formulas'''] O. Hess, M. Caffarel, J. Langlet, J. Caillet, C. Huiszoon, and P. Claverie, in Modeling of Molecular Structures and Properties Studies in Physical and Theoretical Chemistry, Vol. 71, pp.323-335.
* [http://localhost '''A Perturbational Study of some Hydrogen-Bonded Dimers'''] J. Langlet, J. Caillet, and M. Caffarel, J. Chem. Phys. vol. 103, 8043 (1995).

 The fermion sign problem 

* [http://localhost '''Lanczos-type Algorithm for Quantum Monte Carlo Data'''] M. Caffarel , F.X. Gadea, and D.M. Ceperley, Europhys. Lett. vol. 16 249 (1991)
* [http://dx.doi.org/10.1063/1.463411'''A Bayesian Analysis of Green's Function Monte Carlo Correlation Functions'''] M. Caffarel and D.M. Ceperley, J. Chem. Phys. vol. 97, 8415 (1992)
* [http://localhost '''The Fermion Monte Carlo Revisited'''] R. Assaraf, M. Caffarel, and A. Khelif, J. Phys. A : Math. Theor. vol. 40, 1181 (2007)

 Nodal properties of wavefunctions 

* [http://localhost '''On the Nonconservation of the Number of Nodel Cells of Eigenfunctions'''] M. Caffarel, X. Krokidis, and C. Mijoule, Europhys. Lett. vol. 20, 581 (1992)

 Chemical applications 

* [http://dx.doi.org/10.1007/s00214-009-0713-y '''The lithium-thiophene interaction: a critical study using highly-correlated electronic structure approaches of quantum chemistry'''] M. Caffarel, A. Scemama, A. Ramirez-Solis Theoretical Chemistry Accounts 126(3) 275, (2010).
* [http://dx.doi.org/10.1021/jp902028g '''Bond breaking and bond making in tetraoxygen: analysis of the O2(X3Sigma(g)-) + O2(X3Sigma(g)-) <==> O4 reaction using the electron pair localization function'''] A. Scemama, M. Caffarel, A. Ramírez-Solís, J. Phys. Chem. A 113(31) 9014–9021 (2009)
* [http://dx.doi.org/10.1103/PhysRevLett.99.153001 '''Multireference quantum Monte Carlo study of the O4 molecule'''] M. Caffarel, R. Hernandez-Lamoneda, A. Scemama, A. Ramirez-Solis, Phys. Rev. Lett., 99, 153001 (2007)
* [http://dx.doi.org/10.1063/1.2011393'''Towards accurate all-electron quantum Monte Carlo calculations of transition metal systems: Spectroscopy of the copper atom'''] M. Caffarel, J.P. Daudey, J.L. Heully, and A. Ramirez-Solis, J. Chem. Phys. vol.123, 094102 (2005)
* [http://dx.doi.org/10.1063/1.3086023 '''A quantum Monte Carlo study of the n ---->pi*(CO) transition in acrolein: Role of the nodal hypersurfaces'''] T. Bouabça, M. Caffarel, N. Ben Amor, and D. Maynau, J. Chem. Phys. vol. 130, 114107 (2009)
* [http://localhost '''Structural and optical properties of a neutral Nickel bisdithiolene complex. Density Functional versus Ab initio methods'''] F. Alary, J.-L. Heully, A. Scemama, B. Garreau-de-Bonneval, K.I. Chane-Ching, and M. Caffarel, to be published in Theoretical Chemistry Accounts (TCA), (2009)
* [http://dx.doi.org/10.1007/s00214-009-0713-y '''The lithium-thiophene interaction: a critical study using highly-correlated electronic structure approaches of quantum chemistry'''] M. Caffarel, A. Scemama, A. Ramirez-Solis Theoretical Chemistry Accounts 126(3) 275, (2010).

 Theoretical condensed-matter physics (Hubbard and Heisenberg models) 

* [http://localhost '''Gutzwiller Wave Function for a Model of Strongly Interacting Bosons'''] W. Krauth, M. Caffarel and J.P. Bouchaud, Phys. Rev B vol. 45, 3137 (1992).
* [http://localhost '''Exact Diagonalization Approach to Correlated Fermions in Infinite Dimensions: Mott Transition and Superconductivity Model'''] M. Caffarel and W. Krauth, Phys. Rev. Lett. vol.72, 1545 (1994)
* [http://localhost '''Exact Diagonalization Approach for the infinite D Hubbard Model'''] M. Caffarel and W. Krauth, 7 pages, cond-mat/9306057, extended version of first part of previous paper.
* [http://localhost '''Superconductivity in the Two-Band Hubbard Model in Infinite D: an Exact Diagonalization Study'''] W. Krauth and M. Caffarel, 7 pages, cond-mat/9306056, extended version of second part of the previous paper.
* [http://localhost '''Monte Carlo Calculation of the Spin-stiffness of the two-dimensional Heisenberg Model'''] M. Caffarel, P. Azaria, B. Delamotte, and D. Mouhanna, Europhys. Lett. vol. 26, 493 (1994)
* [http://localhost '''One-dimensional pair-hopping and attractive Hubbard models: A comparative study'''] M. van den Bossche and M. Caffarel, Phys. Rev. B vol. 54, 17414 (1996)
* [http://localhost '''Hubbard model on d-dimensional hypercubes: Exact solution for the two-electron case'''] M. Caffarel and R. Mosseri, Phys. Rev. B {\bf }, 12651 (1998).
* [http://localhost '''Hubbard model on hypercubes'''] R. Assaraf, M. Caffarel, and R. Mosseri, Physica B p.259-261, 787 (1999)
* [http://localhost '''Metal-insulator transition in the one-dimensional SU(N) Hubbard model'''] R. Assaraf, P. Azaria, M. Caffarel, and P. Lecheminant, Phys. Rev. B vol. 60, 2299 (1999)
* [http://localhost '''Spin-stiffness and topological defects in two-dimensional frustrated spin systems'''] M. Caffarel, P. Azaria, B. Delamotte, and D. Mouhanna, Phys. Rev. B vol. 64, 014412 (2001)
* [http://localhost '''Block-diagonalization of Pairing Hamiltonians using spin-transpositions'''] J. Szeftel and M. Caffarel, J. Phys. A : Math.Gen. vol. 37 623 (2004)
* [http://localhost '''Dynamical Symmetry Enlargement versus Spin-Charge Decoupling in the one-dimensional SU(4) Hubbard Model'''] R. Assaraf, P. Azaria, E. Boulat, M. Caffarel, and P. Lecheminant, Phys. Rev. Lett. vol. 93, 016407 (2004)

 Quantum aesthetics 

* [http://qmcchem.ups-tlse.fr/files/caffarel/grospapier_esthetique_quantique.pdf '''L’esthétique quantique : un regard croisé Arts et Sciences'''] M. Martinez et M. Caffarel in Science, Fables and Chimera: Strange Encounters, edited by Laurence Roussillon- Constanty and Philippe Murillo, Cambridge, Cambridge Scholars Publishing, 2012. Actes du Colloque International "Science, fables et chimères: croisements" Toulouse,10-11 Juin 2011.

* [http://qmcchem.ups-tlse.fr/files/caffarel/martinez_caffarel_aesthetics.pdf '''Quantum aesthetics: When quantum theory stimulates the artistic and scientific imagination. A critical assessment'''] M. Martinez et M. Caffarel[http://qmcchem.ups-tlse.fr/files/caffarel/martinez_caffarel_esthetique.pdf '''french version'''] [http://qmcchem.ups-tlse.fr/files/caffarel/esthetique_quantique_roumain.pdf '''romanian version''']

 Other publications 

* [http://qmcchem.ups-tlse.fr/files/caffarel/Obernai.pdf'''Méthodes d'intégration fonctionnelle et méthodes stochastiques pour le traitement de problèmes quantiques. Application à la physique atomique et moléculaire'''] M. Caffarel, Doctorat de l'Université Paris 6, 27 Mars 1987.

2012-04-06T09:39:29Z

Caffarel:

This website is devoted to the scientific and software
activities of the quantum Monte Carlo (QMC) group of Toulouse, France.
The grand objective of our project is to make of QMC an alternative and efficient tool for electronic structure in chemistry. Our group -- headed by Michel Caffarel -- is located at the
[http://www.lcpq.ups-tlse.fr Laboratoire de Chimie et Physique Quantiques], [http://www.cnrs.fr CNRS] and [http://www.ups-tlse.fr/ Université Paul Sabatier].

The QMC=Chem project is supported by the french Agence Nationale de la Recherche Scientifique (ANR) under Grant No. ANR2011 BS08 004 01

[[File:Anr.gif|200px|right]]

[http://qmcchem.ups-tlse.fr/files/caffarel/these_FR.pdf ''' PROPOSITION DE THESE (FINANCEE) A PARTIR DE SEPTEMBRE 2012 ''']

[http://qmcchem.ups-tlse.fr/files/caffarel/these_ENG.pdf ''' Ph.D. THESIS PROPOSAL ''']

== QMC in a few words ==
[[File:Qmc.png|400px|right]]
Quantum Monte Carlo (QMC) is a set of probabilistic approaches for solving the Schrödinger equation. In short, QMC consists in simulating the probabilities of quantum mechanics by using the probabilities of random walks (Brownian motion and its generalizations). During the simulations each electron is moved randomly and quantum averages are computed as ordinary averages.

<center>
<html>
<table style="width:auto;"><tr><td><a href="https://picasaweb.google.com/lh/photo/7HFDA1WUJg2SgpWdsopVZdMTjNZETYmyPJy0liipFm0?feat=embedwebsite"><img src="https://lh5.googleusercontent.com/-tftU32oJ1c0/T2JhwNLCv0I/AAAAAAAAEO4/GfDH1K_v3LQ/s144/1amb.jpg" height="216" width="288" /></a></td></tr>
<tr><td style="font-family:arial,sans-serif; font-size:11px; text-align:center"><a href="http://www.pdb.org/pdb/explore/explore.do?structureId=1amb"> Amyloid Beta peptide</a>, 28 residues 
A stochastic trajectory for the 1731 electrons of systems. 
 Click on the image to see the animation. </td></tr></table>
</html>

</center>

In practice, the major steps of a QMC simulation are as follows (See, Figure): 
Input: The molecular geometry, the number of electrons, and an approximate electronic trial wave function, ψT, obtained from a preliminary DFT or ab initio wave function-based calculation. 
 At each Monte Carlo step : The values of ψT, its gradient, and its Laplacian calculated at each spatial configuration (r1,r2, ...,rN). 
Output: Quantum averages as ordinary averages along stochastic trajectories. 

 Key property of QMC : Fully parallelizable.. This property could be critical in making QMC a successful approach.

[http://qmcchem.ups-tlse.fr/files/caffarel/qmc_eacm.pdf '''More about quantum Monte Carlo methods in chemistry here''']
 
__NOTOC__

== QMC an alternative to DFT or post-HF methods ? ==

In practice, both DFT and post-Hartree-Fock approaches and their numerous variants rely on solving (very) large linear systems using iterative algorithms, where the finite dimension of the eigenvectors may become very large and is limited in practice to a few billion of components due to the finite aspects of the hardware. Because of such a mathematical structure, present intensive simulations of computational chemistry are characterized by i) the need of important computational resources both in terms of CPU and central memory requirements, ii) massive I/O, and iii) unavoidable frequent communications between processors. As a consequence, the algorithms are by their very nature extremely difficult to parallelize. Although computational chemistry is very present on HPC platforms as illustrated above, it is difficult to envision how standard algorithms could take advantage in the near future of massively parallel platforms (exascale) and cloud computing.

=== DFT ===

Advantages:
<ul>
<li> The fully-correlated N-body electronic problem is replaced by
an effective one-body problem. Only approximation: Choice of the effective (exchange-correlation) potential,
a point leading to various levels of accuracy (local DFT, gradient-corrected DFT, hybrid DFT, etc...). One-body framework particularly attractive for interpreting electronic processes in a simple manner using one-electron pictures.
<li> Computational effort of DFT has a very good scaling, of order <math>O(N^3)</math> where N is the number of electrons.

<li> The various exchange-correlation potentials developped have now reached an accuracy allowing reasonable quantitative results, even for (very) large molecular systems.
</ul>
Limitation: Strong limitation of DFT: the error made is not controlled and there is no known procedure to reduce it in a systematic way.

=== Post-HF methods ===

Post-HF = expansion of the wave function over a sum of
antisymmetrized products of one-particle orbitals

Popular versions: MP2, MPn, CCSD(T), CI, MRCI, etc.

In contrast with DFT: Error much more easy to control but price to pay very high (defavorable scaling).

=== QMC: an alternative approach? ===

Advantages:
<ul>
<li> Method easy to implement and having a very favorable scaling, typically <math>O(N^3)</math>.

<li> Accurate total energies.

<li> Unlike DFT and post-HF methods, QMC ideally suited to High Performance Computing (HPC) (very modest central memory requirements, very limited input/output flows, codes perfectly parallelized).
</ul>
Present limitations:
<ul>
<li> The only systematic error left -the fixed-node error- may have an important impact when differences of energies are considered. The heavy compensation of errors at work in both DFT and post-HF schemes is much less effective in Fixed-Node QMC calculations.

<li> No general and robust algorithm for computing forces in QMC.

<li> No simple and systematic way of constructing complex trial wavefunctions of good quality without massive parameter reoptimizations. No "black-box" way for QMC.
</ul>

File:Anr.gif

2012-04-06T09:37:43Z

Caffarel:

Quantum Monte Carlo for Chemistry @ Toulouse

2012-04-02T14:24:09Z

Caffarel:

This website is devoted to the scientific and software
activities of the quantum Monte Carlo (QMC) group of Toulouse, France.
The grand objective of our project is to make of QMC an alternative and efficient tool for electronic structure in chemistry. Our group -- headed by Michel Caffarel -- is located at the
[http://www.lcpq.ups-tlse.fr Laboratoire de Chimie et Physique Quantiques], [http://www.cnrs.fr CNRS] and [http://www.ups-tlse.fr/ Université Paul Sabatier].

[http://qmcchem.ups-tlse.fr/files/caffarel/these_FR.pdf ''' PROPOSITION DE THESE (FINANCEE) A PARTIR DE SEPTEMBRE 2012 ''']

[http://qmcchem.ups-tlse.fr/files/caffarel/these_ENG.pdf ''' Ph.D. THESIS PROPOSAL ''']

== QMC in a few words ==
[[File:Qmc.png|400px|right]]
Quantum Monte Carlo (QMC) is a set of probabilistic approaches for solving the Schrödinger equation. In short, QMC consists in simulating the probabilities of quantum mechanics by using the probabilities of random walks (Brownian motion and its generalizations). During the simulations each electron is moved randomly and quantum averages are computed as ordinary averages.

<center>
<html>
<table style="width:auto;"><tr><td><a href="https://picasaweb.google.com/lh/photo/7HFDA1WUJg2SgpWdsopVZdMTjNZETYmyPJy0liipFm0?feat=embedwebsite"><img src="https://lh5.googleusercontent.com/-tftU32oJ1c0/T2JhwNLCv0I/AAAAAAAAEO4/GfDH1K_v3LQ/s144/1amb.jpg" height="216" width="288" /></a></td></tr>
<tr><td style="font-family:arial,sans-serif; font-size:11px; text-align:center"><a href="http://www.pdb.org/pdb/explore/explore.do?structureId=1amb"> Amyloid Beta peptide</a>, 28 residues 
A stochastic trajectory for the 1731 electrons of systems. 
 Click on the image to see the animation. </td></tr></table>
</html>

</center>

In practice, the major steps of a QMC simulation are as follows (See, Figure): 
Input: The molecular geometry, the number of electrons, and an approximate electronic trial wave function, ψT, obtained from a preliminary DFT or ab initio wave function-based calculation. 
 At each Monte Carlo step : The values of ψT, its gradient, and its Laplacian calculated at each spatial configuration (r1,r2, ...,rN). 
Output: Quantum averages as ordinary averages along stochastic trajectories. 

 Key property of QMC : Fully parallelizable.. This property could be critical in making QMC a successful approach.

[http://qmcchem.ups-tlse.fr/files/caffarel/qmc_eacm.pdf '''More about quantum Monte Carlo methods in chemistry here''']
 
__NOTOC__

== QMC an alternative to DFT or post-HF methods ? ==

In practice, both DFT and post-Hartree-Fock approaches and their numerous variants rely on solving (very) large linear systems using iterative algorithms, where the finite dimension of the eigenvectors may become very large and is limited in practice to a few billion of components due to the finite aspects of the hardware. Because of such a mathematical structure, present intensive simulations of computational chemistry are characterized by i) the need of important computational resources both in terms of CPU and central memory requirements, ii) massive I/O, and iii) unavoidable frequent communications between processors. As a consequence, the algorithms are by their very nature extremely difficult to parallelize. Although computational chemistry is very present on HPC platforms as illustrated above, it is difficult to envision how standard algorithms could take advantage in the near future of massively parallel platforms (exascale) and cloud computing.

=== DFT ===

Advantages:
<ul>
<li> The fully-correlated N-body electronic problem is replaced by
an effective one-body problem. Only approximation: Choice of the effective (exchange-correlation) potential,
a point leading to various levels of accuracy (local DFT, gradient-corrected DFT, hybrid DFT, etc...). One-body framework particularly attractive for interpreting electronic processes in a simple manner using one-electron pictures.
<li> Computational effort of DFT has a very good scaling, of order <math>O(N^3)</math> where N is the number of electrons.

<li> The various exchange-correlation potentials developped have now reached an accuracy allowing reasonable quantitative results, even for (very) large molecular systems.
</ul>
Limitation: Strong limitation of DFT: the error made is not controlled and there is no known procedure to reduce it in a systematic way.

=== Post-HF methods ===

Post-HF = expansion of the wave function over a sum of
antisymmetrized products of one-particle orbitals

Popular versions: MP2, MPn, CCSD(T), CI, MRCI, etc.

In contrast with DFT: Error much more easy to control but price to pay very high (defavorable scaling).

=== QMC: an alternative approach? ===

Advantages:
<ul>
<li> Method easy to implement and having a very favorable scaling, typically <math>O(N^3)</math>.

<li> Accurate total energies.

<li> Unlike DFT and post-HF methods, QMC ideally suited to High Performance Computing (HPC) (very modest central memory requirements, very limited input/output flows, codes perfectly parallelized).
</ul>
Present limitations:
<ul>
<li> The only systematic error left -the fixed-node error- may have an important impact when differences of energies are considered. The heavy compensation of errors at work in both DFT and post-HF schemes is much less effective in Fixed-Node QMC calculations.

<li> No general and robust algorithm for computing forces in QMC.

<li> No simple and systematic way of constructing complex trial wavefunctions of good quality without massive parameter reoptimizations. No "black-box" way for QMC.
</ul>

Quantum Monte Carlo for Chemistry @ Toulouse

2012-04-02T14:17:36Z

Caffarel:

This website is devoted to the scientific and software
activities of the quantum Monte Carlo (QMC) group of Toulouse, France.
The grand objective of our project is to make of QMC an alternative and efficient tool for electronic structure in chemistry. Our group -- headed by Michel Caffarel -- is located at the
[http://www.lcpq.ups-tlse.fr Laboratoire de Chimie et Physique Quantiques], [http://www.cnrs.fr CNRS] and [http://www.ups-tlse.fr/ Université Paul Sabatier].

[http://qmcchem.ups-tlse.fr/files/caffarel/thesis_FR.pdf ''' PROPOSITION DE THESE (FINANCEE) A PARTIR DE SEPTEMBRE 2012 ''']

[http://qmcchem.ups-tlse.fr/files/caffarel/thesis_FR.pdf ''' Ph.D. THESIS PROPOSAL ''']

== QMC in a few words ==
[[File:Qmc.png|400px|right]]
Quantum Monte Carlo (QMC) is a set of probabilistic approaches for solving the Schrödinger equation. In short, QMC consists in simulating the probabilities of quantum mechanics by using the probabilities of random walks (Brownian motion and its generalizations). During the simulations each electron is moved randomly and quantum averages are computed as ordinary averages.

<center>
<html>
<table style="width:auto;"><tr><td><a href="https://picasaweb.google.com/lh/photo/7HFDA1WUJg2SgpWdsopVZdMTjNZETYmyPJy0liipFm0?feat=embedwebsite"><img src="https://lh5.googleusercontent.com/-tftU32oJ1c0/T2JhwNLCv0I/AAAAAAAAEO4/GfDH1K_v3LQ/s144/1amb.jpg" height="216" width="288" /></a></td></tr>
<tr><td style="font-family:arial,sans-serif; font-size:11px; text-align:center"><a href="http://www.pdb.org/pdb/explore/explore.do?structureId=1amb"> Amyloid Beta peptide</a>, 28 residues 
A stochastic trajectory for the 1731 electrons of systems. 
 Click on the image to see the animation. </td></tr></table>
</html>

</center>

In practice, the major steps of a QMC simulation are as follows (See, Figure): 
Input: The molecular geometry, the number of electrons, and an approximate electronic trial wave function, ψT, obtained from a preliminary DFT or ab initio wave function-based calculation. 
 At each Monte Carlo step : The values of ψT, its gradient, and its Laplacian calculated at each spatial configuration (r1,r2, ...,rN). 
Output: Quantum averages as ordinary averages along stochastic trajectories. 

 Key property of QMC : Fully parallelizable.. This property could be critical in making QMC a successful approach.

[http://qmcchem.ups-tlse.fr/files/caffarel/qmc_eacm.pdf '''More about quantum Monte Carlo methods in chemistry here''']
 
__NOTOC__

== QMC an alternative to DFT or post-HF methods ? ==

In practice, both DFT and post-Hartree-Fock approaches and their numerous variants rely on solving (very) large linear systems using iterative algorithms, where the finite dimension of the eigenvectors may become very large and is limited in practice to a few billion of components due to the finite aspects of the hardware. Because of such a mathematical structure, present intensive simulations of computational chemistry are characterized by i) the need of important computational resources both in terms of CPU and central memory requirements, ii) massive I/O, and iii) unavoidable frequent communications between processors. As a consequence, the algorithms are by their very nature extremely difficult to parallelize. Although computational chemistry is very present on HPC platforms as illustrated above, it is difficult to envision how standard algorithms could take advantage in the near future of massively parallel platforms (exascale) and cloud computing.

=== DFT ===

Advantages:
<ul>
<li> The fully-correlated N-body electronic problem is replaced by
an effective one-body problem. Only approximation: Choice of the effective (exchange-correlation) potential,
a point leading to various levels of accuracy (local DFT, gradient-corrected DFT, hybrid DFT, etc...). One-body framework particularly attractive for interpreting electronic processes in a simple manner using one-electron pictures.
<li> Computational effort of DFT has a very good scaling, of order <math>O(N^3)</math> where N is the number of electrons.

<li> The various exchange-correlation potentials developped have now reached an accuracy allowing reasonable quantitative results, even for (very) large molecular systems.
</ul>
Limitation: Strong limitation of DFT: the error made is not controlled and there is no known procedure to reduce it in a systematic way.

=== Post-HF methods ===

Post-HF = expansion of the wave function over a sum of
antisymmetrized products of one-particle orbitals

Popular versions: MP2, MPn, CCSD(T), CI, MRCI, etc.

In contrast with DFT: Error much more easy to control but price to pay very high (defavorable scaling).

=== QMC: an alternative approach? ===

Advantages:
<ul>
<li> Method easy to implement and having a very favorable scaling, typically <math>O(N^3)</math>.

<li> Accurate total energies.

<li> Unlike DFT and post-HF methods, QMC ideally suited to High Performance Computing (HPC) (very modest central memory requirements, very limited input/output flows, codes perfectly parallelized).
</ul>
Present limitations:
<ul>
<li> The only systematic error left -the fixed-node error- may have an important impact when differences of energies are considered. The heavy compensation of errors at work in both DFT and post-HF schemes is much less effective in Fixed-Node QMC calculations.

<li> No general and robust algorithm for computing forces in QMC.

<li> No simple and systematic way of constructing complex trial wavefunctions of good quality without massive parameter reoptimizations. No "black-box" way for QMC.
</ul>