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[[File:peptide_cu.png|350px|right]]
 
This website is devoted to the scientific and software
 
This website is devoted to the scientific and software
 
activities of the quantum Monte Carlo (QMC) group of Toulouse, France.  
 
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
 
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://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].
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[[File:Anr.gif|100px|center]]
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<B>The QMC=Chem project is supported by the french Agence Nationale de la Recherche Scientifique (ANR) under Grant No. ANR2011 BS08 004 01
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</B>
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== News ==
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* June 2015: [http://www8.hp.com/h20195/v2/GetPDF.aspx/4AA5-9253ENW.pdf Université Paul Sabatier saves space and energy with HP Moonshot]
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* December 2014: QMC=Chem was selected for the France-Grilles Cloud Challenge. [https://webcast.in2p3.fr/videos-retour_dexperience_sur_lutilisation_de_services_francegrilles_projet_challenge_fg Video]
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* June 2014: QMC=Chem was selected for a meso-challenge on the new CALMIP system [http://www.calmip.univ-toulouse.fr/spip/spip.php?article388 EOS]. 12000 cores ran for 48 hours.
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* July 2013: QMC=Chem tutorial, Cecam workshop [http://www.cecam.org/workshop-942.html Atomistic and molecular simulations on massively parallel architectures], Paris. [{{SERVER}}/files/scemama/Tutorial_QMC=Chem.pdf Slides available here]
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* November 2012: Our results were presented for the 5 years of GENCI (Paris).
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* October 2012: QMC=Chem was presented at the [http://services-numeriques.unistra.fr/hpc.html Equip@Meso meeting]  "Chimie et sciences de la vie : de la simulation numérique au HPC", Strasbourg
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* July 2012: QMC=Chem was presented at the [http://nkl.cc.u-tokyo.ac.jp/VECPAR2012/ VECPAR 2012] Conference, Kobe.
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* June 2012: QMC=Chem was presented on the Intel booth at the International Supercomputing Conference 2012, Hamburg.
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* March 2012: Beta-amyloid results presented for the Intel Xeon E5 release. [http://www.intel.com/content/dam/www/public/us/en/documents/case-studies/high-performance-xeon-e5-2680-genci-study.pdf Read more]
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* Dec 2011: Two structures of a beta-amyloid involved in Alzheimer's disease were simulated on [http://www-hpc.cea.fr/fr/complexe/tgcc-curie.htm Curie (TGCC, France)] with QMC=Chem using up to 76 800 cores. 38.5% of the peak performance of the machine (960 TFlops/s) was obtained.
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* Nov 2011: Performance of QMC=Chem presented at Supercomputing 2011 in [http://sc11.supercomputing.org/schedule/event_detail.php?evid=bof156 BoF session “1000 x 0 = 0. Single-node optimisation does matter.”]
  
 
== QMC in a few words ==
 
== QMC in a few words ==
[[File:Qmc.png|400px|right]]
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Quantum Monte Carlo (QMC) is a set of probabilistic approaches for solving the Schr&ouml;dinger 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.
 
Quantum Monte Carlo (QMC) is a set of probabilistic approaches for solving the Schr&ouml;dinger 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.
  
In practice, the major steps of a QMC simulation are as follows:
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<br style="clear: both" />
 +
[[File:Qmc.png|400px|center]]
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[[File:qmc_hydrogen.png|1000px|center]]
  
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In practice, the major steps of a QMC simulation are as follows (See, Figure):<br>
 
<B>Input</B>: The molecular geometry, the number of electrons, and an approximate electronic trial wave function, &psi;<sub>T</sub>, obtained from a preliminary DFT or ab initio wave function-based calculation.<br>
 
<B>Input</B>: The molecular geometry, the number of electrons, and an approximate electronic trial wave function, &psi;<sub>T</sub>, obtained from a preliminary DFT or ab initio wave function-based calculation.<br>
 
<B> At each Monte Carlo step </B>: The values of &psi;<sub>T</sub>, its gradient, and its Laplacian calculated at each spatial configuration (<B>r</B><sub>1</sub>,<B>r</B><sub>2</sub>, ...,<B>r</B><sub>N</sub>).<br>
 
<B> At each Monte Carlo step </B>: The values of &psi;<sub>T</sub>, its gradient, and its Laplacian calculated at each spatial configuration (<B>r</B><sub>1</sub>,<B>r</B><sub>2</sub>, ...,<B>r</B><sub>N</sub>).<br>
 
<B>Output</B>: Quantum averages as ordinary averages along stochastic trajectories.<br>
 
<B>Output</B>: Quantum averages as ordinary averages along stochastic trajectories.<br>
  
<font color="red"> Key property of QMC : Fully parallelizable approaches. </font> = Global averages can be computed as independent averages over one or a subset of trajectories.
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<font color="red"> Key property of QMC : Fully parallelizable.</font>. This property could be critical in making QMC a successful approach.
  
 
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[http://qmcchem.ups-tlse.fr/files/caffarel/qmc_eacm.pdf '''More about quantum Monte Carlo methods in chemistry here''']
[[Much more about QMC here]]
 
 
<br style="clear: both" />
 
<br style="clear: both" />
 
__NOTOC__
 
__NOTOC__
  
== Our project: QMC as an alternative to DFT and post-HF methods ==
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== QMC an alternative to DFT or post-HF methods ? ==
 
 
To present our project, we first need to briefly summarize the present status of electronic structure calculations. As well-known, there essentially exist two main approaches : the Density Functional Theory (DFT) and the post-Hartree-Fock (post-HF) methods.
 
 
 
'''DFT is clearly the most popular method''' thanks to a number of favorable aspects.
 
 
 
=== Attractive features of DFT ===
 
 
 
i.) In DFT the fully-correlated N-body electronic problem is replaced by
 
an effective one-body problem (nuclei attraction + average electrostatic electronic repulsion
 
+ exchange-correlation potential). The only approximation made is the choice of the exchange-correlation potential,
 
a point which leads to various levels of accuracy for DFT :local DFT, gradient-corrected DFT, hybrid DFT, etc..
 
Such a one-body framework is particularly attractive at the conceptual level since electronic processes can
 
be interpreted in a simple manner using one-electron pictures,
 
a point which is clearly in sharp contrast with wavefunction-based approaches (post-HF methods) where (very) large determinantal expansions
 
have almost no physical meaning.
 
 
 
ii.) Thanks to this one-body formalism the computational effort of DFT has also a very good scaling, the typical scaling being
 
of order <math>O(N^3)</math> where N is the number of electrons.
 
 
 
iii.) The various exchange-correlation potentials developped in the last years have now reached a point where reasonable quantitative results
 
can be obtained, even for a large molecular systems.
 
  
=== Limitation of DFT ===
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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.
  
However, DFT has also a strong limitation related to the fact that the error made in such calculations is basically not controlled and
 
that there exists no known procedure to reduce it in a systematic way.
 
  
 +
=== DFT ===
  
Regarding post-Hartree-Fock methods, they are quite different from DFT and are based on the expansion of the wavefunction over a sum of
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<font color="blue">Advantages</font>:
antisymmetrized products of one-particle orbitals, the various parameters entering the expansion being optimized
+
<ul>
by using the variational principle. Many variants of these methods exist. Among the most famous ones we can cite the CCSD(T) approaches
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<li> The fully-correlated N-body electronic problem is replaced by
well-adapted to systems having a strong mono-configurational character and the MRCI approaches used when multi-configurational effects are
+
an effective one-body problem. Only approximation: Choice of the effective (exchange-correlation) potential,
significant.
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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.
In contrast with DFT, the error is now much more easy to control but, unfortunately, the price to pay for that is in general too high.
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<li> Computational effort of DFT has a very good scaling, of order <math>O(N^3)</math> where N is the number of electrons.
Indeed, typical scalings [for example, N7 for CCSD(T)] forbid to attack systems beyong those of intermediate sizes (let us say more than one
 
hundred active electrons).
 
  
'''In conclusion, it can be legitimately considered that there does not exist a satisfactory electronic approach combining both efficiency and accuracy for (very) large molecular systems.'''
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<li> The various exchange-correlation potentials developped have now reached an accuracy allowing reasonable quantitative results, even for (very) large molecular systems.
 +
</ul>
 +
<font color="blue">Limitation</font>: Strong limitation of DFT: the error made is not controlled and there is no known procedure to reduce it in a systematic way.
  
=== The project presented here is an attempt to promote an alternative third way: the quantum Monte Carlo approach ===
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=== Post-HF methods ===
  
The advantages of QMC are indeed attractive:
+
Post-HF = expansion of the wave function over a sum of
 +
antisymmetrized products of one-particle orbitals
  
i.) Like DFT, the method is simple to implement and has a very favorable scaling (typicallly, O(N3) for a general system).
+
Popular versions: MP2, MPn, CCSD(T), CI, MRCI, etc.  
  
ii.) Like post-HF methods, the accuracy is in general very good.
+
In contrast with DFT: Error much more easy to control but price to pay very high (defavorable scaling).
  
iii.) Unlike DFT and post-HF methods, QMC is particularly well-adapted to High Performance Computing (HPC):
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=== QMC: an alternative approach? ===
central memory requirements are very modest and bounded (no increase of memory as a function of some parameter like the basis set size in post-HF),
 
the Input/Output flows are very limited, and the codes are perfectly parallelized (QMC codes can be easily implemented on massively parallel
 
machines, on heterogeneous grids, etc. ).
 
  
Unfortunately, QMC has also some strong limitations :
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<font color="blue">Advantages:</font>
 +
<ul>
 +
<li> Method easy to implement and having a very favorable scaling, typically <math>O(N^3)</math>.
  
i.) Besides the usual statistical error inherent to any Monte Carlo scheme and which can be easily controlled (for example, by making longer and
+
<li> Accurate total energies.
longer simulations), there is some systematic error left, known as the fixed-node error.
 
Although this error is small in terms of total energis, it can play a central role when differences of energies are considered.
 
Unfortunately, it is well-known that differences of energies are at the very center of chemistry
 
(e.g., electronic affinities, ionization potentials, binding energies, reaction barriers, etc.). Numerical experience has shown that the compensations of
 
errors at work in both DFT and post-HF schemes are in general much important than in Fixed-Node QMC calculations.
 
  
ii.) In contrast with DFT and post-HF there does not exist yet a general and robust algorithm for computing forces in QMC (gradients of total energy with
+
<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).
respecti to nuclear coordinates).
+
</ul>
 +
<font color="blue">Present limitations:</font>
 +
<ul>
 +
<li> The only systematic error left -the fixed-node error- may have an important impact when <EM> differences </EM> 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.
  
iii.) For large molecular systems, there is no simple and systematic way of constructing trial wavefunctions of good quality
+
<li> No general and robust algorithm for computing forces in QMC.
without reoptimizing for each system a very large number of variational parameters. This aspect forbids to apply QMC approach in a "black-box" way, thus
 
strongly hampering the diffusion of QMC techniques into the general computational chemistry community.
 
  
In short, the main objectives of our project are to circumvent the previous limitations to make of 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.
a popular approach in computational chemistry.
+
</ul>

Latest revision as of 14:45, 13 July 2015

Peptide cu.png

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 Laboratoire de Chimie et Physique Quantiques, CNRS and Université Paul Sabatier.

Anr.gif

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

News

  • December 2014: QMC=Chem was selected for the France-Grilles Cloud Challenge. Video
  • June 2014: QMC=Chem was selected for a meso-challenge on the new CALMIP system EOS. 12000 cores ran for 48 hours.
  • November 2012: Our results were presented for the 5 years of GENCI (Paris).
  • October 2012: QMC=Chem was presented at the Equip@Meso meeting "Chimie et sciences de la vie : de la simulation numérique au HPC", Strasbourg
  • July 2012: QMC=Chem was presented at the VECPAR 2012 Conference, Kobe.
  • June 2012: QMC=Chem was presented on the Intel booth at the International Supercomputing Conference 2012, Hamburg.
  • March 2012: Beta-amyloid results presented for the Intel Xeon E5 release. Read more
  • Dec 2011: Two structures of a beta-amyloid involved in Alzheimer's disease were simulated on Curie (TGCC, France) with QMC=Chem using up to 76 800 cores. 38.5% of the peak performance of the machine (960 TFlops/s) was obtained.

QMC in a few words

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.


Qmc.png
Qmc hydrogen.png

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.

More about quantum Monte Carlo methods in chemistry here


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:

  • 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.
  • Computational effort of DFT has a very good scaling, of order <math>O(N^3)</math> where N is the number of electrons.
  • The various exchange-correlation potentials developped have now reached an accuracy allowing reasonable quantitative results, even for (very) large molecular systems.

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:

  • Method easy to implement and having a very favorable scaling, typically <math>O(N^3)</math>.
  • Accurate total energies.
  • 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).

Present limitations:

  • 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.
  • No general and robust algorithm for computing forces in QMC.
  • No simple and systematic way of constructing complex trial wavefunctions of good quality without massive parameter reoptimizations. No "black-box" way for QMC.