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Mini-workshop on "Mathematical and numerical challenges in quantum chemistry"
Organizers: Claude Le Bris (Paris, France) & Christian Lubich (Tuebingen, Germany)


Michel Caffarel (Toulouse, France): "Toward systematic improvment of the fixed-node approximation in diffusion Monte Carlo methods"
Monday 24 June 2013, 15:20 - 16:00
Amphi Darboux


Quantum Monte Carlo (QMC) methods are powerful probabilistic approaches for getting accurate solutions of the Schrödinger equation. In quantum chemistry QMC is now able to reach
for some applications an accuracy comparable or even superior to the best available ab initio approaches (Density Functional Theory DFT or post-Hartree-Fock methods). Unfortunately, despite such remarkable results a number of practical and theoretical difficulties still hamper the diffusion of QMC techniques as a standard computational tool that would be accessible to the general quantum chemistry community. Probably, the most fundamental difficulty is the problem of controlling the sole systematic error present in QMC simulations for electrons, namely the fixed-node approximation.
In this talk, we illustrate the impact of this error for various molecular systems and address the problem of its control. A new approach based on the use of selected configuration interaction (CI) expansions obtained by selecting the most important determinants through a perturbative criterion is presented (see, Ref. 1). In this approach, the most important determinants enter first during the selection process (hierarchical construction) and, as a consequence, the main features of the nodal structure of the wavefunction can be expected to be obtained in a systematic way upon increasing the number of determinants. We present a number of numerical results for a variety of molecular systems that seem to confirm such an attractive property.

(1) E. Giner, A. Scemama, and M. Caffarel "Using perturbatively selected configuration interaction in quantum Monte Carlo calculations" (in press).
Can be downloaded at: http://qmcchem.ups-tlse.fr/files/caffarel/cipsi1.pdf

(joint work with  Emmanuel Giner and Anthony Scemama)