Quantum Chemistry.

Teams primarily involved:

• CERMICS, ENPC – Molecular simulation team (Eric Cancès)
  
  
• Molecular Photo-physic Laboratory, Université Paris Sud Orsay (Osman Atabek)
  
  
• Physics of Condensed Matter Unit, CEA-DAM, Ile de France (Gilles Zérah)
  
  
• Theoretical Chemistry Laboratory, Université Paris VI (Andreas Savin)
  
  

Our research in this area involves three main axis.

1) Deterministic and stochastic algorithms for the computation of electronic structures. In the process of treating the problems of large sizes which ask for the simulation of large systems, we not only need to develop new methods but also to revisit already in-use methods. Trying to push them beyond their actual limits would be relevant. Following issues then arise:

• the improvement of SCF algorithms (widely used in this domain)
  
• the adaptation of deflation methods in finance in order to determine the electronic structure of metals
  
• the choice of a basis on which the discretisation is effected
  
• the use of stochastic methods to simulate Schrödinger equation, such as Quantum Monte Carlo (QMC)
  
  

Some work has already been done:

• E. Cancès, T. Lelièvre and B. Jourdain, Quantum Monte Carlo simulations of fermions. The fixed node approach, Rapport de recherche CERMICS, 2004.
  

2) Interpretation of the electronic wave functions. The computation of the electronic structure is based on the determination of a wave function. Although the wave function contains all the information on the electronic state of a system, such a representation is very far from the traditional representation. establishing a connection between these two descriptions is one of the subjects of our interest.

3) Integration of Time Dependent Schrödinger Equation in large dimensions. The objective is to build a numerical simulation of the Schrödinger equation in dimension 2,3, or 4 (dimensions considered as large in the context), describing precisely enough the evolution of a molecular system.

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