**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)** I*** nterpretation
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.