Lab. Physique Quantique, Université Paul Sabatier, Toulouse, France.
Some mathematical questions related to quantum Monte Carlo approaches for molecules.
Quantum Monte Carlo (QMC) approaches are of growing importance in theoretical chemistry. In the last years, they have been applied with great success to a large variety of molecular systems. Although several aspects of QMC need yet to be improved, these methods can already be considered as an interesting alternative to the more standard high-quality ab initio methods (e.g., Coupled Cluster with large basis sets).
In this talk I will present a number of questions and results about the mathematical aspects of QMC. This will include a discussion of the various variants of QMC for molecules, some remarks about the nodal properties of molecular wavefunctions, a presentation of the recently introduced improved estimators, and some comments about the ``sign problem''.