Mathematical Models and Methods for Ab Initio Quantum Chemistry

1. Front Matter

   Pages i-xi

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2. General topics

   1. Front Matter

      Pages 1-1

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   2. Is a molecule in chemistry explicable as a broken symmetry in quantum mechanics?

      • Brian Sutcliffe

      Pages 3-15

   3. SCF algorithms for HF electronic calculations

      • Eric Cancès

      Pages 17-43

   4. A pedagogical introduction to Quantum Monte-Carlo

      • Michel Caffarel, Roland Assaraf

      Pages 45-73

   5. On the controllability of bilinear quantum systems

      • Gabriel Turinici

      Pages 75-92

3. Condensed phases

   1. Front Matter

      Pages 93-93

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   2. Recent mathematical results on the quantum modeling of crystals

      • I. Catto, P.-L. Lions, C. Le Bris

      Pages 95-119

   3. Local density approximations for the energy of a periodic Coulomb model

      • O. Bokanowski, B. Grébert, N. J. Mauser

      Pages 121-131

   4. A mathematical insight into ab initio simulations of the solid phase

      • X. Blanc

      Pages 133-158

   5. Examples of hidden numerical tricks in a solid state determination of electronic structure.

      • Mireille Defranceschi, Vanina Louis-Achille

      Pages 159-169

   6. Quantum mechanical models for systems in solution

      • Benedetta Mennucci

      Pages 171-208

4. Relativistic models

   1. Front Matter

      Pages 209-209

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   2. Variational methods in relativistic quantum mechanics: new approach to the computation of Dirac eigenvalues

      • Jean Dolbeault, Maria J. Esteban, Eric Séré

      Pages 211-226

   3. Quaternion symmetry of the Dirac equation

      • T. Saue, H. J. Aa. Jensen

      Pages 227-246

5. Back Matter

   Pages 245-248

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On the occasion of the fourth International Conference on Industrial and Applied Mathematics!, we decided to organize a sequence of 4 minisymposia devoted to the mathematical aspects and the numerical aspects of Quantum Chemistry. Our goal was to bring together scientists from different communities, namely mathematicians, experts at numerical analysis and computer science, chemists, just to see whether this heterogeneous set of lecturers can produce a rather homogeneous presentation of the domain to an uninitiated audience. To the best of our knowledgde, nothing of this kind had never been tempted so far. It seemed to us that it was the good time for doing it, both . because the interest of applied mathematicians into the world of computational chemistry has exponentially increased in the past few years, and because the community of chemists feels more and more concerned with the numerical issues. Indeed, in the early years of Quantum Chemistry, the pioneers (Coulson, Mac Weeny, just to quote two of them) used to solve fundamental equations modelling toy systems which could be simply numerically handled in view of their very limited size. The true difficulty arose with the need to model larger systems while possibly taking into account their interaction with their environment. Hand calculations were no longer possible, and computing science came into the picture.

• Angewandte Mathematik
• Dirac equation
• Quantenchemie
• applied mathematics
• mathematics
• quantum chemistry
• quantum mechanics

• DPE/SPCP/LEPCA, Gif-sur-Yvette Cedex, France

  Mireille Defranceschi

• C.E.R.M.I.C.S., Ecole Nationale des Ponts et Chaussées, Marne La Vallée Cedex 2, France

  Claude Bris

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