Ebook: Mathematical Models and Methods for Ab Initio Quantum Chemistry

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.

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The goal of this volume is to bring together experts on numerical analysis, computer science and chemistry and produce homogenous contributions on ab initio quantum chemistry. The papers from the different communities collected in this volume are written in a language to be comprehensible to the others. This volume is of interest to applied mathematicians and quantum chemists.

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The goal of this volume is to bring together experts on numerical analysis, computer science and chemistry and produce homogenous contributions on ab initio quantum chemistry. The papers from the different communities collected in this volume are written in a language to be comprehensible to the others. This volume is of interest to applied mathematicians and quantum chemists.
Content:
Front Matter....Pages i-xi
Front Matter....Pages 1-1
Is a molecule in chemistry explicable as a broken symmetry in quantum mechanics?....Pages 3-15
SCF algorithms for HF electronic calculations....Pages 17-43
A pedagogical introduction to Quantum Monte-Carlo....Pages 45-73
On the controllability of bilinear quantum systems....Pages 75-92
Front Matter....Pages 93-93
Recent mathematical results on the quantum modeling of crystals....Pages 95-119
Local density approximations for the energy of a periodic Coulomb model....Pages 121-131
A mathematical insight into ab initio simulations of the solid phase....Pages 133-158
Examples of hidden numerical tricks in a solid state determination of electronic structure.....Pages 159-169
Quantum mechanical models for systems in solution....Pages 171-208
Front Matter....Pages 209-209
Variational methods in relativistic quantum mechanics: new approach to the computation of Dirac eigenvalues....Pages 211-226
Quaternion symmetry of the Dirac equation....Pages 227-246
Back Matter....Pages 245-248

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The goal of this volume is to bring together experts on numerical analysis, computer science and chemistry and produce homogenous contributions on ab initio quantum chemistry. The papers from the different communities collected in this volume are written in a language to be comprehensible to the others. This volume is of interest to applied mathematicians and quantum chemists.
Content:
Front Matter....Pages i-xi
Front Matter....Pages 1-1
Is a molecule in chemistry explicable as a broken symmetry in quantum mechanics?....Pages 3-15
SCF algorithms for HF electronic calculations....Pages 17-43
A pedagogical introduction to Quantum Monte-Carlo....Pages 45-73
On the controllability of bilinear quantum systems....Pages 75-92
Front Matter....Pages 93-93
Recent mathematical results on the quantum modeling of crystals....Pages 95-119
Local density approximations for the energy of a periodic Coulomb model....Pages 121-131
A mathematical insight into ab initio simulations of the solid phase....Pages 133-158
Examples of hidden numerical tricks in a solid state determination of electronic structure.....Pages 159-169
Quantum mechanical models for systems in solution....Pages 171-208
Front Matter....Pages 209-209
Variational methods in relativistic quantum mechanics: new approach to the computation of Dirac eigenvalues....Pages 211-226
Quaternion symmetry of the Dirac equation....Pages 227-246
Back Matter....Pages 245-248
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