Titlebook: Many-Electron Approaches in Physics, Chemistry and Mathematics; A Multidisciplinary Volker Bach,Luigi Delle Site Book 2014 Springer Intern

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978-3-319-34304-4Springer International Publishing Switzerland 2014

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Towards the Computational Design of Compounds from First Principles minimization of objective functions in chemical compound space. We discuss applications involving high-throughput calculations, stochastic algorithms, gradients, and hybrids thereof. Recent efforts based on machine learning in chemical compound space are also mentioned.

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Mathematical Aspects of Density Functionals and Density Matrix Functionals in Quantum Chemistry approximations for the exchange correlations—the Hartree–Fock approximation, the local density approximation, and the Müller approximation—are defined and discussed. The G-, P-, Q-Conditions and also the .- and .-Conditons deriving from .-representability are introduced and used to derive lower bounds on the ground state energy.

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Spurious Modes in Dirac Calculations and How to Avoid ThemIn this paper we consider the problem of the occurrence of spurious modes when computing the eigenvalues of Dirac operators, with the motivation to describe relativistic electrons in an atom or a molecule. We present recent mathematical results which we illustrate by simple numerical experiments. We also discuss open problems.

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The Quantum Energy Agrees with the Müller Energy up to Third OrderWe show that the ground state energy . of the Müller functional of (neutral) atoms of atomic number . equals to the quantum mechanical ground state energy . up order ., i.e., .