How electrons guard the space: shape optimization with probability distribution criteria |
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Authors: | Eric Cancès Renaud Keriven François Lodier Andreas Savin |
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Affiliation: | (1) CERMICSEcole Nationale des Ponts et Chaussées, 6 & 8 Av. Pascal, 77455 Champs-sur-Marne, France;(2) Laboratoire de Chimie Théorique, CNRS et Université Paris 6, 4 Pl. Jussieu, 75252 Paris, France |
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Abstract: | Efficient formulas for computing the probabilities of finding exactly electrons in an arbitrarily chosen volume 3 for Hartree–Fock wavefunctions are presented. These formulas allow the use of shape optimization techniques, such as level set methods, for optimizing with respect to various criteria involving such probabilities. The criterion defined as the difference between the Hartree–Fock and the independent-particle model probabilities of finding electrons in stresses the quantum effects due to the Pauli principle. We have implemented a 2D level set method for optimizing this criterion in order to study spatial separation of electron pairs in linear molecules. The method is described and the illustrative example of the BH molecule is reported.Contribution to the Jacopo Tomasi Honorary Issue |
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Keywords: | Shape optimization Hartree Fock Electron pairs Probability distribution Spatial seperator |
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