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A Guided Tour Through Modern Charge Density Analysis

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Modern Charge-Density Analysis

Abstract

A concise summary is provided on the basic aspects of charge density (CD) analysis and an overview of the charge density research and developments over the last 10 years. A glimpse is given to the issues which are treated in more details in the remaining chapters of this book and to those few that, although of some importance, could not be covered. Advances in experimental methodologies and in the charge density model refinements, along with progresses in quantum mechanical methods and in the interpretation/understanding of chemical bonding and interactions are briefly summarized. The increasingly stronger connection between charge density research and challenging questions of relevance to chemistry and to materials and life science is overviewed.

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Notes

  1. 1.

    The ½ multiplicative factor in Eq. 1.19 complies with the adopted normalization of ρ2 to the number of distinct electron pairs N(N-1)/2, as used in Parr’s book [36]. In the literature on the exchange-correlation density, the Mc Weeney [8] ρ2 normalization to N(N-1) electron pairs is often adopted. Though somewhat less physically meaningful, such a normalization has undoubtedly some advantages in the derivations of quantities related to ρ2,xc. However, we prefer to retain our initial choice and be consistent with the normalization adopted in Eq. 1.13 throughout all this chapter. Moreover, some authors prefer to precede ρ2,xc by a plus rather than a minus sign in Eq. 1.19 and, within such definition, ρ2,xc will integrate to –N. The different normalization on ρ2 (and the difference in sign for ρ2,xc) have clearly a consequence on some of the formula reported from now on in this section.

  2. 2.

    For instance, ten versions of the Wien-2 k code – one among the most accurate schemes for band structure calculations – have been released during the last decade and a separate version, WIEN-ncm able to handle the case of non collinear magnetism has also appeared.

  3. 3.

    Dirac’s operator is defined in terms of the linear momentum operator and of a 3-vector whose components are (4 × 4) matrices built, on the off diagonal blocks, from Pauli’s spin matrices.

  4. 4.

    ZORA represents another approach for reducing the four-component Dirac equation to an effective two-component form.

  5. 5.

    The fact that apparently contradictory descriptions of bonding may come out when using the bond path criterion or the delocalization index values should not be a source of particular concern, despite both these bonding indicators are defined within QTAIM. Indeed, information from different spaces is being analyzed and complementary information is thus obtained: bond path are made manifest in the 3D position space, whereas delocalization indices are defined in the 6D pair density space, where competition between electron localization within atomic basins and two-center or multi-center electron delocalization is observed and evaluated.

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Acknowledgements

This book was planned in autumn 2008, after the successful organization of the 5th European Charge Density Meeting (Gravedona, Italy, 6–11 June 2008). We accepted the invitation from Springer, by proposing a challenging project, that was to provide a broad overview of the many applications of charge density analysis, involving many scientists who were requested, whenever possible, to write joint contributions. We believe that this goal has been achieved, although with strong efforts, given its complexity.We are indebted to a number of colleagues, especially to all the authors of contributions reported in this book, for their excellent cooperation and many useful suggestions. We also thank those colleagues who acted as anonymous referees and largely contributed to the improvement of this project.

We wish to dedicate this book to some colleagues who have unfortunately passed away during the production of this book, in particular Prof. M. A. Blanco (University of Oviedo), Prof. A. Goeta (University of Durham), Prof. C. Pisani and Prof. C. Roetti, both at University of Turin.

P.M. thanks the Swiss National Science Foundation for financial support of his research (project 200021_125313).

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  1. Istituto di Scienze e Tecnologie Molecolari del CNR (CNR-ISTM) e Dipartimento di Chimica Fisica ed Elettrochimica, Università di Milano, Via Golgi 19, I-20133, Milan, Italy

    Carlo Gatti

  2. Center for Materials Crystallography, Aarhus University, Langelandsgade 140, DK-8000, Aarhus C, Denmark

    Carlo Gatti

  3. Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH3012, Bern, Switzerland

    Piero Macchi

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  1. Carlo Gatti
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Correspondence to Carlo Gatti or Piero Macchi .

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  1. Istit. di Scienze e Tecn. Molec. del CNR, c/o Dipt di Chim. Fis. ed Elettrochim., CNR-ISTM, Via Golgi 19, Milano, 20133, Italy

    Carlo Gatti

  2. , Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, Bern, 3012, Switzerland

    Piero Macchi

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Gatti, C., Macchi, P. (2011). A Guided Tour Through Modern Charge Density Analysis. In: Gatti, C., Macchi, P. (eds) Modern Charge-Density Analysis. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3836-4_1

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