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Charge Density and Chemical Reactions: A Unified View from Conceptual DFT

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Modern Charge-Density Analysis

Abstract

Conceptual density-functional theory (DFT) provides a mathematical framework for using changes of the electron density to understand chemical reactions and chemical reactivity. The key idea is that by studying the response of a molecule or materials to perturbations, one can decipher its reactivity preferences. If a system reacts favorably to a perturbation, then this indicates that the system will react favorably with a certain class of reagents. Differentials of the energy may thus be interpreted as reactivity indicators. Because of the key role of energy differentials, the mathematical framework of conceptual DFT is similar to classical thermodynamics, with state functions, variational principles, and Legendre transforms. In this chapter we use this thermodynamic simile to present the mathematical underpinnings of conceptual DFT. Applications to systems of interest to organic, inorganic, and biological chemists are used to demonstrate how these abstract concepts may be applied to concrete chemical problems.

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Notes

  1. 1.

    The relationship between Eqs. 21.5 and 21.6 will be more clear if one imagines the integral as a Riemann sum or, alternatively, conceives of the change in the function, δf(r), as a vector in a Hilbert (or, more generally, a Banach) space.

  2. 2.

    This is obvious from the fact that the number of electrons in, for example, a solvated ion is usual not an integer. However, any measurement of the number of electrons will always produce an integer answer.

  3. 3.

    Unfortunately, it is difficult to formulate the open-system picture at zero temperature because the Legendre transform from the number of electrons to the chemical potential is no longer well-defined. The electron-preceding picture may be formulated, but the hardness kernel has derivative discontinuities in both variables and is therefore difficult to work with.

  4. 4.

    Of course, matters are more complicated. A soft electrophile whose highest occupied orbital(s) do not have the appropriate size/symmetry to interact strongly with the sulfur atom may prefer to bind through the nitrogen atom. Similarly, a hard electrophile for which the charge on the active site is small (a rare, but not impossible occurrence) may prefer to bind through the sulfur atom. Finally, in some cases a molecular rearrangement subsequent to the initial attack may change the binding pattern. Complications like these arise in any qualitative theory of chemical reactivity, but the DFT-based approach is perhaps unique in that they can be addressed within the context of the theory, although capturing such effects usually require difficult to compute higher-order reactivity indicators.

  5. 5.

    The Fluorines do not react because the Fluorine atoms hold their charge very tightly and, in TeF5–, they are nowhere nearly as negative as their formal −1 charge might lead one to anticipate. The Hirshfeld charges on the Fluorine atoms range from −26 to −35 and the Mulliken charges range from −46 to −53. The least charged Fluorine atom is the “exposed” atom at the top of the deformed square pyramid, which one might otherwise expect to be the most reactive.

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Acknowledgments

Paul Johnson thanks the governments of Ontario and Canada for OGS-M and CGS-M graduate fellowships. Paul Ayers acknowledges research support for NSERC, Sharcnet, and the Canada Research Chairs. Paul Geerlings acknowledges the Fund for Sciengific Reasearch-Flanders (FWO) and the Free University of Brussels (VUB) for continuous support to his group. He thanks all present and past group members for many years of intellectually stimulating work in the area of Conceptual DFT. Tim Fievez thanks the FWO-Flanders for a Predoctoral Fellowhip as Aspirant. Lee Bartolotti acknowledges financial support from RENCI@ECU.

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  1. Department of Chemistry, McMaster University, Hamilton, ON, Canada, L8S4M1

    Paul A. Johnson & Paul W. Ayers

  2. Department of Chemistry, East Carolina University, Greenville, NC, 27858, USA

    Libero J. Bartolotti

  3. Eenheid Algemene Chemie (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, 1050, Brussel, Belgium

    Tim Fievez & Paul Geerlings

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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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Johnson, P.A., Bartolotti, L.J., Ayers, P.W., Fievez, T., Geerlings, P. (2011). Charge Density and Chemical Reactions: A Unified View from Conceptual DFT. In: Gatti, C., Macchi, P. (eds) Modern Charge-Density Analysis. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3836-4_21

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