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2.R. G. Parr and W. Yang, Density Functional Theory of Atoms and Molecules (Oxford University Press, NewYork, 1989).
3.R. F. W. Bader, Atoms in Molecules: A Quantum Theory (Oxford University Press, Oxford, U.K., 1990).
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10.notice that we will use the common term of “bond” even if its use has been criticized [see for instance R. F. W. Bader, J. Phys. Chem. A 113, 10391 (2009)].
11.Atomic units will be used unless explicitly otherwise stated.
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14.Note that the exchange conventional gauge is used. Besides, it is also assumed that the inhomogeneity of the Laplacian near a BCP will only have a small impact on the energy densities variations. As, from the best of our knowledge, the role of the higher density derivatives are unknown at least for correlation, it is anyway not possible to go behind this order; moreover, Eq. (2) is rigorously valid only in the high density limit, see C. D. Hu and D. C. Langreth, Phys. Rev. B 33, 943 (1986);
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29.The molecules were fully optimized using Gaussian 03 (Ref. 31) at the PBE0 level (Ref. 32), the nonmetallic atoms being described by the standard Pople basis set and the metals by the one (Ref. 33). The topological analysis has been carried out with the MORPHY98 software (Refs. 34 and 35).
30.Notice that the information carried by is lost, but is not relevant for our purpose. The ellipticity (which only focuses on the plane that is orthogonal to the bond path) would constitute an alternative. For the H bonds in Ref. 24, it lies in the [0.005–1.394] range, whereas the one for the agostic bonds in Ref. 25 is [0.703,1.534], so that overlap exists; thus ellipticity cannot be discriminative.
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A first (local) bridge between Kohn–Sham density functional theory and the quantum theory of atoms in molecules of Bader is built by means of a second order reduced density gradient expansion of the exchange-correlation energy density at a given bondcritical point. This approach leads to the definition of new “mixed” descriptors that are particularly useful for the classification of the chemical interactions for which the traditional atoms in molecules characterization reveals insufficient, as for instance the distinction between hydrogen and agostic bonds.


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