On the applicability of local softness and hardness

9 pages, 5 figures, 3 schemes, 2 tables.-- PMID: 20094672 [PubMed].Global hardness and softness and the associated hard/soft acid/base (HSAB) principle have been used to explain many experimental observed reactivity patterns and these concepts can be found in textbooks of general, inorganic, and organic chemistry. In addition, local versions of these reactivity indices and principles have been defined to describe the regioselectivity of systems. In a very recent article (Chem.–Eur. J. 2008, 14, 8652), the present authors have shown that the picture of these well-known descriptors is incomplete and that the understanding of these reactivity indices must be reinterpreted. In fact, the local softness and hardness contain the same potential information and they should be interpreted as the local abundance or concentration of their corresponding global properties. In this contribution, we analyze the implications of this new point of view for the applicability of these well-known descriptors when comparing two sites in three situations: two sites within one molecule, two sites in two different, but noninteracting molecules, and two sites in two different, but interacting, molecules. The implications on the HSAB principle are highlighted, leading to the discussion of the role of the electrostatic interaction.M. T. thanks the European Community for financial help through the postdoctoral grant MEIF-CT-2006-025362. P. G. and F. D. P are indebted to the Fund for Scientific Research—Flanders (FWO) and to the Free University of Brussels for continuous support to their group. P. W. A. thanks NSERC, the Canada Research Chairs, and Sharcnet for research support.Peer reviewe

Parity Fluctuations Between Coulomb Blockaded Superconducting Islands

We find that if two superconducting islands of different number parity are linked by a tunnel junction the unpaired electron in the odd island has a tendency to tunnel into the even island. This process leads to fluctuations in time of the number parity of each island, giving rise to a random telegraph noise spectrum with a characteristic frequency that has an unusual temperature dependence. This new phenomenon should be observable in a Cooper-pair pump and similar single-electron tunneling devices.Comment: 4 pages, self-unpacking uuencoded gz-compressed postscript file with 3 figures included; also available at http://www.lassp.cornell.edu/janko/publications.htm

Asymptotic tunneling conductance in Luttinger liquids

Conductance through weak constrictions in Luttinger liquids is shown to vanish with frequency $\omega$ as $c_1 \omega^2 + c_2 \omega^{2/g - 2}$, where $g$ is a dimensionless parameter characterizing the Luttinger liquid phase, and $c_1$ and $c_2$ are nonuniversal constants. The first term arises from the ^^ Coulomb blockade' effect and dominates for $g < 1/2$, whereas the second results from eliminating high-energy modes and dominates for $g > 1/2$.Comment: Latex file + one appended postcript figur

A new approach to local hardness

The applicability of the local hardness as defined by the derivative of the chemical potential with respect to the electron density is undermined by an essential ambiguity arising from this definition. Further, the local quantity defined in this way does not integrate to the (global) hardness - in contrast with the local softness, which integrates to the softness. It has also been shown recently that with the conventional formulae, the largest values of local hardness do not necessarily correspond to the hardest regions of a molecule. Here, in an attempt to fix these drawbacks, we propose a new approach to define and evaluate the local hardness. We define a local chemical potential, utilizing the fact that the chemical potential emerges as the additive constant term in the number-conserving functional derivative of the energy density functional. Then, differentiation of this local chemical potential with respect to the number of electrons leads to a local hardness that integrates to the hardness, and possesses a favourable property; namely, within any given electron system, it is in a local inverse relation with the Fukui function, which is known to be a proper indicator of local softness in the case of soft systems. Numerical tests for a few selected molecules and a detailed analysis, comparing the new definition of local hardness with the previous ones, show promising results.Comment: 30 pages (including 6 figures, 1 table

N-representability and stationarity in time-dependent density functional theory

To construct an N-representable time-dependent density-functional theory, a generalization to the time domain of the Levy-Lieb (LL) constrained search algorithm is required. That the action is only stationary in the Dirac-Frenkel variational principle eliminates the possibility of basing the search on the action itself. Instead, we use the norm of the partial functional derivative of the action in the Hilbert space of the wave functions in place of the energy of the LL search. The electron densities entering the formalism are $N$-representable, and the resulting universal action functional has a unique stationary point in the density at that corresponding to the solution of the Schr\"{o}dinger equation. The original Runge-Gross (RG) formulation is subsumed within the new formalism. Concerns in the literature about the meaning of the functional derivatives and the internal consistency of the RG formulation are allayed by clarifying the nature of the functional derivatives entering the formalism.Comment: 9 pages, 0 figures, Phys. Rev. A accepted. Introduction was expanded, subsections reorganized, appendix and new references adde