Do the Local Softness and Hardness Indicate the Softest and Hardest Regions of a Molecule?

In this work, we will show that the largest values of the local softness and hardness do not necessarily correspond to the softest and hardest regions of the molecule, respectively. Based on our results, we will argue that it is more useful to interpret the local softness and the local hardness as functions that measure the "local abundance" or "concentration" of the corresponding global properties. This new point of view helps reveal how and when these local reactivity indices are most useful.     

Beyond electronegativity and local hardness: Higher-order equalization criteria for determination of a ground-state electron density

Higher-order global softnesses, local softnesses, and softness kernels are defined along with their hardness inverses. The local hardness equalization principle recently derived by the authors is extended to arbitrary order. The resulting hierarchy of equalization principles indicates that the electronegativity/chemical potential, local hardness, and local hyperhardnesses all are constant when evaluated for the ground-state electron density. The new equalization principles can be used to test whether a trial electron density is an accurate approximation to the true ground-state density and to discover molecules with desired reactive properties, as encapsulated by their chemical reactivity indicators.     

Critical thoughts on computing atom condensed Fukui functions

Different procedures to obtain atom condensed Fukui functions are described. It is shown how the resulting values may differ depending on the exact approach to atom condensed Fukui functions. The condensed Fukui function can be computed using either the fragment of molecular response approach or the response of molecular fragment approach. The two approaches are nonequivalent; only the latter approach corresponds in general with a population difference expression. The Mulliken approach does not depend on the approach taken but has some computational drawbacks. The different resulting expressions are tested for a wide set of molecules. In practice one must make seemingly arbitrary choices about how to compute condensed Fukui functions, which suggests questioning the role of these indicators in conceptual density-functional theory.     

Predicting the reactivity of ambidentate nucleophiles and electrophiles using a single, general-purpose, reactivity indicator

We recently proposed a new reactivity indicator, termed the "general-purpose reactivity indicator", Xi, which describes not only the classical reactivity paradigms, but also describes reactions that are neither frontier-orbital nor electrostatically controlled. This indicator was proposed to be especially useful for reactants with multiple reactive sites, especially if the nature of the reactivity at those sites was different. This suggests that this reactivity indicator is especially appropriate for ambidentate molecules; this paper confirms this hypothesis. The general-purpose reactivity indicator not only identifies the most reactive sites, it also identifies which substrates prefer which reactive sites. In particular, the reactivity indicator allows one to clearly distinguish which sites of an ambidentate molecule are most reactive when electron transfer from the attacking reagent is large (a soft reagent) and which sites are most reactive when the attacking reagent is hard and highly charged (so that electron transfer is relatively insignificant). To illustrate the efficacy of the indicator for nucleophiles we consider SCN(-), SeCN(-), NO(2)(-), SO(3)(2-). For electrophiles we consider dimethyl carbonate, N-methyl-N-nitrosotoluene-p-sulfonamide (MNTS), and 1-chloro-2,4,6-trinitrobenzene (CNB).     

The relationship between the eigenvalues and eigenvectors of a similarity matrix and its associated Carbó index matrix

The eigenvalues and eigenvectors of a quantum similarity matrix are also generalized eigenvalues and eigenvectors of the associated matrix of Carbó indices. This establishes bounds on the spectrum of the Carbó index matrix; for example, a quantum similarity matrix is positive semidefinite if and only if the associated Carbó index matrix is also positive semidefinite. The generalized eigenvalue problem for the Carbó index matrix has a diagonal metric matrix on the right-hand-side. Every generalized eigenvalue problem can be written in this diagonal form (i.e., this form is not special to this application). This diagonally structure generalized eigenvalue problem is especially convenient because it can be converted to a conventional eigenvalue problem by a particularly simple partial Löwdin transformation.     

Obionin B: An o-pyranonaphthoquinone decaketide from an unidentified fungus (MSX 63619) from the Order Pleosporales

A fungal extract (MSX 63619), from the Mycosynthetix library of over 50,000 fungi, displayed promising cytotoxicity against a human tumor cell panel. Bioactivity-directed fractionation led to the isolation of an o-pyranonaphthoquinone decaketide, which we termed obionin B (1). The structure of 1 was deduced via spectroscopic and spectrometric techniques. The IC₅₀ value of 1 was moderate, ranging from 3 to 13 μM, depending on the cell line tested.     

Newton trajectories for finding stationary points on molecular potential energy surfaces

We present a new algorithm for computing Newton trajectories based on the Quadratic String Method (QSM) and explain how this can be used to find key stationary points on the molecular potential energy surface (PES). This method starts by using the intersections of Newton trajectories to locate stationary points on the PES. These points could then be used to determine the minimum energy path. The new method, called QSM-NT, is shown to be efficient and reliable for both analytical potential energy surfaces and potential energy surfaces computed from quantum chemistry calculations. The advantages and pitfalls of this method for exploring PES are discussed. In particular, the problem of discontinuous Newton trajectories is elucidated.     

Stability conditions for density functional reactivity theory: an interpretation of the total local hardness

The second-order Taylor series expansions commonly used in the density functional chemical reactivity theory are used to define local stability conditions for electronic states. Systems which satisfy these conditions are stable to infinitesimal perturbations due to approaching chemical reagents. The basic formalism considered here supersedes previous variational approaches to chemical reactivity theory like the electrophilicity, potentialphilicity, and chargephilicity. The total local hardness emerges naturally in this analysis, and can be clearly interpreted. When the total local hardness is small, the system is relatively insensitive to perturbations. Furthermore, minus the total local hardness is an energetically favorable perturbation of the external potential.     

Natural orbital Fukui function and application in understanding cycloaddition reaction mechanisms

A new condensed form of the Fukui function, the natural orbital Fukui function (NOFF), is proposed and derived from natural bond orbital occupancy. It is defined as the change in natural bond orbital occupancy upon electronic perturbation (electron addition to, or depletion from, a molecular system). Applying NOFF to a series of cycloaddition reactions (e.g., [4 + 2] and [2 + 1] cycloadditions) illustrates the effectiveness of the concept in interpreting bond breakage and formation mechanisms.