The generalized maximum hardness principle revisited and applied to atoms and molecules

Abstract

In this perspective contribution, we revisit the Maximum Hardness Principle (MHP), formulated by Pearson in 1987, and an equivalent Minimum Polarizability Principle (MPP) from Chattaraj and Parr, with particular emphasis on the cases where nuclear potential acting on electrons does not remain constant, and where substantial modifications of the nuclear geometry take place (Generalized MHP, GMHP). We first bring basic concepts related to electronic hardness, and then we present an overview of important manifestations of the GMHP for molecular systems such as (i) the tendency of two free radicals to couple, (ii) reduced reactivity of noble gases, (iii) symmetry-breaking distortions related to the Jahn-Teller effect, and/or these connected with (anti)aromatic character of certain organic molecules, (iv) enhanced reactivity of excited states, (v) high-low spin transitions, etc. GMHP is an important qualitative indicator in studies of molecular isomerism and reactivity. Quantitative aspects, traditionally measured by changes of electronic plus nuclear energy, are readily explained by changes of hardness (or polarizability) of a molecular system. Several important exceptions from (G)MHP are discussed.

High-temperature superconductivity as viewed from the maximum hardness principle

“…The Maximum Hardness Principle [ 6 ] – and its reformulation by Chattaraj as the Minimum Polarizability Principle [ 7 ] – is an immensely useful qualitative concept which works in support of a chemical intuition, and it may be applied to a vast array of important problems [ 8 , 9 ]. The hardness in question, η, is the electronic (and not mechanical) hardness, i.e.…”

“…The MHP in its original formulation states that the chemical system adopts such geometry of nuclei that the associated electronic hardness is maximized. This statement, first voiced by Pearson [ 6 ], founder of the hardness concept [ 10 ], in fact is a generalized form of MHP, abbreviated here as GMHP [ 8 , 9 ]. The GMHP does not universally hold and it cannot be proved, since it has one important exception – namely it does not apply to totally symmetric vibrations of the chemical system.…”

“…Ref. [ 8 , 9 ] and numerous examples from literature discussed therein). This behaviour is nicely exemplified by elemental tin for which the semimetallic gray form with the direct band gap of ca.…”

Unconventional Look at the Diameters of Quantum Systems: Could the Characteristic Atomic Radius Be Interpreted as a Reactivity Measure?

“…Nevertheless, atomic dimensions should reflect atom predispositions to adopt hard or soft attributes, − which are referred to by electronic response functions and conceptual density functional theory reactivity descriptors. − Regardless of classical roots and its presumed role (of the closest distance to another atom, under equilibrium conditions with respect to distinct types of strong or weak interactions), the arguments raised imply that characteristic radius could be defined as a latent variable in regard to measurable parameters or quantum mechanical expectation values. Such attempts have been made, resulting in loose correlations. ,,,,,,, Among measurable physical quantities, those related to atom size and reactivity as well include electron density, ,,,, electric dipole polarizability, − or ionization potential. − ,,, …”

“…However, these relations between classification based on equilibrium constants and the characteristic radii are qualitative at most. The picture could be complemented with a quantitative interpretation based on fundamental electronic response functions. ,− However, a single-parameter description of acid–base interactions has been shown to be insufficient. − From another standpoint, chemical reactions involve bond-breaking and -forming processes, which implicate changes in the electronic structure described by ground-state electron density (or overall atomic electron population), and distortion in the geometrical structure characterized by positions of the nuclei. The electron density is determined via nuclear potential, which exemplifies “electron-following” mapping of chemical activity. − In the complementary “electron-preceding” view, the displacements of electron distribution are aimed at adjusting nuclear positions via the preceding step to reduce regional electronic strain due to external potential .…”