A generalized operational formula based on total electronic densities to obtain 3D pictures of the dual descriptor to reveal nucleophilic and electrophilic sites accurately on closed-shell molecules

The Dual Descriptor Reveals the Janus–Faced Behaviour of Diiodine

The Janus–faced ligand behavior of diiodine (I₂) was evidenced after applying the dual descriptor (DD or second-order Fukui function), thus providing additional support to the work performed by Rogachev and Hoffmann in 2013. Along with its capacity to reveal sites susceptible to undergo attacks simultaneously of nucleophilic and electrophilic types, another advantage of DD lies in being an orbital-free descriptor. That means it is based only upon total electron densities when written in its most accurate operational formula. This quality is not exclusive of DD because when Fukui functions are written in terms of electron densities instead of densities of frontier molecular orbitals, they become orbital-free descriptors too. Furthermore, the present work is an application of the generalized operational formula of the dual descriptor published in 2016 that takes into account any possible degeneracy in frontier molecular orbitals. As a proof about capabilities of DD, the possible sites for a favorable interaction between I₂ with two organometallic compounds [Rh₂(O₂CCF₃)₄] and [(C₈H₁₁N₂)Pt (CH₃)] were correctly revealed by overlapping the biggest lobe for receiving nucleophilic attacks of one molecule with the biggest lobe for receiving electrophilic attacks of the other molecule, so allowing to predict the same coordination modes as experimentally known: linear “end–on” for the [(C₈H₁₁N₂)Pt (CH₃)]…I₂, and bent “end–on” for the [Rh₂(O₂CCF₃)₄]…I₂ interactions.

From the Electron Density Gradient to the Quantitative Reactivity Indicators: Local Softness and the Fukui Function

Important reactivity measures such as the local softness, the Fukui function, and the global hardness have been calculated directly from first principles with the use of the electron density function, beyond the finite difference approximation. Our recently derived density gradient theorem and the principle of nearsightedness of the electronic matter have been instrumental in obtaining the original, albeit approximate, result on the local softness of an atom. By integration of the local softness s(r), we obtain the global softness S and the Fukui function f(r) = s(r)/S. Local and global softness values have also been calculated analytically for the basic hydrogenic orbitals; the general relation to the atomic number S = σZ ^-2 has been demonstrated, with constants σ characteristic for each orbital type. Global hardness η = 1/S calculated for atoms and ions has been favorably tested against its conventional measure given by the finite difference approximation: (I - A). Calculated test results for atoms and ions in rows 1-4 of the periodic table have been presented.

Analysis in silico of chemical reactivity employing the local hyper-softness in some classic aromatic compounds, boron aromatic clusters and all-metal aromatic clusters

In the current work, the authors analyzed and compared the chemical behavior of some (anti)aromatic compounds. The species selected are benzene and cyclobutadiene as the aromatic and antiaromatic classical examples, respectively. Next, the anion Al 4 2 - , which is the first all-metal molecule catalogued as aromatic and its non-metallic isoelectronic analog, B 4 2 - were also analyzed. The antiaromatic clusters Al 4 4 - and B 4 4 - were studied in form of lithium salts. And the end, the non-planar B 12 boron cluster and its isoelectronic analogs ( B 11 Be - and B 11 C + ) were considered for being analyzed under the same criterium. The analysis was realized employing the following descriptors: molecular electrostatic potential and local hyper-softness to get insights concerning local reactivity when facing reagents leading to ionic or covalent interactions. The results show that all the molecules analyzed presented some specific variations in their respective local reactivity despite being labeled as aromatic compounds. This analysis provides a notion that the local reactivity is more based on the nature of the atoms and the molecular geometry than the aromatic character by itself.

Proposal of a Fermi-Dirac-Derived Reactivity Descriptor: Beyond the Frontier MO Model

In this paper, we derive a reactivity descriptor stemming from the Fermi-Dirac population scheme, applied to density functional calculations on molecular systems. Assuming that molecular orbitals only marginally change when temperature is slightly increased from 0 K, we study the response of electron density to a change in temperature. Connection with usual conceptual density functional theory descriptors is made, and the T-variation of electron density for some representative examples is given and discussed.

Orbital-Weighted Dual Descriptor for the Study of Local Reactivity of Systems with (Quasi-) Degenerate States

An alternative response function, based on the dual descriptor in terms of Koopmans' approximation, is hereby proposed for the description of chemical reactivity in systems with (quasi-) degenerate frontier molecular orbitals. This descriptor is constructed from Fukui functions that include contributions from different orbitals, i.e., orbital-weighted Fukui functions. The methodology is applied to three case studies: the first case consists of a series of benchmark organic and inorganic molecules from which the dual descriptor, based only on frontier orbitals, is not appropriate to describe their reactivity. The second case deals with the proper description of chemical reactivity in Diels-Alder reactions between fullerene C₆₀ and cyclopentadiene (CP), revealing the importance of considering secondary orbital interactions for an adequate regioselectivity description. The third, and last case, consists of a series of polycyclic aromatic hydrocarbons (PAHs) possessing molecular orbital degeneracy. By means of analyzing of this descriptor, an alternative approach to the description of aromaticity is proposed. In all cases, the proposed index called "orbital-weighted dual descriptor" has proven to accurately describe the chemical reactivity and aromaticity of the studied systems.

New advances in conceptual-DFT: an alternative way to calculate the Fukui function and dual descriptor

An alternative way of calculating the Fukui function and the partial derivative of second order of the electronic density with respect to the number of electrons N is presented, the new formulas agree with the usual ones but only in cases without degeneracy. The new operative formulas are more general than the previous ones and are the right ones for those problematic cases where one or both of the frontier molecular orbitals are degenerate. Finally, we present a new way of applying the finite difference approximation that leads to more realistic results than the usual formulas. Graphical abstract A new way of calculating the Fukui function is presented that results in a new operative formula of the function. It has also been obtained the partial derivative of second order of the electronic density with respect to the number of electrons N, and it agree with the usual formula of the dual descriptor function but only in cases without degeneration.

A 3D visualization of the substituent effect : A brief analysis of two components of the operational formula of dual descriptor for open-shell systems

Six organometallic compounds coming from a basic Mo-based complex were analyzed from the perspective of the dual descriptor in order to detect subtle influences that a substituent group could exert on the reactive core at a long range. Since the aforementioned complexes are open-shell systems, the used operational formula for the dual descriptor is that one defined for those aforementioned systems, which was then compared with spin density. In addition, dual descriptor was decomposed into two terms, each of which was also applied on every molecular system. The obtained results indicated that components of dual descriptor could become more useful than the operational formula of dual descriptor because differences exerted by the substituents at the para position were better detected by components of dual descriptor rather than the dual descriptor by itself.