Reactivity indicators for degenerate states in the density-functional theoretic chemical reactivity theory

Density-functional-theory-based chemical reactivity indicators are formulated for degenerate and near-degenerate ground states. For degenerate states, the functional derivatives of the energy with respect to the external potential do not exist, and must be replaced by the weaker concept of functional variation. The resultant reactivity indicators depend on the specific perturbation. Because it is sometimes impractical to compute reactivity indicators for a specific perturbation, we consider two special cases: point-charge perturbations and Dirac delta function perturbations. The Dirac delta function perturbations provide upper bounds on the chemical reactivity. Reactivity indicators using the common used "average of degenerate states approximation" for degenerate states provide a lower bound on the chemical reactivity. Unfortunately, this lower bound is often extremely weak. Approximate formulas for the reactivity indicators within the frontier-molecular-orbital approximation and special cases (two or three degenerate spatial orbitals) are presented in the supplementary material. One remarkable feature that arises in the frontier molecular orbital approximation, and presumably also in the exact theory, is that removing electrons sometimes causes the electron density to increase at the location of a negative (attractive) Dirac delta function perturbation. That is, the energetic response to a reduction in the external potential can increase even when the number of electrons decreases.     

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.     

Phenomenological chemical reactivity theory for mobile electrons

We present herein a model to deal with the chemical reactivity, selectivity and site activation concepts of π electron systems derived by merging the classical Coulson–Longuet-Higgins response function theory based on the Hückel molecular orbital (HMO) theory and the conceptual density functional theory. HMO-like expressions for the electronic chemical potential, chemical hardness and softness, including their local counterparts, atomic and bond Fukui functions and non-local response functions are derived. It is shown that sophisticated non-local concepts as site activation may be cast into deeper physical grounds by introducing a simplified version of static response functions. In this way, useful quantities such as self and mutual polarizabilities originally defined through the HMO parameters can be redefined as self and mutual softnesses. The model is illustrated by discussing the classical Hammett free energy relationship describing inductive substituent effects on the reactivity of benzoic acids.     

Theoretical study of the surface reactivity of alkaline earth oxides: local density of states evaluation of the local softness

The local softness of MgO, CaO, SrO, and BaO (100) surfaces has been studied using a model based on the local density of states. In all the species, the local softness (chemical reactivity) of oxygen atoms at the surface is enhanced as compared to the bulk. The results for the local and the global softness are in agreement with the ionic pattern of the metal-oxygen bond of the series.     

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.     

Theory of non-local (pair site) reactivity from model static-density response functions

Activation is a fundamental and well-known concept in chemistry. It may be qualitatively defined as an increase in the chemical reactivity pattern of a molecule at a given site k when the system is locally perturbed at a different site l, say. This external perturbation arise from a localized molecular rearrangement, a substitution, a selective solvation or simply by the approach of a reagent of variable hardness. This work presents a theoretical approach intending to quantify this activation concept in the density functional framework. This is done here by first calculating the fluctuation of the electron density at a given site k for the ground state of the isolated substrate (static reactivity model) and then incorporating the substrate and model electrophile reagents in a spatial disposition related to a virtual transition structure for the parent system. This perturbation is assumed representable by local changes in the external potential. It is shown that a local approximation to the softness kernel s(r, r′) yields a simple expression for the fluctuation of the electron density δρ(r _k ), which shows that this change becomes proportional to the variation of an effective potential δu(r _k ), containing the information on the variation in the chemical potential and the external perturbing potential at site k; the proportionality constant being the local softness s ⁰(r k) at that site. The strong local approximation made to the kernel s(r, r′) causes the second reactivity site (l) to implicitly appear in the formulation through the changes in the electronic chemical potential term. It is shown that the introduction of a less restrictive approach to the linear response function, obtained from a model Kohn-Sham one-electron density matrix, leads to the same result. Non-locality is therefore self-contained in the electronic chemical potential contribution to the modified potential, and may be associated with an intramolecular charge transfer between the active sites of the ambident nucleophilic/electrophilic substrate, promoted by the presence of the reagents. The resulting formulation of pair-site reactivity is illustrated for the electrophilic attack on the CN⁻ ion by different model electrophile agents of variable hardness. It is shown that correct reactivity indexes are obtained only when the topology of the transition structure is used as a vantage point to perturb the CN⁻ ion. The calculations were performed at both density functional theory and ab-initio Hartree-Fock levels. The results show that the proposed model is independent of the method used to obtain ρ(r). Received: 30 September 1997 / Accepted: 30 December 1997     

Chemical bonding in excited states: Energy transfer and charge redistribution from a real space perspective

This work provides a novel interpretation of elementary processes of photophysical relevance from the standpoint of the electron density using simple model reactions. These include excited states of H₂ taken as a prototype for a covalent bond, excimer formation of He₂ to analyze non‐covalent interactions, charge transfer by an avoided crossing of electronic states in LiF and conical interesections involved in the intramolecular scrambling in C₂H₄. The changes of the atomic and interaction energy components along the potential energy profiles are described by the interacting quantum atoms approach and the quantum theory of atoms in molecules. Additionally, the topological analysis of one‐ and two‐electron density functions is used to explore basic reaction mechanisms involving excited and degenerate states in connection with the virial theorem. This real space approach allows to describe these processes in a unified way, showing its versatility and utility in the study of chemical systems in excited states. © 2017 Wiley Periodicals, Inc.     

Electronic structure of carbon nanotubes with an impurity point defect

A method for calculating the electronic structure of point defects in nanotubes is developed on the basis of the linear augmented cylindrical wave (LACW) method. The Green function of a defect nanotube is calculated using the Dyson matrix equation. The consideration is carried out in terms of the local density functional theory and the muffin-tin approximation for the electronic potential. Local densities of state are calculated for boron and nitrogen dopants in metal, semimetal, and semiconductor and chiral and nonchiral nanotubes. An increased density of states at the Fermi level is the most significant effect of boron and nitrogen dopants in metal nanotubes. In all semiconductor nanotubes, localized boron states close the optical band-gap. The effect of nitrogen atoms is restricted to a small rise in local densities of state at the Fermi level.     

Local and nonlocal density functional calculations of the molecular structure of isomeric thiadiazoles

The chemistry of thiadiazoles and their derivatives is of considerable interest in chemistry owing to their pharmacological and potential industrial applications. In this context, a detailed study of isomeric thiadiazole molecules has been done using local (SVWN; Slater, and Vosko, Wilk and Nusair) and nonlocal (BLYP; Becke, and Lee, Yang and Parr) density functionals and optimizing the molecular geometries by means of the gradient technique. A charge sensitivity analysis of the studied molecule has been performed by resorting to density functional theory, obtaining several sensitivity coefficients such as the molecular energy, net atomic charges, global and local hardness, global and local softness and Fukui functions. With these results and the analysis of the dipole moments, the molecular electrostatic potentials and the total electron density maps, several conclusions have been inferred about the preferred sites of chemical reaction of the studied compounds. The condensed Fukui functions are shown to be one of the best criteria for predicting chemical reactivity.     

Combination of perturbative and variational methods for calculating molecular spectra: calculation of the upsilon=3-5 CH stretch overtone spectrum of CHF3

Highly excited states of the CHF3 molecule belonging to the third, fourth, and fifth Fermi polyad are calculated using a combination of the Van Vleck perturbation theory and a variational treatment. The perturbation theory preconditions the Hamiltonian matrix by transforming away all couplings except those between nearly degenerate states. This transformation is implemented so that eigenvalues can be found with significantly smaller matrices than that which would be needed in the original normal mode representation. Even with preconditioning, at the energies as high as 3-5 quanta in the CH stretch, it is not possible to directly diagonalize the Hamiltonian matrix due to the large basis sets required. Iterative methods, particularly the block-Davidson method, are explored for finding the eigenvalues. The methods are compared and the advantages discussed.     

A comparison of the effect of nanotube chirality and electronic properties on the π–π interaction of single‐wall carbon nanotubes with pyrazinamide antitubercular drug

Theoretical investigation on local electronic structure and stability of the π–π stacking interaction of pyrazinamide (PZA) with armchair (5,5) and zigzag (9,0) single‐walled carbon nanotubes (SWCNTs) is performed using density functional theory (DFT). PZA is physisorbed onto nanotube sidewall through interaction of π orbitals of PZA and SWCNT and the enhanced structural stability of PZA/SWCNT systems is due to weak side‐on rather than the head‐on π‐interactions. The physisorption of PZA onto SWCNT sidewall is thermodynamically favored; as a consequence, it modulates the electronic properties of pristine nanotube in the vicinity of Fermi region and π–π stacked interactions is stronger in (9,0) SWCNT compared to (5,5) SWCNT. The density of states (DOS) analysis show that PZA contributes toward the enhancement of electronic states. Projected DOS and frontier orbital analysis in the vicinity of Fermi level region suggest the electronic states to be contributed from SWCNT rather than PZA. In addition, hybrid DFT calculation which includes the dispersion correction is employed to explain the non‐covalent π–π stacking interaction between PZA and SWCNT. The local density approximation and GGA results are compared with DFT‐D to explain near about accurately the weak nonbonded van der Waals interactions between PZA and SWCNTs. © 2012 Wiley Periodicals, Inc.     

Face-integrated Fukui function: understanding wettability anisotropy of molecular crystals from density functional theory

Wettability is one of the anisotropic surface properties of molecular crystals that exhibit the structural variance of chemical moieties on various growth faces. The divergence in liquid-solid interactions at different faces is thought to be related to the inherent responding capacity or sensitivity of a solid surface to the perturbation in electronic structures and atomic positions as a result of the contact by a liquid. Since the Fukui function, according to density functional theory (DFT), is a local function for describing such sensitivity to the structural perturbation and is directly related to local softness, it has been proposed and tested to use an integrated Fukui function over a crystallographic plane for describing the anisotropy of solid-liquid interactions. It is found that the contact angle of a polar solvent, such as water, on a crystal surface shows an intimate connection to the integrated Fukui functions of the surface, illustrating an extension of Pearson's HSAB (hard and soft acids and bases) to crystal systems. The concept of face-integrated Fukui function and the approach to apply the HSAB with the DFT-based concepts may provide a powerful means for describing anisotropic properties, including wettability of organic crystals.