Chemical potential, hardness, hardness and softness kernel and local hardness in the isomorphic ensemble of density functional theory

Expanding horizons in conceptual density functional theory: Novel ensembles and descriptors to decipher reactivity patterns

Conceptual density functional theory (CDFT) and the quantum reactivity descriptors stemming from it have proven to be valuable tools for understanding the chemical behavior of molecules. This article is presented as being intrinsically of dual character. In a first part, it briefly reviews, in a deliberately didactical way, the main ensembles in CDFT, while the second half presents two additional ensembles, where the chemical hardness acts as a natural variable, and their respective reactivity descriptors. The evaluation of these reactivity descriptors on common organic chemical reagents are presented and discussed.

Some Recent Advances in Density-Based Reactivity Theory

Establishing a chemical reactivity theory in density functional theory (DFT) language has been our intense research interest in the past two decades, exemplified by the determination of steric effect and stereoselectivity, evaluation of electrophilicity and nucleophilicity, identification of strong and weak interactions, and formulation of cooperativity, frustration, and principle of chirality hierarchy. In this Featured Article, we first overview the four density-based frameworks in DFT to appreciate chemical understanding, including conceptual DFT, use of density associated quantities, information-theoretic approach, and orbital-free DFT, and then present a few recent advances of these frameworks as well as new applications from our studies. To that end, we will introduce the relationship among these frameworks, determining the entire spectrum of interactions with Pauli energy derivatives, performing topological analyses with information-theoretic quantities, and extending the density-based frameworks to excited states. Applications to examine physiochemical properties in external electric fields and to evaluate polarizability for proteins and crystals are discussed. A few possible directions for future development are followed, with the special emphasis on its merger with machine learning.

Extending the Scope of Conceptual Density Functional Theory with Second Order Analytical Methodologies

In the context of the growing impact of conceptual density functional theory (DFT) as one of the most successful chemical reactivity theories, response functions up to second order have now been widely applied; in recent years, among others, particular attention has been focused on the linear response function and also extensions to higher order have been put forward. As the larger part of these studies have been carried using a finite difference approach to compute these concepts, we now embarked on (an extension of) an analytical approach to conceptual DFT. With the ultimate aim of providing a complete set of analytically computable second order properties, including the softness and hardness kernels, the hardness as the simplest second order response function is scrutinized again with numerical results highlighting the difference in nature between the analytical hardness (referred to as hardness condition) and the Parr-Pearson absolute chemical hardness. The hardness condition is investigated for its capability to gauge the (de)localization error of density functional approximations (DFAs). The analytical Fukui function, besides overcoming the difficulties in the finite difference approach in treating negatively charged systems, also showcases the errors of deviating from the straight-line behavior using fractional occupation number calculations. Subsequently, the softness kernel and its atom-condensed inverse, the hardness matrix, are accessed through the Berkowitz-Parr relation. Revisiting the softness kernel confirms and extends previous discussions on how Kohn's Nearsightedness of Electronic Matter principle can be retrieved and identified as the physicist's version of the chemist's "transferability of functional groups" concept. The accurate, analytical hardness matrix evaluation on the other hand provides further support for the basics of Nalewajski's charge sensitivity analysis. Based on Parr and Liu's functional expansion of the energy functional, a new energy decomposition is introduced with an order of magnitude analysis of the different terms for a series of simple molecules both at their equilibrium geometry and upon variation in bond length and dihedral angle. Finally, for the first time, the perturbation expansion of the energy functional is studied numerically up to second order now that all response functions and integration techniques are at hand. The perturbation expansion energies are in excellent agreement with those obtained directly from DFA calculations giving confidence in the convergence of the perturbation series and its use in judging the importance of the different terms in reactivity investigations.

Molecular Interactions From the Density Functional Theory for Chemical Reactivity: The Interaction Energy Between Two-Reagents

Reactivity descriptors indicate where a reagent is most reactive and how it is most likely to react. However, a reaction will only occur when the reagent encounters a suitable reaction partner. Determining whether a pair of reagents is well-matched requires developing reactivity rules that depend on both reagents. This can be achieved using the expression for the minimum-interaction-energy obtained from the density functional reactivity theory. Different terms in this expression will be dominant in different circumstances; depending on which terms control the reactivity, different reactivity indicators will be preferred.

Links among the Fukui potential, the alchemical hardness and the local hardness of an atom in a molecule

This paper presents a brief summary of the difficulty that resides in the definition of the elusive concept of local chemical hardness. We argue that a definition of local hardness should be useful to a reactivity principle and not just as a mere definition. We then continue with a formal discussion about the benefits and difficulties of using the Fukui potential, which is interpreted as an alchemical derivative (alchemical hardness), as descriptor of local hardness of molecules. Computational evidence shows that the alchemical hardness is at least as good a descriptor as the combination of other two well-stabilized descriptors of local hardness, such as the Fukui function and grand canonical local hardness. Although our results are auspicious for the alchemical hardness as descriptor of local hardness, we finish by calling the attention of the community on the importance of discussing the raison d'être of a local hardness function and its main characteristics. We suggest that an axiomatic construction of local hardness could be they way of constructing a local hardness which is both useful and free of arbitrariness.

Evaluation of (Z)-5-(Azulen-1-ylmethylene)-2-thioxothiazolidin-4-ones Properties Using Quantum Mechanical Calculations

Derivatives of (Z)-5-(azulen-1-ylmethylene)-2-thioxothiazolidin-4-one are reported as heavy metal (HM) ligands in heterogeneous systems based on chemically modified electrodes. Their ability to coordinate HMs ions has recently been shown to be very selective. In this context, an additional computer-assisted study of their structure was performed using density functional theory (DFT) to achieve a complex structural analysis. Specific molecular descriptors and properties related to their reactivity and electrochemical behaviour were calculated. The correlation between certain quantum parameters associated with the general chemical reactivity and the complexing properties of the modified electrodes based on these ligands was carried out to facilitate the design of molecular sensors. Good linear correlations between DFT-calculated HOMO/LUMO energies and experimental redox potentials were found. A good agreement between the chemical shifts predicted by the DFT method and those determined experimentally from NMR data for these ligands demonstrated the accuracy of the calculations to assess the structural data. Such a computational approach can be used to evaluate other properties, such as electrochemical properties for similar azulene derivatives.

Conceptual density functional theory based electronic structure principles

In this review article, we intend to highlight the basic electronic structure principles and various reactivity descriptors as defined within the premise of conceptual density functional theory (CDFT). Over the past several decades, CDFT has proven its worth in providing valuable insights into various static as well as time-dependent physicochemical problems. Herein, having briefly outlined the basics of CDFT, we describe various situations where CDFT based reactivity theory could be employed in order to gain insights into the underlying mechanism of several chemical processes.

Comment on “Revisiting the definition of local hardness and hardness kernel” by C. A. Polanco-Ramirez, M. Franco-Pérez, J. Carmona-Espíndola, J. L. Gázquez and P. W. Ayers, Phys. Chem. Chem. Phys., 2017, 19, 12355

In this comment we show that the derivation proposed Polanco-Ramirez et al. appears naturally in the Taylor expansion of the energy, showing that their whole construction is not artificially built.

Local chemical potential, local hardness, and dual descriptors in temperature dependent chemical reactivity theory

From the definition of a local chemical potential, well-behaved expressions for the local hardness and the dual descriptors are derived.

Revisiting the definition of local hardness and hardness kernel

Local hardness is redefined following similar rules to those of local softness. The new concept describes chemical trends correctly.

Investigation of electron density changes at the onset of a chemical reaction using the state-specific dual descriptor from conceptual density functional theory

The electron density changes from reactants towards the transition state of a chemical reaction is expressed as a linear combination of the state-specific dual descriptors (SSDD) of the corresponding reactant complexes.

Revisiting electroaccepting and electrodonating powers: proposals for local electrophilicity and local nucleophilicity descriptors

It is shown that the electrophilicity index is also a rational choice for measuring nucleophilicity.

The physical basis of the hard/soft acid/base principle

The dependence of molecular properties on the chemical hardness is explored. As the chemical hardness of a molecule increases, its size and polarizability typically decrease and its charge and electronegativity typically increase. On the basis of these properties, the interaction energy between hard and soft acids and bases is quantified, and the physical basis of the global and local hard/soft acid/base (HSAB) principles is elucidated.

Generalized nuclear Fukui functions in the framework of spin-polarized density-functional theory

An extension of Cohen's nuclear Fukui function is presented in the spin-polarized framework of density-functional theory (SP-DFT). The resulting new nuclear Fukui function indices PhiNalpha and PhiSalpha are intended to be the natural descriptors for the responses of the nuclei to changes involving charge transfer at constant multiplicity and also the spin polarization at constant number of electrons. These generalized quantities allow us to gain new insights within a perturbative scheme based on DFT. Calculations of the electronic and nuclear SP-DFT quantities are presented within a Kohn-Sham framework of chemical reactivity for a sample of molecules, including H2O, H2CO, and some simple nitrenes (NX) and phosphinidenes (PX), with X=H, Li, F, Cl, OH, SH, NH2, and PH2. Results have been interpreted in terms of chemical bonding in the context of Berlin's theorem, which provides a separation of the molecular space into binding and antibinding regions.

DFT-based QSAR study of testosterone and its derivatives

QSAR study of derivatives of testosterone has been made with the help of quantum mechanical parameters such as Absolute Hardness (eta) and Electronegativity (chi). These two parameters have been derived with the help of density functional theory. The 3-D modeling and geometry optimization of all the compounds have been done with the help of PCMODEL software and semiempirical PM3 calculations performed with the help of WinMOPAC-7.21 software. The absolute hardness provides valuable information due to maximum hardness principle and used in development of QSAR. The information provided by electronegativity is not as clear as in case of absolute hardness.

Theoretical calculation of ionization potentials for disubstituted benzenes: additivity vs non-additivity of substituent effects

The ionization potentials of 55 para- and 55 meta-disubstituted benzenes, consisting of all binary combinations of electron-withdrawing groups (-NO2, -CF3, -CHO, -COOH) and electron-donating groups (-Cl, -CH3, -OH, -OCH3, -NH2, and -N(CH3)2) have been calculated using density functional theory with the B3LYP functional and a 6-31G(d) basis set. Relative ionization potentials (delta IP), referred to benzene, are compared with experimental values and shown to be in good agreement. The disubstituted data were correlated with monosubstituted delta IP data and shown to require quadratic terms in order to achieve a good fit; the validity of this conclusion was possible due to the low scatter in the calculated data. A simple MO analysis gives a semiquantitative interpretation of the observed trends in substitutent effects, including a discussion of combinations of substituents for which nonadditivity should be expected.