Relations among several nuclear and electronic density functional reactivity indexes

On the link between the reaction force constant and conceptual DFT

CONTEXT

The reaction force constant ( κ ), introduced by Professor Alejandro Toro-Labbé, plays a pivotal role in characterizing the reaction pathway by assessing the curvature of the potential energy profile along the intrinsic reaction coordinate. This study establishes a novel link between κ and the reactivity descriptors of conceptual density functional theory (c-DFT). Specifically, we derive expressions that relate the reaction force constant to nuclear softness and variations in chemical potential. Our findings indicate that regions of the reaction pathway where κ is negative match with significant electronic structure rearrangements, while positive κ regions match mostly with geometric rearrangements. This correlation between κ and c-DFT reactivity descriptors enhances our understanding of the underlying forces driving chemical reactions and offers new perspectives for analyzing reaction mechanisms.

METHODS

The internal reaction path for the proton transfer in SNOH, chemical potential, and nuclear softness were computed using DFT with B3LYP exchange-correlation functional and 6-311++G(d,2p) basis set.

Semi-Quantitatively Designing Two-Photon High-Performance Fluorescent Probes for Glutathione S-Transferases

Glutathione S-transferases (GSTs), detoxification enzymes that catalyze the addition of glutathione (GSH) to diverse electrophilic molecules, are often overexpressed in various tumor cells. While fluorescent probes for GSTs have often adopted the 2,4-dinitrobenzenesulfonyl (DNs) group as the receptor unit, they usually suffer from considerable background reaction noise with GSH due to excessive electron deficiency. However, weakening this reactivity is generally accompanied by loss of sensitivity for GSTs, and therefore, finely turning down the reactivity while maintaining certain sensitivity is critical for developing a practical probe. Here, we report a rational semiquantitative strategy for designing such a practical two-photon probe by introducing a parameter adopted from the conceptual density functional theory (CDFT), the local electrophilicity ω _k , to characterize this reactivity. As expected, kinetic studies established ω _k as efficient to predict the reactivity with GSH, and probe NI3 showing the best performance was successfully applied to detecting GST activities in live cells and tissue sections with high sensitivity and signal-to-noise ratio. Photoinduced electron transfer of naphthalimide-based probes, captured by femtosecond transient absorption for the first time and unraveled by theoretical calculations, also contributes to the negligible background noise.

Compensation effects in molecular interactions and the quantum chemical le Chatelier principle

Components of molecular interactions and various changes in the components of total energy changes during molecular processes typically exhibit some degrees of compensation. This may be as prominent as the over 90% compensation of the electronic energy and nuclear repulsion energy components of the total energy in some conformational changes. Some of these compensations are enhanced by solvent effects. For various arrangements of ions in a solvent, however, not only compensation but also a formal, mutual enhancement between the electronic energy and nuclear repulsion energy components of the total energy may also occur, when the tools of nuclear charge variation are applied to establish quantum chemically rigorous energy inequalities.

Conceptual DFT: the chemical relevance of higher response functions

In recent years conceptual density functional theory offered a perspective for the interpretation/prediction of experimental/theoretical reactivity data on the basis of a series of response functions to perturbations in the number of electrons and/or external potential. This approach has enabled the sharp definition and computation, from first principles, of a series of well-known but sometimes vaguely defined chemical concepts such as electronegativity and hardness. In this contribution, a short overview of the shortcomings of the simplest, first order response functions is illustrated leading to a description of chemical bonding in a covalent interaction in terms of interacting atoms or groups, governed by electrostatics with the tendency to polarize bonds on the basis of electronegativity differences. The second order approach, well known until now, introduces the hardness/softness and Fukui function concepts related to polarizability and frontier MO theory, respectively. The introduction of polarizability/softness is also considered in a historical perspective in which polarizability was, with some exceptions, mainly put forward in non covalent interactions. A particular series of response functions, arising when the changes in the external potential are solely provoked by changes in nuclear configurations (the "R-analogues") are also systematically considered. The main part of the contribution is devoted to third order response functions which, at first sight, may be expected not to yield chemically significant information, as turns out to be for the hyperhardness. A counterexample is the dual descriptor and its R analogue, the initial hardness response, which turns out to yield a firm basis to regain the Woodward-Hoffmann rules for pericyclic reactions based on a density-only basis, i.e. without involving the phase, sign, symmetry of the wavefunction. Even the second order nonlinear response functions are shown possibly to bear interesting information, e.g. on the local and global polarizability. Its derivatives may govern the influence of charge on the polarizability, the R-analogues being the nuclear Fukui function and the quadratic and cubic force constants. Although some of the higher order derivatives may be difficult to evaluate a comparison with the energy expansion used in spectroscopy in terms of nuclear displacements, nuclear magnetic moments, electric and magnetic fields leads to the conjecture that, certainly cross terms may contain new, intricate information for understanding chemical reactivity.

Use of nuclear stiffness in search for a maximum hardness principle and for the softest states along the chemical reaction path: A new formula for the energy third derivative γ

Nuclear stiffness, expressed as a hardness derivative, appears to be a good measure of the slope of global hardness. The authors analyze molecular states for which hardness has a maximum value. Maximum hardness principle (MHP) has been discussed. At the ground state hardness function does not obtain a maximum value versus spatial coordinates within a constant number of electrons (N), but is so within constant chemical potential (mu) constraint. The authors apply this feature to evaluate an energy third derivative (gamma). MHP has been analyzed via symmetry considerations of nuclear stiffness and nuclear reactivity. Nuclear stiffness has been also applied to study the hardness profile for a chemical reaction. In this case, the authors seek molecular states for which hardness is at a minimum. They have examined systems for which they have recently obtained regional chemical potentials [P. Ordon and A. Tachibana, J. Mol. Model. 11, 312 (2005); J. Chem. Sci. 117, 583 (2005)]. The transition state is found not to be the softest along the chemical reaction path. Nuclear stiffness reflects well the softest conformation of a molecule, which has been found independently along the intrinsic reaction coordinate profile. Electronic energy-density [A. Tachibana, J. Mol. Mod. 11, 301 (2005)] has been used to visualize the reactivity difference between the softest state and the transition state.

Chemical hardness and the discontinuity of the Kohn-Sham exchange-correlation potential

Chemical hardness, identified as the difference between the vertical first ionization potential I and the vertical electron affinity A, is analyzed in the context of the ionization theorems to derive expressions for its evaluation at different levels of approximation that arise as a direct consequence of the derivative discontinuity of the exchange-correlation potential. The quantities involved in these expressions incorporate indirectly the effects of the discontinuity, but their values may be calculated with any functional of the local density approximation, generalized gradient approximation, or optimized effective potential type, with or without derivative discontinuity, and with or without the correct asymptotic behavior. By comparison with the vertical energy difference values of I and A, which requires the calculation of the N-, (N-1)-, and (N+1)-electron systems, it is found, for a set of 14 closed shell molecules, that the difference between the eigenvalues of the highest occupied molecular orbitals of the N- and (N+1)-electron systems leads to rather accurate values, when the correct asymptotic behavior is incorporated, and that a second-order one-body perturbation approach that only requires information from the N-electron system leads to reasonable values.

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.

Stiffness and Raman Intensity: a Conceptual and Computational DFT Study

A DFT-based reactivity descriptor, the nuclear stiffness, is related to the Raman scattering intensity, which is experimentally accessible. The application of this new relationship obtained within certain approximations has been checked in two different sets of molecules. First, we study a favorable case, where the contribution of the anisotropy to the Raman intensity is zero (symmetric stretching mode in 15 tetrahedral molecules). Second, we consider a "worst" case scenario, where the anisotropy contribution can be expected to be important (stretching mode in 32 diatomic molecules). The numerical results clearly show a relationship between stiffness and Raman intensity reflecting the expected anisotropy influence.

Do Fukui Function Maxima Relate to Sites of Metabolism? A Critical Case Study

The usefulness of local reactivity descriptors for understanding drug metabolism is investigated. Electrophilic Fukui functions are calculated for 18 drugs and 11 agrochemicals and their relation to experimentally observed metabolites is discussed. Maxima of the Fukui functions correspond to major sites of metabolic attack in many examples, facilitating a posteriori understanding of experimental findings. In the second part of the paper, the nature of the electrophilic oxidant species in cytochromes, called "Compound I" (Cpd I), is investigated within the Fukui framework. Nucleophilic Fukui functions are calculated involving the relevant spin states of Cpd I, allowing a more qualitative, intuitive understanding of its reactivity.