Woodward-Hoffmann rules in density functional theory: Initial hardness response

Hyperhardness and hypersoftness of atoms and their ions

CONTEXT

The theory of reactivity based on cDFT has been supplemented with the new method of calculating the atomic and local indices. With the use of previously derived relationship of the electron density gradient to the softness kernel and to the linear response function, we deliver theoretical analysis to obtain significant reactivity indices-the electron density derivatives: local softness and local hypersoftness together with the global hyperhardness index and the derivative of the global softness with respect to the number of electrons. The local derivatives have been applied in the calculation of responses of atoms to perturbation by an external potential by the alchemical approach. The vital role of the local softness has been confirmed; the potential role of the hypersoftness has been indicated.

METHOD

Our original theoretical scheme has been numerically illustrated with the results obtained with electron density calculations with B3LYP method implemented in Gaussian 16 package. The aug-cc-pvqz basis set has been routinely applied, except for the Ca atom (cc-pvqz). Using the pVTZ basis set recommended by Sadlej was necessary for the potassium atom.

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.

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.

Synthesis, Crystal Structure, Hirshfeld Surface Analysis, and Computational Approach of a New Pyrazolo[3,4-g]isoquinoline Derivative as Potent against Leucine-Rich Repeat Kinase 2 (LRRK2)

Ethyl-2-((8-cyano-3,5,9a-trimethyl-1-(4-oxo-4,5-dihydrothiazol-2-yl)-4-phenyl-3a,4,9,9a-tetrahydro-1H-pyrazolo[3,4-g]isoquinolin-7-yl)thio)acetate (5) was synthesized, and its structure was characterized by IR, MS, and NMR (1H and 13C) and verified by a single-crystal X-ray structure determination. Compound 5 adopts a "pincer" conformation. In the crystal, the hydrogen bonds of -H···O, C-H···O, and O-H···S form thick layers of molecules that are parallel to (101). The layers are linked by C-H···π(ring) interactions. The Hirshfeld surface analysis shows that intermolecular hydrogen bonding plays a more important role than both intramolecular hydrogen bonding and π···π stacking in the crystal. The intramolecular noncovalent interactions in 5 were studied by QTAIM, NCI, and DFT-NBO calculations. Based on structural activity relationship studies, leucine-rich repeat kinase 2 (LRRK2) was found to bind 5 and was further subjected to molecular docking studies, molecular dynamics, and ADMET analysis to probe potential drug candidacy.

New tetrahydroisoquinoline-4-carbonitrile derivatives as potent agents against cyclin-dependent kinases, crystal structures, and computational studies

The synthesis of two new hexahydroisoquinoline-4-carbonitrile derivatives (3a and 3b) is reported along with spectroscopic data and their crystal structures. In compound 3a, the intramolecular O-H···O hydrogen bond constraints the acetyl and hydroxyl groups to be syn. In the crystal, inversion dimers are generated by C-H···O hydrogen bonds and are connected into layers parallel to (10-1) by additional C-H···O hydrogen bonds. The layers are stacked with Cl···S contacts 0.17 Å less than the sum of the respective van der Waals radii. The conformation of the compound 3b is partially determined by the intramolecular O-H···O hydrogen bond. A puckering analysis of the tetrahydroisoquinoline unit was performed. In the crystal, O-H···O and C-H···O hydrogen bonds together with C-H···π(ring) interactions form layers parallel to (01-1) which pack with normal van der Waals interactions. To understand the binding efficiency and stability of the title molecules, molecular docking, and 100 ns dynamic simulation analyses were performed with CDK5A1. To rationalize their structure-activity relationship(s), a DFT study at the B3LYP/6-311++G** theoretical level was also done. The 3D Hirshfled surfaces were also taken to investigate the crystal packings of both compounds. In addition, their ADMET properties were explored.Communicated by Ramaswamy H. Sarma.

Spin-Polarized Conceptual Density Functional Theory from the Convex Hull

We present a new, nonarbitrary, internally consistent, and unambiguous framework for spin-polarized conceptual density-functional theory (SP-DFT). We explicitly characterize the convex hull of energy, as a function of the number of electrons and their spin, as the only accessible ground states in spin-polarized density functional theory. Then, we construct continuous linear and quadratic models for the energy. The nondifferentiable linear model exactly captures the simplicial geometry of the complex hull about the point of interest and gives exact representations for the conceptual DFT reactivity indicators. The continuous quadratic energy model is the paraboloid of maximum curvature, which most tightly encloses the point of interest and neighboring vertices. The quadratic model is invariant to the choice of coordinate system (i.e., {N, S} vs {Nα, Nβ}) and reduces to a sensible formulation of spin-free conceptual DFT in the appropriate limit. Using the quadratic model, we generalize the Parr functions {P+(r), P-(r)} (and their derivatives with respect to number of electrons) to this new spin-polarized framework, integrating the Parr function concept into the context of (spin-polarized) conceptual DFT, and extending it to include higher-order effects.

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.

Wandering through quantum-mechanochemistry: from concepts to reactivity and switches

Mechanochemistry has experienced a renaissance in recent years witnessing, at the molecular level, a remarkable interplay between theory and experiment. Molecular mechanochemistry has welcomed a broad spectrum of quantum-chemical methods to evaluate the influence of an external mechanical force on molecular properties. In this contribution, an overview is given on recent work on quantum mechanochemistry in the Brussels Quantum Chemistry group (ALGC). The effect of an external force was scrutinized both in fundamental topics, like reactivity descriptors in Conceptual DFT, and in applied topics, such as designing molecular force probes and tuning the stereoselectivity of certain types of reactions. In the conceptual part, a brief overview of the techniques introducing mechanical forces into a quantum-mechanical description of a molecule is followed by an introduction to conceptual DFT. The evolution of the electronic chemical potential (or electronegativity), chemical hardness and electrophilicity are investigated when a chemical bond in a series of diatomics is put under mechanical stress. Its counterpart, the influence of mechanical stress on bond angles, is analyzed by varying the strain present in alkyne triple bonds by applying a bending force, taking the strain promoted alkyne-azide coupling cycloaddition as an example. The increase of reactivity of the alkyne upon bending is probed by Fukui functions and the local softness. In the applied part, a new molecular force probe is presented based on an intramolecular 6π-electrocyclization in constrained polyenes operating under thermal conditions. A cyclic process is conceived where ring opening and closure are triggered by applying or removing an external pulling force. The efficiency of mechanical activation strongly depends on the magnitude of the applied force and the distance between the pulling points. The idea of pulling point distances as a tool to identify new mechanochemical processes is then tested in [28]hexaphyrins with an intricate equilibrium between Möbius aromatic and Hückel antiaromatic topologies. A mechanical force is shown to trigger the interconversion between the two topologies, using the distance matrix as a guide to select appropriate pulling points. In a final application, the Felkin-Anh model for the addition of nucleophiles to chiral carbonyls under the presence of an external mechanical force is scrutinized. By applying a force for restricting the conformational freedom of the chiral ketone, otherwise inaccessible reaction pathways are promoted on the force-modified potential energy surfaces resulting in a diastereoselectivity different from the force-free reaction.

Data-driven tailoring of molecular dipole polarizability and frontier orbital energies in chemical compound space

Understanding correlations - or lack thereof - between molecular properties is crucial for enabling fast and accurate molecular design strategies. In this contribution, we explore the relation between two key quantities describing the electronic structure and chemical properties of molecular systems: the energy gap between the frontier orbitals and the dipole polarizability. Based on the recently introduced QM7-X dataset, augmented with accurate molecular polarizability calculations as well as analysis of functional group compositions, we show that polarizability and HOMO-LUMO gap are uncorrelated when considering sufficiently extended subsets of the chemical compound space. The relation between these two properties is further analyzed on specific examples of molecules with similar composition as well as homooligomers. Remarkably, the freedom brought by the lack of correlation between molecular polarizability and HOMO-LUMO gap enables the design of novel materials, as we demonstrate on the example of organic photodetector candidates.

Molecular interactions from the density functional theory for chemical reactivity: Interaction chemical potential, hardness, and reactivity principles

In the first paper of this series, the authors derived an expression for the interaction energy between two reagents in terms of the chemical reactivity indicators that can be derived from density functional perturbation theory. While negative interaction energies can explain reactivity, reactivity is often more simply explained using the “|dμ| big is good” rule or the maximum hardness principle. Expressions for the change in chemical potential (μ) and hardness when two reagents interact are derived. A partial justification for the maximum hardness principle is that the terms that appear in the interaction energy expression often reappear in the expression for the interaction hardness, but with opposite sign.

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.

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.

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.

N-Derivatives of Shannon entropy density as response functions

The exact first and second order partial derivatives of Shannon entropy density with respect to the number of electrons at constant external potential are introduced as new descriptors for prediction of the active sites of a molecule. The derivatives, which are a measure of the inhomogeneity of electron density, are calculated both exactly (from analytical forms) and approximately (using the finite difference method) for some molecular systems. According to the maximum entropy principle, the extreme value of the first order derivative on the surface of a given molecule should determine the active sites of the molecule in electrophilic and nucleophilic attack. The second order derivative indicates where the Shannon entropy is more concentrated or depleted during the electron exchange. Although these derivatives on the surfaces of helium and neon atoms are uniform, the corresponding values for argon, krypton and xenon atoms are not. This could explain the greater tendency of heavy noble gas atoms to form stable compounds. A dual descriptor is also defined as the difference between the left and right first order derivatives of Shannon entropy density, which allows one to simultaneously predict the preferable sites for electrophilic and nucleophilic attack over the system at point r. Therefore, the reactivity of an atom in a molecule requires the non-uniformity of the first and second order derivatives of Shannon entropy density on the surface of that atom.

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.

Global and local aromaticity of acenes from the information-theoretic approach in density functional reactivity theory

In this work, we report a systematic study on the global and local aromaticity of acenes using a series of model structures from 2-acene to 11-acene. A recently developed ansatz, an information-theoretic approach coached into density functional reactivity theory has been employed, which essentially provides different density functionals characterizing the molecular electron density distribution. Based on the correlation analysis of six conventional aromaticity indices with eight information-theoretic quantities, we examined the aromaticity of acenes from both global and local perspectives. From the global aromaticity viewpoint, our results suggest that different descriptors based on various physicochemical properties are intrinsically dependent. A novel laminated feature ruling local aromaticity of acenes has been unveiled, from which we found that the distance from the terminal rings plays the critical role. Based on the shape of the correlation plots between the conventional aromaticity indices and information-theoretic quantities, the latter could be separated into three subgroups. The seemingly contradictory results from global and local aromaticity perspectives not only present us the uniqueness of the acene systems but all demonstrate the effectiveness of the information-theoretic approach from density functional reactivity theory. Besides strengthening the validity of a series of new aromaticity descriptors, our results should lead to more clear insights into the chemical significance of the information-theoretic quantities.

Benchmark values of chemical potential and chemical hardness for atoms and atomic ions (including unstable anions) from the energies of isoelectronic series

We present benchmark values for the electronic chemical potential and chemical hardness from reference data for ionization potentials and electron affinities. In cases where the energies needed to compute these quantities are not available, we estimate the ionization potential of the metastable (di)anions by extrapolation along the isoelectronic series, taking care to ensure that the extrapolated data satisfy reasonable intuitive rules to the maximum possible extent. We also propose suitable values for the chemical potential and chemical hardness of zero-electron species. Because the values we report are faithful to the trends in accurate data on atomic energies, we believe that our proposed values for the chemical potential and chemical hardness are ideally suited to conceptual studies of chemical trends across the periodic table. The critical nuclear charge (Z critical) of the isoelectronic series with 2 < N < 96 has also been reported for the first time.

Towards the rationalization of catalytic activity values by means of local hyper-softness on the catalytic site: a criticism about the use of net electric charges

By means of the Spin-Polarized Conceptual Density Functional Theory (SP-CDFT), three 2,6-bis(imino)pyridine catalysts based on iron(II), used for polymerization of ethylene, were studied. The catalysts differed by the substituent group, bearing either -H, -NO2 or -OCH3. To date, catalytic activity, a purely experimental parameter measuring the mass of polyethylene produced per millimole of iron per time and pressure unit at a fixed temperature, has not been explained in terms of local hyper-softness. The latter is a purely theoretical parameter designed for quantifying electronic effects; it is measured using the metal atom responsible for the coordination process with the monomer (ethylene). Because steric effects are not relevant in these kinds of catalysts and only electronic effects drive the catalytic process, an interesting link is found between catalytic activity and the local hyper-softness condensed on the iron atom by means of four functionals (B3LYP, BP86, B97D, and VSXC). This work demonstrates that the use of local hyper-softness, predicted by the SP-CDFT, is a suitable parameter for explaining order relationships among catalytic activity values, thus quantifying the electronic influence of the substituent group inducing this difference; the use of only net electric charges does not lead to clear conclusions. This finding can aid in estimating catalytic activities leading to a more rational design of new catalysts via computational chemistry.

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.

Computational nanochemistry report on the oxicams--conceptual DFT indices and chemical reactivity

A density functional theory study of eight oxicams was carried out in order to determine their global and local reactivities. These types of reactivities were measured by means of global and local reactivity descriptors coming from the conceptual density functional theory. Net electrophilicity as a global reactivity descriptor and local hypersoftness as a local reactivity descriptor were the used tools to distinguish reactivity and selectivity among these oxicams. Globally, isoxicam presents the highest electron donating capacity; meanwhile, the highest electron accepting capacity is exhibited by droxicam. Locally, two oxicams present neither nucleophilic nor electrophilic relevant reactivity in their peripheral pyridine ring, droxicam and tenoxicam, so that their more reactive zones are found on the respective fused rings. Oxicams have been divided into two subgroups in order to facilitate the local analysis of reactivity. One group is characterized because their most important condensed values for local hypersoftnes are well-separated: 4-meloxicam, lornoxicam, meloxicam, and normeloxicam. Meanwhile, the opposite situation is found in droxicam, isoxicam, piroxicam, and tenoxicam. As a whole, the nucleophilic characteristic noticeably predominates in these eight oxicams instead of an electrophilic behavior, thus meaning a greater tendency to donate electrons rather than withdrawing them; a consequence of this behavior implies a favorable interaction with a hypothetical receptor bearing one or more electron acceptor functional groups rather than electron donor functional groups; this would imply a maximization of this interaction from the covalent point of view.

σ, π aromaticity and anti-aromaticity as retrieved by the linear response kernel

The chemical importance of the linear response kernel from conceptual Density Functional Theory (DFT) is investigated for some σ and π aromatic and anti-aromatic systems. The effect of the ring size is studied by looking at some well known aromatic and anti-aromatic molecules of different sizes, showing that the linear response is capable of correctly classifying and quantifying the aromaticity for five- to eight-membered aromatic and anti-aromatic molecules. The splitting of the linear response in σ and π contributions is introduced and its significance is illustrated using some σ-aromatic molecules. The linear response also correctly predicts the aromatic transition states of the Diels-Alder reaction and the acetylene trimerisation and shows the expected behavior along the reaction coordinate, proving that the method is accurate not only at the minimum of the potential energy surface, but also in non-equilibrium states. Finally, the reason for the close correlation between the linear response and the Para Delocalisation Index (PDI), found in previous and the present study, is proven mathematically. These results show the linear response to be a reliable DFT-index to probe the σ and π aromaticity or anti-aromaticity of a broad range of molecules.

Computational Nutraceutics: Chemical Reactivity Properties of the Flavonoid Naringin by Means of Conceptual DFT

The M06 family of density functionals has been assessed for the calculation of the molecular structure and properties of the Naringin molecule. The chemical reactivity descriptors have been calculated through Conceptual DFT. The active sites for nucleophilic and electrophilic attacks have been chosen by relating them to the Fukui function indices and the dual descriptorf(2)(r). A comparison between the descriptors calculated through vertical energy values and those arising from the Koopmans' theorem approximation has been performed in order to check for the validity of the last procedure.

The Woodward-Hoffmann rules reinterpreted by conceptual density functional theory

In an attempt to master the overwhelming amount of data on the properties of substances and their reactions, chemists scrutinize them for underlying common patterns. In modern times quantum mechanics (QM) has played a leading role in the understanding of chemical reactivity. In the late 1960s, Woodward and Hoffmann (WH) proposed one of the most successful and elegant approaches to interpret the outcome of an important type of reaction: they could predict the allowed or forbidden character of pericyclic reactions through inspection of the phase and symmetry of the orbitals of the reactants obtained by simple extended Hückel theory. Today much more powerful computational techniques, such as density functional theory (DFT), are available that yield highly accurate results even for large systems. By focusing on the electron density, ρ(r), a fundamental carrier of information compared with the much more complicated wave function in conventional QM, DFT became the computational workhorse for systems of ever increasing complexity. However, the need for the interpretation of computational (and obviously experimental) results remains, and "conceptual DFT" has provided the answer to this challenge within the context of DFT. This branch of DFT has given precision to chemical concepts such as electronegativity, hardness, and softness and has embedded them in a perturbational approach to chemical reactivity. Previously, researchers have successfully applied conceptual DFT to generalized acid-base and, more recently, to radical and redox reactions. In this Account, we present a conceptual DFT ansatz for pericyclic reactions, a stringent test for this density-only approach, because the density has trivial symmetry and no phase. A density response function is the key quantity in a first approach: the dual descriptor f((2))(r), the second derivative of the electron density with respect to the number of electrons. Overlapping regions of the dual descriptor of the reactant(s) with different or the same sign yield pictorial representations similar to the orbital phase and symmetry-based pictures in the WH formulation. In a second approach, a key quantity is the evolution of the chemical hardness at the onset of the reaction. This quantity makes contact with Zimmerman's alternative approach to the WH rules based on the aromaticity of the transition state. Using the dual descriptor and the initial hardness response, we reinterpret the WH results for the four types of pericyclic reactions (cycloadditions, electrocyclizations, and sigmatropic and chelotropic reactions), both thermodynamically and photochemically. We demonstrate that these two approaches, which require only simple quantum chemical procedures (overlapping densities and HOMO-LUMO gap type calculations along a few points of a model reaction coordinate), are intimately related through a relation that converts the local (i.e., position-dependent) dual descriptor into the global (i.e., position-independent) (initial) hardness response. Our results show that with a density-only based approach the WH rules can be reinterpreted, pointing to the fundamental importance of the electron density as carrier of information as highlighted in the basic theorems of DFT.

The linear response kernel of conceptual DFT as a measure of aromaticity

We continue a series of papers in which the chemical importance of the linear response kernel χ(r,r') of conceptual DFT is investigated. In previous contributions (J. Chem. Theory Comput. 2010, 6, 3671; J. Phys. Chem. Lett. 2010, 1, 1228; Chem. Phys. Lett. 2010, 498, 192), two computational methodologies were presented and it was observed that the linear response kernel could serve as a measure of electron delocalisation, discerning inductive, resonance and hyperconjugation effects. This study takes the analysis one step further, linking the linear response kernel to the concept of aromaticity. Based on a detailed analysis of a series of organic and inorganic (poly)cyclic molecules, we show that the atom-condensed linear response kernel discriminates between aromatic and non-aromatic systems. Moreover, a new quantitative measure of aromaticity, termed the para linear response (PLR) index, is introduced. Its definition was inspired by the recent work published around the para delocalisation index (PDI). Both indices are shown to correlate very well, which emphasises the linear response kernel's value in the theoretical description of aromaticity.

Application of the electron density force to chemical reactivity

In this paper the concept of force experienced by the electron density is applied to chemical reactivity. The force is based upon the gradient of a local chemical potential. Closely related concepts such as force field lines and local electron flux are defined to provide insight in chemical reactivity. The time evolution of a molecular site density is also proposed. From the divergence of the force, the nucleophilic and electrophilic behaviour of atomic sites are characterized. Finally, the relations between the force and local conceptual DFT descriptors are also given.

Regaining the Woodward–Hoffmann rules for chelotropic reactions via conceptual DFT

In our continuous effort to retrieve the Woodward–Hoffmann rules from conceptual density functional theory (DFT), we have examined the last type of pericyclic reactions, i.e., chelotropic reactions. Both the initial hardness response and the dual descriptor have been investigated to predict the allowed and forbidden character for the addition of SO2 to butadiene (4n system) and 1,3,5-hexatriene (4n + 2 system). It is shown that with both electronic descriptors, the conrotatory/disrotatory mode for the linear and nonlinear mechanisms are retrieved based on a density-only approach, free from consideration of orbital and (or) wave function symmetry. The dual descriptor moreover reveals that stabilizing interactions are presented only for the linear path, which can be considered as an overall favourable mechanism for a chelotropic reaction.

Enzymatic catalysis: the emerging role of conceptual density functional theory

Experimentalists and quantum chemists are living in a different world. A wealth of theoretical enzymology-related publications is hardly known by experimentalists, and vice versa. Our aim is to bring both worlds together and to show the powerful possibilities of a multidisciplinary approach to study subtle details of complicated enzymatic processes to a broad readership. MD simulations and QM/MM approaches often focus on the calculation of reaction paths based on activation energies, which is a time-consuming task. A valuable alternative is the reactivity descriptors founded in conceptual DFT like softness, electrophilicity, and the Fukui function, which describe the kinetic aspects of a reaction in terms of the response to perturbations in N and/or upsilon(r), typical for a chemical reaction, of the reagents in the ground state. As such, the relative energies at the beginning of the reaction predict a sequence of activation energies only based on the properties of the reactants (Figure 5 ). In 2003, Geerlings et al. published a key review giving a detailed description of the principles and concepts of conceptual DFT and highlighting its success to study generalized acid/base reactions including addition, substitution, and elimination reactions. Since the time that this review appeared, conceptual DFT has proven its strength in literally hundreds of papers with application to organic and inorganic reactions. Its role in unravelling enzymatic reaction mechanisms, in handling experimentally difficult accessible biochemical problems, and in the interpretation of biochemical experimental observations is emerging and very promising.

Polarization justified Fukui functions

New Fukui functions have been derived within the conceptual density functional theory by the analysis of the polarization effect of a system in static electric field. Resulting Fukui functions accurately reproduce the global softness and electronic dipolar polarizability; they meet the condition integral[f(r)/r]dr = -(partial differential mu/partial differential Z)(N) and lead to very reasonable values of the global hardness for atoms for the group of 29 main group elements. Computational clarity makes the new Fukui functions a promising tool in studies of molecular reactivity.