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.

Predicting the activity of methoxyphenol derivatives antioxidants: II-Importance of the nature of the solvent on the mechanism, a DFT study.

The various mechanisms of primary antioxidant action of a series of 2-Methoxyphenols are investigated in the present work. The electronic properties have just been studied in a joint article, so that we focus here on Hydrogen Atom Transfer (HAT), Single Electron Transfer-Proton Transfer (SET-PT) and Sequential Proton-Loss Electron-Transfer (SPLET) mechanisms. The two computational approaches used in the previous study of the structure and reactivity of these compounds [Computational and Theoretical Chemistry 1229 (2023) 114287] provide identical mechanisms trends in gas phase. In gas media, hydrogen atom transfer (HAT) is more favored. On the contrary, the solvent polarity has a significant effect on the mechanism of the antioxidant activity, since the polarity of the solvent increases the contribution of the SPLET mechanism.

Insight into the Varying Reactivity of Different Catalysts for CO2 Cycloaddition into Styrene Oxide: An Experimental and DFT Study.

The cycloaddition of CO2 into epoxides to form cyclic carbonates is a highly sought-after reaction for its potential to both reduce and use CO2, which is a greenhouse gas. In this paper, we present experimental and theoretical studies and a mechanistic approach for three catalytic systems. First, as Lewis base catalysts, imidazole and its derivatives, then as a Lewis acid catalyst, ZnI2 alone, and after that, the combined system of ZnI2 and imidazole. In the former, we aimed to discover the reasons for the varied reactivities of five Lewis base catalysts. Furthermore, we succeeded in reproducing the experimental results and trends using DFT. To add, we emphasized the importance of non-covalent interactions and their role in reactivity. In our case, the presence of a hydrogen bond was a key factor in decreasing the reactivity of some catalysts, thus leading to lower conversion rates. Finally, mechanistically understanding this 100% atom economy reaction can aid experimental chemists in designing better and more efficient catalytic systems.

Understanding the mechanism and regio- and stereo selectivity of [3 + 2] cycloaddition reactions between substituted azomethine ylide and 3,3,3-trifluoro-1-nitroprop-1-ene, within the molecular electron density theory.

The selectivity and the nature of the molecular mechanism of the [3 + 2] cycloaddition (32CA) reaction between 2-(dimethylamino)-1H-indene-1,3(2H)-dione (AY11) and trans(E)-3,3,3-trifluoro-1-nitroprop-1-ene(FNP10) has been studied, in which the molecular electron density theory using density functional theory methods at the MPWB1K/6-31G(d) computational level was used. Analysis of the global reactivity indices permits us to characterize FNP10 as a strong electrophile and AY11 as a strong nucleophile. Four reactive pathways associated with the ortho/meta regioselective channels and endo/exo stereoselective approaches modes have been explored and characterized in the gas phase and in the benzene solvent. The analysis of the relative energies associated with the different reaction pathways indicates that the 32CA reactions of the azomethine ylide (AY) with the nitroalkene (FNP) is meta regioselective with high endo stereoselectivity. This result is in good agreement with the experimental observations. electron localization function topological analysis of the most favored reactive pathways allows for characterizing the mechanism of this 32CA reactions as a non-concerted two-stage one-step mechanism. Finally, non-covalent interactions and quantum theory of atoms in molecule analyses at the meta/endo transition state structure indicate that the presence of different several weak interactions, namely, CF and NH contributed in favoring the formation of a meta-endo cycloadduct.

DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science.

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.

Reactivity and a Charge-Transfer Model Analysis in Aminopolycarboxylic-Metal Complexes.

In the present work, we have calculated several density functional theory (DFT) reactivity descriptors for the aminopolycarboxylate (APC) acids at the B3LYP/6311++G (d,p) levels of theory, aiming to analyze their reactivity. Reactivity descriptors such as ionization energy, molecular hardness, electrophilicity, and condensed Fukui function local indices have been determined to predict the reactivity of APCs. The influence of the solvent was taken into account by employing the CPCM model. The results indicate that the solvation slightly modifies the tendency of the reactivity of the APCs studied. On the other hand, we applied a global and local charge-transfer partitioning model, which introduces two charge-transfer channels [one for accepting electrons (electrophilic) and another for donating one (nucleophilic)] to the complexation reaction of a set of APC acids with transition metals (Mn, Co, and Ni targets enlarged by Fe, Cu, and Zn). The correlation between the charges obtained for the interaction between APC acids and transition metal stability constants provides support for their interpretation as measures of the electrophilicity and nucleophilicity of a chemical species and, at the same time, allows one to describe the donation and back-donation processes in terms of the DFT of chemical reactivity. Also, the application of dual descriptors for these acids provides valuable information concerning the atoms in the reactants playing the most important roles in the reaction, thus helping to improve our understanding of the reaction under study.

Electronic Energy and Local Property Errors at QTAIM Critical Points while Climbing Perdew's Ladder of Density-Functional Approximations.

We investigate the relationships between electron-density and electronic-energy errors produced by modern exchange-correlation density-functional approximations belonging to all of the rungs of Perdew's ladder. To this aim, a panel of relevant (semi)local properties evaluated at critical points of the electron-density field (as defined within the framework of Bader's atoms-in-molecules theory) are computed on a large selection of molecular systems involved in thermodynamic, kinetic, and noncovalent interaction chemical databases using density functionals developed in a nonempirical and minimally and highly parametrized fashion. The comparison of their density- and energy-based performance, also discussed in terms of density-driven errors, casts light on the strengths and weaknesses of the most recent and efficient density-functional approximations.

Polarisation of Electron Density and Electronic Effects: Revisiting the Carbon-Halogen Bonds.

Electronic effects (inductive and mesomeric) are of fundamental importance to understand the reactivity and selectivity of a molecule. In this article, polarisation temperature is used as a principal index to describe how electronic effects propagate in halogeno-alkanes and halogeno-alkenes. It is found that as chain length increases, polarisation temperature decreases. As expected, polarisation is much larger for alkenes than for alkanes. Finally, the polarisation mode of the carbon-fluorine bond is found to be quite different and might explain the unusual reactivity of fluoride compounds.

Understanding the intermolecular Diels-Alder cycloaddition promotion: Activation strain model/energy decomposition analysis model and conceptual density functional theory viewpoints.

The present work reports the computational study of the major Diels-Alder reaction between 2-bromocycloalkenone and a variety of mono- and di-substituted dienes. Through density functional theory (DFT) calculations and subsequent activation strain model/energy decomposition analysis/conceptual DFT (C-DFT) analyses, the key factors governing the activation barriers heights, and thus reactivity, are characterized. In contrast with a previous study, steric effects do not appear to control reactivity. Conversely, in all presented cases, a subtle interplay between deformation and interaction energies is evidenced at transition states. In the end, neither term alone is enough to explain or predict reactivity. Yet a simple C-DFT descriptor allows to predict with a reasonable efficiency the activation barriers: the excitation energy needed to observe a charge transfer from the diene to the dienophile. Theoretical elements are provided to support the use of this descriptor.

A computational investigation of the selectivity and mechanism of the Lewis acid catalyzed oxa-Diels-Alder cycloaddition of substituted diene with benzaldehyde.

The selectivity and the mechanism of the uncatalyzed and AlCl3 catalyzed hetero-Diels-Alder reaction (HDR) between ([E]-4-methylpenta-2,4-dienyloxy)(tert-butyl)dimethylsilane 1 and benzaldehyde 2 have been studied using density functional theory at the MPWB1K/6-31G(d) level of theory. The uncatalyzed HDR between diene 1 and alkene 2 is characterized by a polar character and proceeds via an asynchronous one-step mechanism for the meta paths and synchronous for the ortho ones. In the presence of AlCl3 catalyst, the mechanism changes to be stepwise, while the first step is the rate-determining step. The activation energies widely decrease, and the polar character increases dramatically. A large analysis of the mechanism is performed using the activation strain model/energy decomposition analysis (ASM/EDA) model, the natural bond orbital (NBO) and state specific dual descriptors (SSDDs). The obtained results indicate that the combined interaction energy associated with the distortion of the reactants in these HDR are at the origin of the observed kinetics. NBO analyses were applied to estimate the Lewis-acid catalyst donor-acceptor interaction with the molecular system. The SSDD analysis shed light into the orientation effects on the reaction kinetics by providing important information about charge transfer interactions during the chemical reaction. It indicates that the more favorable HDR pathway have the lowest excitation energies, facilitating the interaction between diene 1 and benzaldehyde 2 moieties. Non-covalent interaction (NCI) and QTAIM analyses of the meta-endo structure indicate that the presence of several weak NCIs formed at this approach is at the origin of the meta-endo selectivity.

Correlation between Second Ionization Potential and Nonlinear Optical Properties of Bivalent Transition-Metal Complexes: A Quantum Chemical Study.

Discovering new materials with excellent nonlinear optical responses has recently become a very interesting research topic in the different domains of materials science. Currently, density functional theory (DFT) has been shown to be a powerful tool in the explanation and prediction of the performance of novel nonlinear optical (NLO) materials. Quantum chemical calculations using DFT/TD-DFT with the B3LYP exchange-correlation functional are reported to study the NLO properties of 26 bivalent transition-metal (TM) complexed by six acyclic hexadentate ligands providing pyridyl/pyrazine-amide-thioether/ether coordination and differing by the nature of the methylene dichalcogenate spacer between the rings. However, the geometry parameters and the theoretically predicted UV-vis absorption spectra of the optimized compounds M(II)Li are in excellent agreement with the experiment, when available, the trends among the nature of the TM, the importance of the ligand spacer, and of the substituents of the pyridine/pyrazine amide ligand are discussed. To the best of our knowledge, our work evidences for the first time that the hyper-polarizability, second harmonic generation, and hyper-Rayleigh scattering response of TM coordination complexes can be correlated to the second ionization potential of metal and spin state of complexes.

A statistical thermodynamics view of electron density polarisation: application to chemical selectivity.

A fundamental link between conceptual density functional theory and statistical thermodynamics is herein drawn, showing that intermolecular electrostatic interactions can be understood in terms of effective work and heat exchange. From a more detailed analysis of the heat exchange in a perturbation theory framework, an associated entropy can be subsequently derived, which appears to be a suitable descriptor for the local polarisability of the electron density. A general rule of thumb is evidenced: the more the perturbation can be spread, both through space and among the excited states, the larger the heat exchange and entropy.

Electronic Structure and Photoluminescence Properties of Eu(η9-C9H9)2.

The electronic structure of Eu2+ compounds results from a complex combination of strongly correlated electrons and relativistic effects as well as weak ligand-field interaction. There is tremendous interest in calculating the electronic structure as nowadays the Eu2+ ion is becoming more and more crucial, for instance, in lighting technologies. Recently, interest in semiempirical methods to qualitatively evaluate the electronic structure and to model the optical spectra has gained popularity, although the theoretical methods strongly rely upon empirical inputs, hindering their prediction capabilities. Besides, ab initio multireference models are computationally heavy and demand very elaborative theoretical background. Herein, application of the ligand-field density functional theory (LFDFT) method that is recently available in the Amsterdam Modeling Suite is shown: (i) to elucidate the electronic structure properties on the basis of the multiplet energy levels of Eu configurations 4f7 and 4f65d1 and (ii) to model the optical spectra quite accurately if compared to the conventional time-dependent density functional theory tool. We present a theoretical study of the molecular Eu(η9-C9H9)2 complex and its underlying photoluminescence properties with respect to the Eu 4f-5d electron transitions. We model the excitation and emission spectra with good agreement with the experiments, opening up the possibility of modeling lanthanides in complex environment like nanomaterials by means of LFDFT at much-reduced computational resources and cost.

Substituent Effect on the Himbert Intramolecular Arene/Allene Diels-Alder Reaction: NBO Analysis and State Specific Dual Descriptors.

Conceptual density functional theory has been applied to study the Himbert intramolecular arene/allene Diels-Alder reaction. The effect of substitutions at different positions on the kinetics of these reactions has been analyzed. Therefore, from the calculation of the activation energies of more than 27 reactions involving concerted mechanisms, the selectivity of these reactions can be predicted and rationalized with the aid of conceptual DFT descriptors. An application of the two concepts, natural population analysis (NBO) and the state-specific dual descriptor (SSDD) for evaluating substituent effects, allows the investigation of the different interactions that promote a reaction compared to another. The SSDDs computed for the transition state structures provide important information about charge transfer interactions during the chemical reaction. In our case, the SSDD results show that the substituents promoting Himbert reaction have the lowest excitation energies, a fact which facilitates the allene/arene interaction. The NBO results show that according to the nature of the substituent, the Himbert reaction stands as a normal-electron demand or reverse. Thus, the interactions favoring each reaction are mentioned. The geometric deformation observed in the case of OCH3 is at the origin to the emergence of other low interactions between diene and dienophile as well as a strong electronic delocalization stabilizing the arene moiety. The calculated synchronicity indexes show that the Himbert intramolecular Diels-Alder reactions are very synchronous.

Nine questions on energy decomposition analysis.

The paper collects the answers of the authors to the following questions: Is the lack of precision in the definition of many chemical concepts one of the reasons for the coexistence of many partition schemes? Does the adoption of a given partition scheme imply a set of more precise definitions of the underlying chemical concepts? How can one use the results of a partition scheme to improve the clarity of definitions of concepts? Are partition schemes subject to scientific Darwinism? If so, what is the influence of a community's sociological pressure in the "natural selection" process? To what extent does/can/should investigated systems influence the choice of a particular partition scheme? Do we need more focused chemical validation of Energy Decomposition Analysis (EDA) methodology and descriptors/terms in general? Is there any interest in developing common benchmarks and test sets for cross-validation of methods? Is it possible to contemplate a unified partition scheme (let us call it the "standard model" of partitioning), that is proper for all applications in chemistry, in the foreseeable future or even in principle? In the end, science is about experiments and the real world. Can one, therefore, use any experiment or experimental data be used to favor one partition scheme over another? © 2019 Wiley Periodicals, Inc.

Combined QTAIM and ETS-NOCV investigation of the interactions in ClnM[PhB(NtBu)2] complexes with M = Si & Ge (n = 0), As & Sb (n = 1), Te & Po (n = 2).

In this work, the nature of the chemical interactions between the metalloid atom (M = Si, Ge, As, Sb, Te, Po) and the nitrogen atoms in the bora-amidinate (bam) complexes (ClnM[PhB(NtBu)2]) are investigated, mainly via density-based indices. The descriptors used are derived using the quantum theory of atoms in molecules and natural orbitals for chemical valence approaches. It is shown that the strongest interaction is achieved with silicon. Indeed, it is generally the lightest metalloid in a particular group of the periodic table (i.e., Si, As, and Te for groups 14-16, respectively) that exhibits the strongest bond in the bam complex. This suggests that the atomic radius of the metalloid is a useful parameter for predicting the bonding strength. Extended transition state (ETS) decomposition results indicate that the interactions are more electrostatic than due to orbital interactions.

Unexpected Structure of a Helical N4 -Schiff-Base Zn(II) Complex and Its Demetallation: Experimental and Theoretical Studies.

A new Zn-N4 -Schiff base L=((±)-trans-N,N'-Bis(2-aminobenzylidene)-1,2-diaminocyclohexane) complex was synthesized and fully characterized, showing an unexpected self-assembled double-stranded helicate structure. The X-ray crystal analysis of the Zn2 L2 complex ((C40 H44 N8 Zn2 ,CH2 Cl2 , a=14.2375(3) Å, b=16.7976(4) Å, c=16.1613(4) Å, monoclinic, P21 /n, Z=4) shows a centrosymmetrical structure in which zinc atoms are in distorted tetrahedral environments, revealing an M- (R, R) left-handed helicity in its asymmetric unit. However, it was observed that this dinuclear complex is thermodynamically unstable in the presence of small water amounts and undergoes demetallation into free N4-Schiff base ligand and ZnO nanoparticles. This hydrolysis process was thoroughly identified and monitored through detailed 1 H NMR, DOSY NMR analysis. The reaction mechanism of this demetallation event was elucidated by using the DFT method, involving an activation energy smaller than 13 kcal/mol. Besides, a theoretical mechanism of the demetallation process is given for the first time.

Fluorine substituent effect on the stereochemistry of catalyzed and non-catalyzed Diels-Alder reactions. The case of R-butenone with cyclopentadiene: a computational assessment of the mechanism.

The present work studies theoretically the mechanisms involved in the fluorine substituent effect on the stereochemistry of Diels-Alder reactions. The case of R-butenone with cyclopentadiene is used for the purpose of modelling more general α-fluoro-α,ß-unsaturated carbonyl compounds, in catalyzed and uncatalyzed cases. A thorough analysis of the mechanism is performed using energy decomposition analysis (EDA) and conceptual DFT tools. It is shown that the endo conformation is privileged in all the studied cases with the exception of the α-fluorinated ketone. It is found that the endo selectivity of the non-fluorinated reactions is only due to the decrease of dispersion energy. On the other hand, the presence of a fluorine atom in the dienophile moieties increases remarkably the magnitude not only of the interaction energy between the reactants but that of the strain energy as well. Moreover, it is the strong destabilization strain energy occurring at the transition state of the endo pathway of the reaction cyclopentadiene/3-fluorobutenone that is mainly responsible for the exo selectivity. The effect of a Lewis acid catalyst on these reactions is also studied. The Lewis acid catalyst affects the activation energy of the studied Diels-Alder reactions but not their stereoselectivity. Furthermore, the dual descriptor results shed light onto the mechanism. Besides, natural bond orbital analysis (NBO) and determination of the condensed values of the state-specific dual descriptors (SSDD) are carried out to evaluate the donor-acceptor properties in these reactions. For the first time, a semiquantitative prediction of stereoselectivity due to substitutions of dienophile is obtained, thus complementing the previous interpretations (R. Hoffmann and R. B. Woodward, J. Am. Chem. Soc., 1965, 87, 4388; I. Fernández and F. M. Bickelhaupt, Chem. Soc. Rev., 2014, 43, 4953). Finally, since the role of dispersion forces is evidenced in some cases, a comparison between some popular exchange-correlation functionals is presented, assessing the performance of some standard functionals besides functionals with explicit dispersion corrections.

Electronic structure of BN-aromatics: Choice of reliable computational tools.

The importance of having reliable calculation tools to interpret and predict the electronic properties of BN-aromatics is directly linked to the growing interest for these very promising new systems in the field of materials science, biomedical research, or energy sustainability. Ionization energy (IE) is one of the most important parameters to approach the electronic structure of molecules. It can be theoretically estimated, but in order to evaluate their persistence and propose the most reliable tools for the evaluation of different electronic properties of existent or only imagined BN-containing compounds, we took as reference experimental values of ionization energies provided by ultra-violet photoelectron spectroscopy (UV-PES) in gas phase-the only technique giving access to the energy levels of filled molecular orbitals. Thus, a set of 21 aromatic molecules containing B-N bonds and B-N-B patterns has been merged for a comparison between experimental IEs obtained by UV-PES and various theoretical approaches for their estimation. Time-Dependent Density Functional Theory (TD-DFT) methods using B3LYP and long-range corrected CAM-B3LYP functionals are used, combined with the ΔSCF approach, and compared with electron propagator theory such as outer valence Green's function (OVGF, P3) and symmetry adapted cluster-configuration interaction ab initio methods. Direct Kohn-Sham estimation and "corrected" Kohn-Sham estimation are also given. The deviation between experimental and theoretical values is computed for each molecule, and a statistical study is performed over the average and the root mean square for the whole set and sub-sets of molecules. It is shown that (i) ΔSCF+TDDFT(CAM-B3LYP), OVGF, and P3 are the most efficient way for a good agreement with UV-PES values, (ii) a CAM-B3LYP range-separated hybrid functional is significantly better than B3LYP for the purpose, especially for extended conjugated systems, and (iii) the "corrected" Kohn-Sham result is a fast and simple way to predict IEs.