Atom and Bond Fukui Functions and Matrices: A Hirshfeld‐I Atoms‐in‐Molecule Approach

Oña, Ofelia B.; Clercq, Olivier De; Alcoba, Diego R.; Torre, Alícia; Laín, Luis; Neck, Dimitri Van; Bultinck, Patrick

doi:10.1002/cphc.201600433

Cited by 14 publications

(7 citation statements)

References 52 publications

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“…The second goal is to atom condense the dual descriptor matrix in both single atom and diatomic (or where chemically applicable, bond) terms. This is reminiscent of recent work by the present authors for the Fukui matrix where an atom and bond condensation is carried out over both the r and r coordinate 19 . Doing this for the dual descriptor matrix makes it different from the work of Zielinski et al 18 or e.g., Glossman-Mitnik 20 or Cao et al 21 who all atom condense the dual descriptor function and therefore cannot distinguish bond terms.…”

Section: Introductionmentioning

confidence: 56%

“…For all molecules, first both the electron addition and electron removal Fukui matrices have been computed using the expressions presented previously and yielding the data reported by Oña et al 19 . These matrices are then used to compute the dual descriptor matrices according to eq.…”

Section: Resultsmentioning

confidence: 99%

“…We first use the FMR approach using the weight functions from the Hirshfeld-I method for the molecule with N 0 electrons. This entails that, based on earlier matrix partitioning studies for electron density 28 and the Fukui function 19 , we use the following working expression:…”

Section: Resultsmentioning

confidence: 99%

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Analysis of molecular and (di)atomic dual-descriptor functions and matrices

et al. 2017

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In this work, the dual descriptor is studied in matrix form f (2) (r, r ) and both coordinates condensed to atoms, resulting in atomic and diatomic (or where applicable, bond) condensed single values. This double partitioning method of the dual descriptor matrix is proposed within the Hirshfeld-I atoms-in-molecule framework although it is easily extended to other atoms-in-molecules methods. Diagonalising the resulting atomic and bond dual descriptor matrices gives eigenvalues and eigenvectors describing the reactivity of atoms and bonds. The dual descriptor function is the diagonal element of the underlying matrix. The extra information contained in the atom and bond resolution is highlighted and the effect of choosing either the fragment of molecular response or response of molecular fragment approach is quantified. IntroductionOne of the essential tasks in chemistry is the analysis of chemical observations and their classification to ultimately be able to rationalise them in a model that even allows predicting the outcome of future experiments. This quite ambitious task has been met to admirable extent by introducing such classifications as acids and bases, hard and soft substances and many more. Over time, a vast toolbox of concepts and quantities was introduced with many of these developed either before the advent of quantum mechanics or without relying on the latter theory. This has resulted in a sort of gap between much of chemical theory and quantum mechanics although clearly quantum mechanics can give rise to much more and deeper insight in the underlying mechanisms of chemical reactivity. Fortunately, some eminent scientists have, over the years, picked up the challenge of closing this gap. One of the leading persons in this, is Robert G. Parr who is among the founding fathers of what is now known as chemical density functional theory (often still referred to as conceptual density functional theory, cDFT) 1-3 , and who was able to link many existing theories to the energy of a chemical system and its derivatives with respect to its basic variables, including the number of electrons and the external potential. This Taylor expansion of the energy has already given rise to numerous new reactivity descriptors or has allowed previously known key quantities like electronegativity to be identified with some of these derivatives.In this work we are interested in the dual descriptor introduced by Morell et al. 4,5 as the difference between the Fukui function for the addition of an electron minus that for the removal of an electron, or alternatively as the functional derivative of the hardness which in itself is the second derivative of the energy with respect to the number of electrons. As such, the dual descriptor is a mixed third order derivative of the energy 6 :In Eq.(1), f (2) (r) is the dual descriptor evaluated at a point r, E is the energy, N the number of electrons and v(r) the external potential. Provided that the system has no degenerate states, δ E δ v(r) N corresponds to ρ (r), the electron ...

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Section: Introductionmentioning

confidence: 56%

Section: Resultsmentioning

confidence: 99%

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Analysis of molecular and (di)atomic dual-descriptor functions and matrices

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“…Nucleophilicity [52] and hardness [53] were calculated by using Multiwfn [54] (version 3.6) software. The graphs of Fukui function (f -) [55] and LUMO orbitals [56] were plotted with Multiwfn and rendered by VMD [57]. According to the experimental results [41], we assumed that the hydroxide acted as a proton acceptor and metal iridium center acted as a hydrogen anion acceptor.…”

Section: Computational Details and Modelsmentioning

confidence: 99%

Mechanistic Investigations of the Synthesis of Lactic Acid from Glycerol Catalyzed by an Iridium–NHC Complex

Chen

et al. 2022

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In the present work, the reaction pathways and the origin of catalytic activity for the production of lactic acid from glycerol catalyzed by an iridium–heterocyclic carbene (Iridium-NHC) complex at 383.15 K were investigated by DFT study at the M06-D3/6-311++G (d, p)//SDD level. Compared to the noncatalytic reaction pathway, the energy barrier sharply decreased from 75.2 kcal mol−1 to 16.8 kcal mol−1 with the introduction of the iridium–NHC complex. The catalytic reaction pathway catalyzed by the iridium–NHC complex with a coordinated hydroxide included two stages: the dehydrogenation of glycerol to 2,3-dihydroxypropanal, and the subsequent isomerization to lactic acid. Two reaction pathways, including dehydrogenation in terminal and that in C2-H, were studied. It was found that the formation of dihydroxyacetone from the H-removal in C2-H was more favorable, which might have been due to the lower energy of LUMO, whereas dihydroxyacetone could be easily transferred to 2,3-dihydroxypropanal. The analyses of electrostatic potential (ESP), hardness, and f- Fukui function also confirmed that the iridium–NHC complex acted as a hydrogen anion receptor and nucleophilic reaction center to highly promote the conversion of glycerol to lactic acid.

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“…At correlated levels, the Fukui matrix allows the Frontier Molecular Orbital concept to be extended beyond the single determinant level, by defining it as the Fukui natural that has the largest Fukui occupation . Despite successful applications − and contributions to the debate whether the Fukui function can be negative in parts of 3D-space, − the question remains if replacing a quantity derived from a purely density-based framework by its matrix extension is theoretically well-founded. In this study, we show that when one extends densities to first-order reduced density matrices in the CDFT framework, one should also generalize the external potential to become nonlocal.…”

Section: Introductionmentioning

confidence: 99%

Extending Conceptual Density Functional Theory toward First-Order Reduced Density Matrices: An Open Subsystems Viewpoint on the Fukui Matrix

Acke

Hende

Vriendt

et al. 2023

J. Chem. Theory Comput.

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As a matrix extension of the Fukui function, a reactivity descriptor grounded within Conceptual Density Functional Theory, the Fukui matrix extends Frontier Molecular Orbital Theory to correlated regimes with its eigendecomposition in Fukui occupations and Fukui naturals. Despite successful applications, the questions remain as to whether replacing a quantity derived from a purely density-based framework by its matrix extension is theoretically well-founded and what chemical information is contained in the corresponding eigendecomposition. In this study, we show that the matrix extension of the Fukui function is only well-defined if one also generalizes the external potential to become nonlocal, leading to the introduction of Conceptual First-Order Reduced Density Matrix Functional Theory. By interpreting the Anderson impurity model from an interacting open subsystem perspective, we show how Fukui occupations and Fukui naturals reflect the influence of an increasing (static) correlation and which characteristic patterns we should expect within a molecular context. This study represents a step in generalizing Conceptual Density Functional Theory beyond its density-based perspective.

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Atom and Bond Fukui Functions and Matrices: A Hirshfeld‐I Atoms‐in‐Molecule Approach

Cited by 14 publications

References 52 publications

Analysis of molecular and (di)atomic dual-descriptor functions and matrices

Analysis of molecular and (di)atomic dual-descriptor functions and matrices

Mechanistic Investigations of the Synthesis of Lactic Acid from Glycerol Catalyzed by an Iridium–NHC Complex

Extending Conceptual Density Functional Theory toward First-Order Reduced Density Matrices: An Open Subsystems Viewpoint on the Fukui Matrix

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