Bond fukui indices: Comparison of frozen molecular orbital and finite differences through mulliken populations

Bultinck, Patrick; Damme, Sofie Van; Cedillo, Andrés

doi:10.1002/jcc.23405

Cited by 15 publications

(12 citation statements)

References 52 publications

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“…In order to illustrate the newly introduced dual descriptor functions, matrices and their atom and bond counterparts, B3LYP/6-31G* calculations were performed on the set of ethylene derivatives shown in Figure 1, recently used by Gonzalez-Suarez et al 24 and Bultinck et al 25 to derive atom and bond condensed Fukui functions and matrices using the Hirshfeld-I AIM method (i.e. molecules 1-18 from Gonzalez-Suarez et al 24 ).…”

Section: Methodsmentioning

confidence: 99%

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: Methodsmentioning

confidence: 99%

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

et al. 2017

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“…Fukui functions associated with natural bond orbitals (NBO), and the related bond reactivity indices:

f_{i}^{+ ((), NBO)}

and

f_{i}^{- ((), NBO)}

have been used starting from the orbitals of the N‐electron system . Their effective occupancies.…”

Section: Computational Detailsmentioning

confidence: 99%

“…Fukui functions associated with natural bond orbitals (NBO), [8,9] and the related bond reactivity indices: f…”

Section: Bond Reactivity Indices: Philicities For Natural Bond Orbimentioning

confidence: 99%

Analyzing torquoselectivity in a series of unusual ring‐opening reactions through bond reactivity indices and the adaptive natural density partitioning method

Morales‐Bayuelo

Sánchez‐Márquez

Jana

et al. 2018

Int J of Quantum Chemistry

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In this study, a theoretical analysis of the torquoselectivity in a set of unusual ring‐opening reactions (R1‐R5) is presented. To describe the mechanism of the reactions, a recent methodology has been used to estimate the electrophilicities of the natural bond orbitals of the reagents and has been complemented with a second‐order perturbation theory analysis. The adaptive natural density partitioning method has also been used to verify the results and conclusions of the analysis. The concordant results of the three methodologies provide us with a better understanding of the reaction mechanism involving the torquoselectivity. We also carried out the analysis in both directions of the reaction to verify the conclusions obtained.

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“…Numerical data using the Mulliken AIM are compared with the Hirshfeld‐I results to examine the influence of the AIM method. No derivation is explicitly presented for the Mulliken case as it can be directly derived through repeated application of the Mulliken operator . The Hirshfeld‐I weight functions are derived from a so‐called promolecular density

ρ_{promol}^{0} (𝐫, N)

, which is the sum of isolated atomic densities of the atoms in the molecule.…”

Section: Theorymentioning

confidence: 99%

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

et al. 2016

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The Fukui function is often used in its atom-condensed form by isolating it from the molecular Fukui function using a chosen weight function for the atom in the molecule. Recently, Fukui functions and matrices for both atoms and bonds separately were introduced for semiempirical and ab initio levels of theory using Hückel and Mulliken atoms-in-molecule models. In this work, a double partitioning method of the Fukui matrix is proposed within the Hirshfeld-I atoms-in-molecule framework. Diagonalizing the resulting atomic and bond matrices gives eigenvalues and eigenvectors (Fukui orbitals) describing the reactivity of atoms and bonds. The Fukui function is the diagonal element of the Fukui matrix and may be resolved in atom and bond contributions. The extra information contained in the atom and bond resolution of the Fukui matrices and functions is highlighted. The effect of the choice of weight function arising from the Hirshfeld-I approach to obtain atom- and bond-condensed Fukui functions is studied. A comparison of the results with those generated by using the Mulliken atoms-in-molecule approach shows low correlation between the two partitioning schemes.

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Bond fukui indices: Comparison of frozen molecular orbital and finite differences through mulliken populations

Cited by 15 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

Analyzing torquoselectivity in a series of unusual ring‐opening reactions through bond reactivity indices and the adaptive natural density partitioning method

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

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